Математическое моделирование самоорганизующихся экономич. процессов(Диссертация)

ɋɌȺȼɊɈɉɈɅɖɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ ɇɚ ɩɪɚɜɚɯ ɪɭɤɨɩɢɫɢ Ɂɚɣɰɟɜɚ ɂɪɢɧɚ ȼɥɚɞɢɦɢɪɨɜɧɚ Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ...

Author: Зайцева И.В.

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ɋɌȺȼɊɈɉɈɅɖɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ

ɇɚ ɩɪɚɜɚɯ ɪɭɤɨɩɢɫɢ

Ɂɚɣɰɟɜɚ ɂɪɢɧɚ ȼɥɚɞɢɦɢɪɨɜɧɚ

Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫɚɦɨɨɪɝɚɧɢɡɭɸɳɢɯɫɹ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ 05.13.18 – Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ, ɱɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ ɢ ɤɨɦɩɥɟɤɫɵ ɩɪɨɝɪɚɦɦ

Ⱦɢɫɫɟɪɬɚɰɢɹ ɧɚ ɫɨɢɫɤɚɧɢɟ ɭɱɟɧɨɣ ɫɬɟɩɟɧɢ ɤɚɧɞɢɞɚɬɚ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ

ɇɚɭɱɧɵɣ ɪɭɤɨɜɨɞɢɬɟɥɶ: ɞɨɤɬɨɪ ɮɢɡɢɤɨɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ ɋɟɦɟɧɱɢɧ ȿ.Ⱥ.

ɋɬɚɜɪɨɩɨɥɶ – 2005

ɋɈȾȿɊɀȺɇɂȿ

ȼȼȿȾȿɇɂȿ................................................................................................................. 4 ȽɅȺȼȺ 1. ȺɇȺɅɂɁ ɗɎɎȿɄɌɂȼɇɈɋɌɂ ɂ ɉɊɈȻɅȿɆ ɆɈȾȿɅɂɊɈȼȺɇɂə ɊɕɇɄȺ ɌɊɍȾȺ ............................................................... 13 1.1. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ....................................... 13 1.2. Ɉɛɡɨɪ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɯ ɫɪɟɞɫɬɜ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ....................................................................................................................... 16 1.3. Ɉɫɨɛɟɧɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ............................. 21 1.4. Ⱥɧɚɥɢɡ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɨɬɞɟɥɶɧɨɣ ɨɬɪɚɫɥɢ......... 24 1.5. ɇɟɤɨɬɨɪɵɟ ɪɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɥɢɧɟɣɧɵɯ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɢɫɬɟɦ........................................................................................... 28 1.6. ɇɟɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢɦɵɟ ɫɜɟɞɟɧɢɹ ɢɡ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ 32 1.6.1. ɍɪɚɜɧɟɧɢɹ Ʉɨɥɦɨɝɨɪɨɜɚ ɞɥɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɣ ........................ 32 1.6.2. ɉɪɨɫɬɟɣɲɢɣ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ............................................................... 35 1.6.3. ɋɢɫɬɟɦɵ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ......................................................... 40 1.7. ȼɵɜɨɞɵ............................................................................................................. 46 ȽɅȺȼȺ 2. ɆȺɌȿɆȺɌɂɑȿɋɄȺə ɆɈȾȿɅɖ ɋȺɆɈɈɊȽȺɇɂɁȺɐɂɂ ɊɕɇɄȺ ɌɊɍȾȺ ....................................................................................................... 48 2.1. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ .............................................................................................. 48 2.2. Ɇɟɬɨɞɢɤɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ.............. 51 2.3. ɉɪɢɦɟɪɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɞɜɭɯ ɢ ɬɪɟɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ............. 54 2.4. Ⱥɥɝɨɪɢɬɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ........................................................................................................... 60 2.4.1. ɉɨɫɬɪɨɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ .............................................................................................................................. 62 2.4.2. Ɉɫɨɛɟɧɧɨɫɬɢ ɜɵɱɢɫɥɟɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ................................................................ 70 2.4.3. Ⱥɧɚɥɢɡ ɭɫɬɨɣɱɢɜɨɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ MathCad................................................................... 73 2.5. ȼɵɜɨɞɵ............................................................................................................. 78 ȽɅȺȼȺ 3. ȼȿɊɈəɌɇɈɋɌɇȺə ɆɈȾȿɅɖ ȻɂɊɀɂ ɌɊɍȾȺ ɄȺɄ ɆȿɌɈȾɂɄȺ ȼɕɑɂɋɅȿɇɂə ɈɋɇɈȼɇɕɏ ɏȺɊȺɄɌȿɊɂɋɌɂɄ ɊɕɇɄȺ ɌɊɍȾȺ ....................................................................................................................... 80 2

3.1. Ɉɛɨɫɧɨɜɚɧɢɟ ɜɟɪɨɹɬɧɨɫɬɧɨɝɨ ɩɨɞɯɨɞɚ ɤ ɨɩɢɫɚɧɢɸ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ .................................................................................................................................. 80 3.2. Ɋɚɡɪɚɛɨɬɤɚ ɜɟɪɨɹɬɧɨɫɬɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ.................................... 81 3.2.1. ɉɪɢɦɟɪɵ ɜɵɱɢɫɥɟɧɢɹ ɨɫɧɨɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɛɢɪɠɢ ɬɪɭɞɚ ............ 88 3.3. Ɋɚɡɪɚɛɨɬɤɚ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ ..................................... 90 3.3.1. Ɉɫɨɛɟɧɧɨɫɬɢ ɪɟɚɥɢɡɚɰɢɢ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ .......... 90 3.3.2. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ...... 92 3.3.3. Ⱥɧɚɥɢɡ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɫɬɪɭɤɬɭɪɵ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ .................. 93 3.3.4. Ɋɚɡɪɚɛɨɬɤɚ ɫɬɪɭɤɬɭɪɵ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ.......................................... 98 3.3.5. Ɋɟɡɭɥɶɬɚɬɵ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ................. 101 3.3.5.1. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɨɛɡɨɪ ɪɟɡɭɥɶɬɚɬɨɜ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ .......... 101 3.4. ȼɵɜɨɞɵ........................................................................................................... 109 ɁȺɄɅɘɑȿɇɂȿ ..................................................................................................... 111 ɋɉɂɋɈɄ ɂɋɉɈɅɖɁɈȼȺɇɇɕɏ ɂɋɌɈɑɇɂɄɈȼ ....................................... 112 ɉɪɢɥɨɠɟɧɢɟ Ⱥ ........................................................................................................ 121 ɉɪɢɥɨɠɟɧɢɟ Ȼ ........................................................................................................ 122 ɉɪɢɥɨɠɟɧɢɟ ȼ ........................................................................................................ 123 ɉɪɢɥɨɠɟɧɢɟ Ƚ ........................................................................................................ 124

3

ȼȼȿȾȿɇɂȿ ɗɤɨɧɨɦɢɤɚ - ɨɞɧɚ ɢɡ ɫɚɦɵɯ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɯ ɫɮɟɪ ɩɪɢɦɟɧɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ. Ɂɚ ɩɨɫɥɟɞɧɢɟ 30-40 ɥɟɬ ɦɟɬɨɞɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɷɤɨɧɨɦɢɤɟ ɪɚɡɪɚɛɚɬɵɜɚɥɢɫɶ ɨɱɟɧɶ ɢɧɬɟɧɫɢɜɧɨ. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɹɜɥɹɟɬɫɹ ɜɚɠɧɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ. ɉɪɢɦɟɧɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɩɨɞɯɨɞɚ ɤ ɷɤɨɧɨɦɢɱɟɫɤɨɦɭ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɫɩɨɫɨɛɫɬɜɭɟɬ ɪɟɲɟɧɢɸ ɦɧɨɝɢɯ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɡɚɞɚɱ. ɐɟɥɶɸ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɫɢɫɬɟɦ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɦɟɬɨɞɨɜ ɦɚɬɟɦɚɬɢɤɢ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ, ɜɨɡɧɢɤɚɸɳɢɯ ɜ ɫɮɟɪɟ ɷɤɨɧɨɦɢɤɢ, ɫ ɩɪɢɦɟɧɟɧɢɟɦ, ɤɚɤ ɩɪɚɜɢɥɨ, ɫɨɜɪɟɦɟɧɧɨɣ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɬɟɯɧɢɤɢ. Ɉɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɫɬɪɭɤɬɭɪɧɵɯ ɷɥɟɦɟɧɬɨɜ ɷɤɨɧɨɦɢɤɢ ɹɜɥɹɟɬɫɹ ɪɵɧɨɤ ɬɪɭɞɚ. ȼ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɩɪɢɧɹɬɨ, ɱɬɨ ɪɵɧɨɤ ɬɪɭɞɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɢɫɬɟɦɭ

ɫɨɰɢɚɥɶɧɨ-ɬɪɭɞɨɜɵɯ

ɨɬɧɨɲɟɧɢɣ

ɩɨ

ɩɨɜɨɞɭ

ɭɞɨɜɥɟɬɜɨɪɟɧɢɹ

ɩɨɬɪɟɛɧɨɫɬɢ ɧɚɪɨɞɧɨɝɨ ɯɨɡɹɣɫɬɜɚ ɜ ɪɚɛɨɱɟɣ ɫɢɥɟ ɢ ɪɟɚɥɢɡɚɰɢɢ ɝɪɚɠɞɚɧɚɦɢ ɩɪɚɜɚ ɧɚ ɬɪɭɞ, ɨɫɭɳɟɫɬɜɥɹɟɦɵɯ ɩɨɫɪɟɞɫɬɜɨɦ ɨɛɦɟɧɚ ɧɚ ɨɫɧɨɜɟ ɫɩɪɨɫɚ ɢ ɩɪɟɞɥɨɠɟɧɢɹ (ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɪɚɛɨɱɟɣ ɫɢɥɵ ɢ ɪɚɛɨɱɢɯ ɦɟɫɬ) [74]. ɉɪɨɛɥɟɦɵ, ɩɪɨɬɢɜɨɪɟɱɢɹ, ɧɨɜɵɟ ɬɟɧɞɟɧɰɢɢ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɪɚɡɜɢɬɢɹ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɟ

ɫɬɚɧɨɜɥɟɧɢɟ

ɫɨɜɪɟɦɟɧɧɨɝɨ

ɪɵɧɤɚ

ɬɪɭɞɚ,

ɬɪɟɛɭɸɬ

ɜɫɟɫɬɨɪɨɧɧɟɝɨ ɢɡɭɱɟɧɢɹ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɩɪɟɞɨɬɜɪɚɬɢɬɶ ɛɭɞɭɳɢɟ ɫɬɪɭɤɬɭɪɧɵɟ ɞɢɫɛɚɥɚɧɫɵ ɜ ɫɮɟɪɟ ɬɪɭɞɚ, ɩɨɞɞɟɪɠɢɜɚɬɶ ɫɨɨɬɜɟɬɫɬɜɢɟ ɫɩɪɨɫɚ ɢ ɩɪɟɞɥɨɠɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ. ɐɟɥɶɸ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ ɩɨɥɭɱɟɧɢɟ ɨɛɴɟɤɬɢɜɧɵɯ

ɞɚɧɧɵɯ,

ɱɬɨ

ɜ

ɤɚɤɨɣ-ɬɨ

ɦɟɪɟ

ɨɛɟɫɩɟɱɢɬ

ɩɨɜɵɲɟɧɢɟ

ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɟɝɨ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ. ɋɨɡɞɚɧɢɟ ɦɨɞɟɥɟɣ ɪɵɧɤɚ ɬɪɭɞɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɜɵɛɨɪ ɫɬɪɚɬɟɝɢɢ ɭɩɪɚɜɥɟɧɢɹ ɜ ɫɮɟɪɟ ɡɚɧɹɬɨɫɬɢ, ɭɱɢɬɵɜɚɹ ɩɪɢ ɷɬɨɦ

ɨɫɨɛɟɧɧɨɫɬɢ

ɷɤɨɧɨɦɢɱɟɫɤɨɝɨ

ɪɚɡɜɢɬɢɹ,

ɫɨɫɬɚɜɚ

ɬɪɭɞɨɫɩɨɫɨɛɧɨɝɨ

ɧɚɫɟɥɟɧɢɹ, ɩɨɥɢɬɢɱɟɫɤɨɣ ɫɢɬɭɚɰɢɢ, ɩɪɢɨɪɢɬɟɬɨɜ ɫɨɰɢɚɥɶɧɨɝɨ ɪɚɡɜɢɬɢɹ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɟɤɬɢɜɧɨ ɨɰɟɧɢɬɶ ɟɝɨ ɬɟɤɭɳɟɟ ɫɨɫɬɨɹɧɢɟ ɢ ɬɟɧɞɟɧɰɢɢ ɢɡɦɟɧɟɧɢɹ, ɚ ɬɚɤɠɟ ɩɪɢɧɢɦɚɬɶ ɨɛɨɫɧɨɜɚɧɧɵɟ 4

ɭɩɪɚɜɥɟɧɱɟɫɤɢɟ

ɪɟɲɟɧɢɹ

ɜ

ɢɫɩɨɥɶɡɨɜɚɧɢɹ

ɱɟɥɨɜɟɱɟɫɤɨɝɨ

ɫɮɟɪɟ

ɬɪɭɞɨɭɫɬɪɨɣɫɬɜɚ

ɤɚɩɢɬɚɥɚ.

ɇɚ

ɢ

ɷɮɮɟɤɬɢɜɧɨɝɨ

ɨɫɧɨɜɟ

ɤɚɱɟɫɬɜɟɧɧɨɣ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɪɵɧɤɚ ɬɪɭɞɚ, ɜɨɡɦɨɠɧɨ: x

ɫɨɡɞɚɧɢɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɛɚɡɵ ɢ ɫɢɫɬɟɦɵ ɦɨɧɢɬɨɪɢɧɝɚ ɪɵɧɤɚ ɬɪɭɞɚ;

x

ɨɩɪɟɞɟɥɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɪɵɧɤɚ ɬɪɭɞɚ;

x

ɩɪɟɞɨɫɬɚɜɥɟɧɢɟ ɡɚɢɧɬɟɪɟɫɨɜɚɧɧɵɦ ɫɥɭɠɛɚɦ ɢɧɮɨɪɦɚɰɢɢ ɞɥɹ ɚɧɚɥɢɡɚ

ɢ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɤɨɧɴɸɧɤɬɭɪɵ ɪɵɧɤɚ ɬɪɭɞɚ ɢ ɬɟɧɞɟɧɰɢɣ ɟɟ ɢɡɦɟɧɟɧɢɹ; x

ɚɧɚɥɢɡ ɩɨɬɪɟɛɢɬɟɥɟɣ ɪɚɛɨɱɟɣ ɫɢɥɵ;

x

ɨɩɪɟɞɟɥɟɧɢɟ ɧɚɢɛɨɥɟɟ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɵɯ, ɩɨɥɶɡɭɸɳɢɯɫɹ ɫɩɪɨɫɨɦ ɧɚ

ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɫɩɟɰɢɚɥɢɫɬɨɜ; x

ɚɧɚɥɢɡ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ ɚɫɩɟɤɬɟ

ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨ ɨɬɪɚɫɥɹɦ ɷɤɨɧɨɦɢɤɢ; x

ɚɧɚɥɢɡ

ɢɦɟɸɳɟɣɫɹ

ɫɢɫɬɟɦɵ

ɫɬɢɦɭɥɢɪɨɜɚɧɢɹ

ɡɚɧɹɬɨɫɬɢ

ɞɥɹ

ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɨɥɢɬɢɤɢ ɡɚɧɹɬɨɫɬɢ; x

ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɟ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ, ɱɢɫɥɚ ɪɚɛɨɱɢɯ ɦɟɫɬ ɢ

ɩɨɬɪɟɛɧɨɫɬɟɣ ɜ ɧɢɯ, ɚ ɬɚɤɠɟ ɭɪɨɜɧɹ ɢ ɫɬɪɭɤɬɭɪɵ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ, ɟɝɨ ɦɢɝɪɚɰɢɢ. ɉɪɢɦɟɧɟɧɢɟ ɫɜɨɣɫɬɜɚ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɞɥɹ ɨɩɢɫɚɧɢɹ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɨɬɤɪɵɜɚɟɬ ɧɨɜɵɟ ɜɨɡɦɨɠɧɨɫɬɢ ɞɥɹ ɢɯ ɢɡɭɱɟɧɢɹ. ɉɨɫɬɪɨɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ, ɢɫɫɥɟɞɨɜɚɧɢɟ ɦɨɞɟɥɢ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ ɬɟɧɞɟɧɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ, ɢɫɫɥɟɞɨɜɚɬɶ ɪɵɧɨɤ ɧɚ ɩɪɟɞɦɟɬ ɟɝɨ ɭɫɬɨɣɱɢɜɨɫɬɢ. Ɋɵɧɨɤ ɬɪɭɞɚ ɜ ɨɬɥɢɱɢɟ ɨɬ ɞɪɭɝɢɯ ɬɢɩɨɜ ɪɵɧɤɨɜ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɭɫɬɨɣɱɢɜɨɫɬɢ. Ɉɞɧɚɤɨ ɢɫɫɥɟɞɨɜɚɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɜ ɭɫɥɨɜɢɹɯ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɧɚ ɩɪɟɞɦɟɬ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɚɧɚɥɢɡ ɞɟɹɬɟɥɶɧɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ ɤɚɤ ɫɨɫɬɚɜɧɨɣ ɱɚɫɬɢ ɮɭɧɤɰɢɨɧɚɥɶɧɨ-ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɪɵɧɤɚ ɬɪɭɞɚ, ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɷɬɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɪɢ ɮɨɪɦɢɪɨɜɚɧɢɢ ɫɨɰɢɚɥɶɧɨɣ ɩɨɥɢɬɢɤɢ ɹɜɥɹɸɬɫɹ ɧɟɞɨɫɬɚɬɨɱɧɨ ɢɡɭɱɟɧɧɵɦɢ ɧɚ ɫɟɝɨɞɧɹɲɧɢɣ ɞɟɧɶ. Ⱥɤɬɭɚɥɶɧɨɫɬɶ ɞɚɧɧɨɝɨ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɨɛɭɫɥɨɜɥɟɧɚ 5

ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ

ɩɨɫɬɪɨɟɧɢɹ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ, ɨɩɢɫɵɜɚɸɳɟɣ ɩɪɨɰɟɫɫ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ. Ɋɟɡɭɥɶɬɚɬɵ ɞɟɹɬɟɥɶɧɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ ɧɟ ɜɫɟɝɞɚ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɡɚɩɪɨɫɚɦ ɪɵɧɤɚ ɬɪɭɞɚ ɧɚ ɫɨɜɪɟɦɟɧɧɨɦ ɷɬɚɩɟ [68]. ɉɪɢɱɢɧɨɣ ɹɜɥɹɟɬɫɹ ɧɟɤɨɦɩɟɬɟɧɬɧɨɫɬɶ ɜ ɨɤɚɡɚɧɢɢ ɭɫɥɭɝ, ɱɬɨ ɩɪɟɩɹɬɫɬɜɭɟɬ ɪɚɡɜɢɬɢɸ

ɩɪɨɰɟɫɫɚ

ɨɪɢɟɧɬɚɰɢɢ ɧɚ

ɚɤɬɭɚɥɶɧɨɫɬɶ ɡɚɩɪɨɫɨɜ ɧɚɫɟɥɟɧɢɹ. ɇɟɞɨɫɬɚɬɨɱɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɨ ɫɨɫɬɨɹɧɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɧɟ ɩɨɡɜɨɥɹɟɬ ɚɞɟɤɜɚɬɧɨ ɜɨɡɞɟɣɫɬɜɨɜɚɬɶ ɧɚ ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɧɟɦ ɩɪɨɰɟɫɫɵ. ȼɨɡɧɢɤɚɟɬ ɪɹɞ ɩɪɨɬɢɜɨɪɟɱɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɪɚɡɥɢɱɢɟɦ ɩɨɤɚɡɚɬɟɥɟɣ ɨɮɢɰɢɚɥɶɧɨɣ ɫɬɚɬɢɫɬɢɤɢ ɢ ɪɟɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ, ɜɨɡɦɨɠɧɨɫɬɹɦɢ ɫɨɜɪɟɦɟɧɧɵɯ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɪɟɫɭɪɫɨɜ ɢ ɨɬɫɭɬɫɬɜɢɟɦ ɬɟɯɧɨɥɨɝɢɣ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɞɟɹɬɟɥɶɧɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ. ȼ ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɣ ɪɚɛɨɬɟ ɪɚɡɪɚɛɨɬɚɧɚ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ, ɩɪɟɞɥɨɠɟɧɚ ɦɟɬɨɞɢɤɚ, ɩɨɡɜɨɥɹɸɳɚɹ ɨɩɪɟɞɟɥɹɬɶ ɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ. ȼ ɪɚɛɨɬɟ ɦɵ ɫɬɪɟɦɢɥɢɫɶ ɨɛɴɟɞɢɧɢɬɶ ɜɨɡɦɨɠɧɨɫɬɢ ɩɪɢɦɟɧɟɧɢɹ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɨɪɢɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɞɥɹ ɪɟɲɟɧɢɹ

ɩɪɚɤɬɢɱɟɫɤɢɯ

ɡɚɞɚɱ

ɨɰɟɧɢɜɚɧɢɹ

ɫɨɫɬɨɹɧɢɹ

ɪɵɧɤɚ

ɬɪɭɞɚ

ɫ

ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɗȼɆ. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɪɟɞɥɚɝɚɸɬɫɹ ɜɟɪɨɹɬɧɨɫɬɧɚɹ ɢ ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɢɟ ɨɩɪɟɞɟɥɢɬɶ ɨɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɵɧɤɚ ɬɪɭɞɚ. Ɉɛɴɟɤɬ ɢ ɩɪɟɞɦɟɬ ɢɫɫɥɟɞɨɜɚɧɢɹ. Ɉɛɴɟɤɬɨɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɹɜɥɹɸɬɫɹ ɪɵɧɨɤ ɬɪɭɞɚ, ɛɢɪɠɚ ɬɪɭɞɚ ɢ ɨɫɧɨɜɧɵɟ ɟɟ ɫɨɫɬɚɜɥɹɸɳɢɟ - ɪɚɛɨɬɨɞɚɬɟɥɢ ɢ ɪɟɫɭɪɫɵ ɞɥɹ ɬɪɭɞɨɜɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ, ɡɚɧɹɬɨɫɬɶ ɧɚɫɟɥɟɧɢɹ ɢ ɛɟɡɪɚɛɨɬɢɰɚ, ɨɫɧɨɜɧɵɟ ɩɪɢɧɰɢɩɵ ɢɯ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚ ɮɟɞɟɪɚɥɶɧɨɦ ɢ ɪɟɝɢɨɧɚɥɶɧɨɦ ɭɪɨɜɧɹɯ,

ɩɪɟɞɦɟɬɨɦ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɹɜɥɹɟɬɫɹ

ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ

ɚɩɩɚɪɚɬ,

ɨɩɢɫɵɜɚɸɳɢɣ ɩɪɢɱɢɧɧɨ-ɫɥɟɞɫɬɜɟɧɧɵɟ ɫɜɹɡɢ ɢ ɜɡɚɢɦɨɡɚɜɢɫɢɦɨɫɬɢ ɦɟɠɞɭ ɪɵɧɤɨɦ ɬɪɭɞɚ ɢ ɛɟɡɪɚɛɨɬɢɰɟɣ. Ƚɢɩɨɬɟɡɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɫɚɦɨɨɪɝɚɧɢɡɭɸɳɢɦɫɹ ɩɪɨɰɟɫɫɨɦ. ɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɫɜɨɣɫɬɜɨ «ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɨɛɴɟɤɬɚ ɦɟɧɹɬɶ ɩɨɜɟɞɟɧɢɟ ɢɥɢ ɫɬɪɭɤɬɭɪɭ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɤɪɭɠɚɸɳɟɣ ɨɛɫɬɚɧɨɜɤɢ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, 6

ɨɬɜɟɱɚɸɳɟɦ ɢɧɬɟɪɟɫɚɦ ɨɛɴɟɤɬɚ» [43]. ɐɟɥɶ ɢ ɡɚɞɚɱɢ ɢɫɫɥɟɞɨɜɚɧɢɹ. ɐɟɥɶɸ ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɣ ɪɚɛɨɬɵ ɹɜɥɹɟɬɫɹ ɪɚɡɪɚɛɨɬɤɚ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɢ ɩɪɨɝɪɚɦɦɧɵɯ ɫɪɟɞɫɬɜ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɢɫɫɥɟɞɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɤ ɜɧɟɲɧɢɦ ɜɨɡɞɟɣɫɬɜɢɹɦ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɢ ɨɩɢɫɚɧɢɟ ɨɫɧɨɜɧɵɯ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤ (ɩɚɪɚɦɟɬɪɨɜ). Ⱦɥɹ ɞɨɫɬɢɠɟɧɢɹ ɩɨɫɬɚɜɥɟɧɧɨɣ ɰɟɥɢ ɬɪɟɛɭɟɬɫɹ ɪɟɲɟɧɢɟ ɫɥɟɞɭɸɳɢɯ ɡɚɞɚɱ: 1.

ɉɨɫɬɪɨɢɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ

ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ ɧɚ ɨɫɧɨɜɟ ɩɪɨɜɟɞɟɧɧɨɝɨ

ɚɧɚɥɢɡɚ ɢ

ɨɛɨɛɳɟɧɢɣ ɧɚɱɚɬɨɝɨ ɜ ɷɬɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɢɫɫɥɟɞɨɜɚɧɢɹ [12] ɩɨ ɚɧɚɥɢɬɢɱɟɫɤɨɦɭ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɪɵɧɤɚ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɭɸ ɩɪɢ ɧɚɱɚɥɶɧɨɦ ɜɨɡɦɭɳɟɧɢɢ ɢɫɫɥɟɞɨɜɚɬɶ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɫɨɫɬɨɹɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ. 2.

Ɋɚɡɪɚɛɨɬɚɬɶ

ɤɨɦɩɥɟɤɫ

ɩɪɨɝɪɚɦɦ,

ɪɟɚɥɢɡɭɸɳɢɣ

ɚɥɝɨɪɢɬɦɵ

ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɨɫɬɪɨɟɧɧɨɣ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɪɵɧɤɚ ɬɪɭɞɚ. 3. ɨɩɪɟɞɟɥɢɬɶ

Ɋɚɡɪɚɛɨɬɚɬɶ ɜɟɪɨɹɬɧɨɫɬɧɭɸ ɦɨɞɟɥɶ ɪɵɧɤɚ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɭɸ ɟɝɨ

ɨɫɧɨɜɧɵɟ

ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ:

ɢɧɬɟɧɫɢɜɧɨɫɬɶ

ɩɨɫɬɭɩɥɟɧɢɹ

ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɪɚɡɥɢɱɧɵɟ ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ; ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɚɯ ɛɢɪɠɢ ɬɪɭɞɚ; ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ; ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɪɟɫɭɪɫɨɜ ɦɟɠɞɭ ɨɬɞɟɥɚɦɢ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɭɧɤɰɢɣ; ɤɨɷɮɮɢɰɢɟɧɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ (ɞɨɥɹ ɜɪɟɦɟɧɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ) ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. 4.

Ɋɚɡɪɚɛɨɬɚɬɶ ɢɦɢɬɚɰɢɨɧɧɭɸ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ

ɬɪɭɞɚ. Ɇɟɬɨɞɵ ɩɪɨɜɟɞɟɧɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ. Ɋɟɲɟɧɢɟ ɩɨɫɬɚɜɥɟɧɧɵɯ ɡɚɞɚɱ ɨɫɧɨɜɵɜɚɟɬɫɹ ɧɚ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɚɩɩɚɪɚɬɚ ɬɟɨɪɢɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɫɢɫɬɟɦ,

ɬɟɨɪɢɢ

ɦɚɫɫɨɜɨɝɨ

ɨɛɫɥɭɠɢɜɚɧɢɹ,

ɱɢɫɥɟɧɧɵɯ

ɦɟɬɨɞɚɯ,

ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɯ ɫɪɟɞɫɬɜɚɯ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. Ⱦɥɹ ɩɪɨɜɟɞɟɧɢɹ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɪɢɜɥɟɤɚɥɢɫɶ ɪɚɛɨɬɵ ɜ ɨɛɥɚɫɬɢ

ɬɟɨɪɢɢ

ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (Ȼ.ȼ. Ƚɧɟɞɟɧɤɨ, ɂ.ɇ. Ʉɨɜɚɥɟɧɤɨ ɢ ɞɪ.) [24]; ɬɟɨɪɢɢ 7

ɜɟɪɨɹɬɧɨɫɬɟɣ (Ȼ.ȼ. Ƚɧɟɞɟɧɤɨ ɢ ɞɪ.) [16, 25, 26]; ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ (Ȼɨɟɜ ȼ.Ⱦ., ȿɦɟɥɶɹɧɨɜ Ⱥ.Ⱥ., Ʉɨɛɟɥɟɜ ɇ.Ȼ. ɢ ɞɪ.) [9, 34, 43, 50]. ɇɟɞɨɫɬɚɬɨɱɧɚɹ

ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɫɬɶ

ɦɟɬɨɞɨɜ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɜ

ɷɦɩɢɪɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɪɵɧɤɚ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɡɚɹɜɢɬɶ ɨ ɧɚɭɱɧɨɣ ɧɨɜɢɡɧɟ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɤɨɬɨɪɚɹ ɫɨɫɬɨɢɬ ɜ ɫɥɟɞɭɸɳɟɦ: 1. Ɉɛɨɛɳɟɧɵ

ɢɡɜɟɫɬɧɵɟ

ɪɟɡɭɥɶɬɚɬɵ

[12]

ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɫ ɨɞɧɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ ɧɚ ɫɥɭɱɚɣ n ɨɬɪɚɫɥɟɣ. 2.

ɉɪɨɜɟɞɟɧɧɵɟ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɧɚ

ɭɫɬɨɣɱɢɜɨɫɬɶ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ

ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ

ɷɤɨɧɨɦɢɤɢ

ɪɟɚɥɢɡɨɜɚɧɵ ɜ ɫɢɫɬɟɦɟ MathCad. 3. Ɋɚɡɪɚɛɨɬɚɧɚ ɜɟɪɨɹɬɧɨɫɬɧɚɹ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ (ɪɚɛɨɬɵ) ɛɢɪɠɢ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɚɹ ɨɩɪɟɞɟɥɹɬɶ ɨɫɧɨɜɧɵɟ ɟɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. 4. ȼɟɪɨɹɬɧɨɫɬɧɚɹ ɦɨɞɟɥɶ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɪɟɚɥɢɡɨɜɚɧɚ ɜ ɜɢɞɟ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɜ ɫɢɫɬɟɦɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World. ɉɪɚɤɬɢɱɟɫɤɚɹ ɡɧɚɱɢɦɨɫɬɶ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ. 1.

ɉɪɟɞɥɨɠɟɧɧɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ

ɞɥɹ ɩɪɨɜɟɞɟɧɢɹ ɚɧɚɥɢɡɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɨɫɬɨɹɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ, ɨɩɪɟɞɟɥɟɧɢɹ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ (ɮɚɤɬɨɪɨɜ) ɩɪɨɰɟɫɫɚ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ. 2. ɉɪɟɞɥɚɝɚɟɦɵɣ ɤɨɦɩɥɟɤɫ ɩɪɨɝɪɚɦɦ ɧɚ ɗȼɆ ɩɨɡɜɨɥɹɟɬ ɢɫɫɥɟɞɨɜɚɬɶ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ. 3. Ɋɚɡɪɚɛɨɬɚɧɧɵɟ ɜ ɩɪɨɰɟɫɫɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɢ ɞɟɹɬɟɥɶɧɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ

ɦɚɬɟɪɢɚɥɵ ɢ ɪɟɤɨɦɟɧɞɚɰɢɢ ɛɵɥɢ

ɢɫɩɨɥɶɡɨɜɚɧɵ ɜ ɪɚɛɨɬɟ ɞɟɩɚɪɬɚɦɟɧɬɚ ɫɨɰɢɚɥɶɧɨɣ ɩɨɥɢɬɢɤɢ ɝ. ɋɬɚɜɪɨɩɨɥɹ. ɉɪɟɞɥɨɠɟɧɧɵɟ

ɦɨɞɟɥɢ

ɛɵɥɢ

ɚɩɪɨɛɢɪɨɜɚɧɵ

ɜ

ɋɬɚɜɪɨɩɨɥɶɫɤɨɦ

ɰɟɧɬɪɟ

ɡɚɧɹɬɨɫɬɢ, ɜ ɤɚɞɪɨɜɨɦ ɚɝɟɧɬɫɬɜɟ ɇɈɍ «Ȼɚɤɚɥɚɜɪ» (ɝ. ɋɬɚɜɪɨɩɨɥɶ). ɇɚɭɱɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɩɪɨɜɟɞɟɧɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɜɧɟɞɪɟɧɵ ɢ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɜ ɭɱɟɛɧɨɦ ɩɪɨɰɟɫɫɟ ɋɟɜɟɪɨ-Ʉɚɜɤɚɡɫɤɨɝɨ ɫɨɰɢɚɥɶɧɨɝɨ ɢɧɫɬɢɬɭɬɚ (ɝ. ɋɬɚɜɪɨɩɨɥɶ) ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɫɬɭɞɟɧɬɨɜ ɫɩɟɰɢɚɥɶɧɨɫɬɢ 351400 «ɉɪɢɤɥɚɞɧɚɹ ɢɧɮɨɪɦɚɬɢɤɚ ɜ ɷɤɨɧɨɦɢɤɟ»

ɜ

ɯɨɞɟ

ɱɬɟɧɢɹ

ɤɭɪɫɚ 8

«ɂɦɢɬɚɰɢɨɧɧɨɟ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ

ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ», ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɫɬɭɞɟɧɬɨɜ ɫɩɟɰɢɚɥɶɧɨɫɬɢ 230700 «ɋɟɪɜɢɫ» ɜ ɯɨɞɟ ɱɬɟɧɢɹ ɤɭɪɫɨɜ «Ɇɟɬɨɞɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɫɟɪɜɢɫɟ», «Ɇɟɬɨɞɵ ɨɩɬɢɦɢɡɚɰɢɢ ɜ ɫɟɪɜɢɫɟ» ɢ ɪɭɤɨɜɨɞɫɬɜɚ ɧɚɩɢɫɚɧɢɟɦ ɞɢɩɥɨɦɧɵɯ ɢ ɤɭɪɫɨɜɵɯ ɪɚɛɨɬ. ɉɨ

ɪɟɡɭɥɶɬɚɬɚɦ

ɩɪɨɜɟɞɟɧɧɵɯ

ɢɫɫɥɟɞɨɜɚɧɢɣ,

ɢɡɥɨɠɟɧɧɵɯ

ɜ

ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɣ ɪɚɛɨɬɟ, ɩɨɥɭɱɟɧɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɚɤɬɵ ɜɧɟɞɪɟɧɢɹ. Ɉɫɧɨɜɧɵɟ ɩɨɥɨɠɟɧɢɹ ɞɢɫɫɟɪɬɚɰɢɢ, ɜɵɧɨɫɢɦɵɟ ɧɚ ɡɚɳɢɬɭ: 1. Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɦɧɨɝɨɨɬɪɚɫɥɟɜɨɣ ɷɤɨɧɨɦɢɤɢ, ɩɨɡɜɨɥɹɸɳɚɹ ɢɫɫɥɟɞɨɜɚɬɶ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɷɬɨɬ ɪɵɧɨɤ ɩɪɢ ɜɨɡɦɭɳɟɧɢɢ ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɪɵɧɤɚ. 2. Ɇɟɬɨɞɢɤɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɪɨɰɟɫɫɚ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ, ɪɟɚɥɢɡɨɜɚɧɧɚɹ ɫ ɩɨɦɨɳɶɸ ɗȼɆ. 3. ȼɟɪɨɹɬɧɨɫɬɧɚɹ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ, ɪɚɡɪɚɛɨɬɚɧɧɚɹ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɨɜ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɢ ɩɨɡɜɨɥɹɸɳɚɹ ɨɩɪɟɞɟɥɹɬɶ ɨɫɧɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɛɢɪɠɢ. 4. ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɚɹ ɜɨɫɩɪɨɢɡɜɨɞɢɬɶ ɩɪɨɰɟɫɫ ɟɟ ɪɚɛɨɬɵ ɜ ɫɢɫɬɟɦɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World. Ⱦɨɫɬɨɜɟɪɧɨɫɬɶ

ɪɟɡɭɥɶɬɚɬɨɜ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ

ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɨɜɪɟɦɟɧɧɨɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ ɢ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɯ ɫɪɟɞɫɬɜ (MathCad, ɫɢɫɬɟɦɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World) ɞɥɹ ɨɩɢɫɚɧɢɹ ɢɫɫɥɟɞɭɟɦɵɯ ɩɪɨɰɟɫɫɨɜ ɢ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɦɧɨɝɨɤɪɚɬɧɨ ɧɚɛɥɸɞɚɜɲɟɣɫɹ ɫɨɝɥɚɫɨɜɚɧɧɨɫɬɶɸ ɪɚɡɪɚɛɨɬɚɧɧɵɯ ɩɨɥɨɠɟɧɢɣ ɢ ɩɪɟɞɥɨɠɟɧɧɵɯ ɦɟɬɨɞɢɤ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ 0,01 %. Ⱥɩɪɨɛɚɰɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɞɢɫɫɟɪɬɚɰɢɢ. Ɋɟɡɭɥɶɬɚɬɵ ɞɨɤɥɚɞɵɜɚɥɢɫɶ «Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ

ɩɪɨɜɟɞɟɧɧɵɯ ɧɚ

ɬɪɟɬɶɟɣ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ

ɢɫɫɥɟɞɨɜɚɧɢɣ ɪɟɝɢɨɧɚɥɶɧɨɣ ɢ

ɛɵɥɢ

ɚɩɪɨɛɢɪɨɜɚɧɵ

ɧɚɭɱɧɨɣ

ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ

ɢ

ɤɨɧɮɟɪɟɧɰɢɢ ɬɟɯɧɨɥɨɝɢɢ

ɜ

ɬɟɯɧɢɱɟɫɤɢɯ, ɟɫɬɟɫɬɜɟɧɧɵɯ ɢ ɝɭɦɚɧɢɬɚɪɧɵɯ ɧɚɭɤɚɯ» (ɝ. Ƚɟɨɪɝɢɟɜɫɤ, 2003 ɝ.); ɉɨɧɬɪɹɝɢɧɫɤɢɯ ɱɬɟɧɢɹɯ-XIV «ɋɨɜɪɟɦɟɧɧɵɟ ɦɟɬɨɞɵ ɬɟɨɪɢɢ ɤɪɚɟɜɵɯ ɡɚɞɚɱ» (ɝ. ȼɨɪɨɧɟɠ, 2003 ɝ.), ɑɟɬɜɟɪɬɨɦ ȼɫɟɪɨɫɫɢɣɫɤɨɦ ɫɢɦɩɨɡɢɭɦɟ ɩɨ ɩɪɢɤɥɚɞɧɨɣ ɢ 9

ɩɪɨɦɵɲɥɟɧɧɨɣ ɦɚɬɟɦɚɬɢɤɟ (ɝ. ɋɨɱɢ, 2003 ɝ.), 49-ɣ ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɣ ɤɨɧɮɟɪɟɧɰɢɢ ɩɪɟɩɨɞɚɜɚɬɟɥɟɣ ɢ ɫɬɭɞɟɧɬɨɜ ɋȽɍ «ɍɧɢɜɟɪɫɢɬɟɬɫɤɚɹ ɧɚɭɤɚ – ɪɟɝɢɨɧɭ» (ɝ. ɋɬɚɜɪɨɩɨɥɶ, 2004 ɝ.), ɉɹɬɨɦ ȼɫɟɪɨɫɫɢɣɫɤɨɦ ɫɢɦɩɨɡɢɭɦɟ

ɩɨ

ɩɪɢɤɥɚɞɧɨɣ ɢ ɩɪɨɦɵɲɥɟɧɧɨɣ ɦɚɬɟɦɚɬɢɤɟ (ɝ. ɉɟɬɪɨɡɚɜɨɞɫɤ, ɝ. Ʉɢɫɥɨɜɨɞɫɤ, 2004 ɝ.), 50-ɣ ɸɛɢɥɟɣɧɨɣ ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɣ ɤɨɧɮɟɪɟɧɰɢɢ ɩɪɟɩɨɞɚɜɚɬɟɥɟɣ ɢ ɫɬɭɞɟɧɬɨɜ ɋȽɍ «ɍɧɢɜɟɪɫɢɬɟɬɫɤɚɹ ɧɚɭɤɚ – ɪɟɝɢɨɧɭ» (ɝ. ɋɬɚɜɪɨɩɨɥɶ, 2005 ɝ.), ɒɟɫɬɨɦ ȼɫɟɪɨɫɫɢɣɫɤɨɦ ɫɢɦɩɨɡɢɭɦɟ

ɩɨ ɩɪɢɤɥɚɞɧɨɣ ɢ ɩɪɨɦɵɲɥɟɧɧɨɣ

ɦɚɬɟɦɚɬɢɤɟ (ɝ. ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝ, 2005 ɝ.), ɜɫɟɪɨɫɫɢɣɫɤɨɣ ɧɚɭɱɧɨ-ɩɪɚɤɬɢɱɟɫɤɨɣ ɤɨɧɮɟɪɟɧɰɢɢ «Ɋɵɧɨɤ

ɬɪɭɞɚ, ɡɚɧɹɬɨɫɬɶ, ɞɨɯɨɞɵ: ɩɪɨɛɥɟɦɵ ɢ ɬɟɧɞɟɧɰɢɢ

ɪɚɡɜɢɬɢɹ» (Ɉɪɟɥ, 2005 ɝ.). Ɇɚɬɟɪɢɚɥɵ ɞɢɫɫɟɪɬɚɰɢɢ ɨɛɫɭɠɞɚɥɢɫɶ ɧɚ ɧɚɭɱɧɵɯ ɫɟɦɢɧɚɪɚɯ ɤɚɮɟɞɪɵ ɩɪɢɤɥɚɞɧɨɣ ɦɚɬɟɦɚɬɢɤɢ ɢ ɢɧɮɨɪɦɚɬɢɤɢ ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ, ɤɚɮɟɞɪɵ ɫɟɪɜɢɫɚ ɋɟɜɟɪɨ-Ʉɚɜɤɚɡɫɤɨɝɨ ɫɨɰɢɚɥɶɧɨɝɨ ɢɧɫɬɢɬɭɬɚ. Ɉɩɭɛɥɢɤɨɜɚɧɧɨɫɬɶ ɪɟɡɭɥɶɬɚɬɨɜ. Ɇɚɬɟɪɢɚɥɵ ɞɢɫɫɟɪɬɚɰɢɢ ɨɩɭɛɥɢɤɨɜɚɧɵ ɜ 12 ɧɚɭɱɧɵɯ ɪɚɛɨɬɚɯ. ɋɬɪɭɤɬɭɪɚ ɢ ɨɛɴɟɦ ɞɢɫɫɟɪɬɚɰɢɢ. Ⱦɢɫɫɟɪɬɚɰɢɹ ɫɨɫɬɨɢɬ ɢɡ ɜɜɟɞɟɧɢɹ, 3 ɝɥɚɜ, ɡɚɤɥɸɱɟɧɢɹ, ɫɩɢɫɤɚ ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ ɢɫɬɨɱɧɢɤɨɜ ɢ ɩɪɢɥɨɠɟɧɢɣ. Ɋɚɛɨɬɚ ɢɡɥɨɠɟɧɚ ɧɚ 120 ɫɬɪɚɧɢɰɚɯ, ɫɨɞɟɪɠɢɬ 26 ɪɢɫɭɧɤɨɜ ɢ 7 ɬɚɛɥɢɰ. ȼ

ɩɟɪɜɨɣ

ɝɥɚɜɟ

ɩɪɢɜɟɞɟɧɵ

ɬɟɨɪɟɬɢɱɟɫɤɢɟ

ɫɜɟɞɟɧɢɹ

ɨ

ɦɟɬɨɞɚɯ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɫɜɨɣɫɬɜɟ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ, ɢɡ ɬɟɨɪɢɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɢ ɢɡ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ

ɨɛɫɥɭɠɢɜɚɧɢɹ,

ɤɨɬɨɪɵɟ

ɬɪɟɛɭɸɬɫɹ

ɞɥɹ

ɩɪɨɜɨɞɢɦɵɯ

ɜ

ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɣ ɪɚɛɨɬɟ ɢɫɫɥɟɞɨɜɚɧɢɣ. Ɉɛɨɫɧɨɜɚɧɨ, ɩɨɥɨɠɟɧɢɟ ɨ ɜɨɡɦɨɠɧɨɫɬɢ ɨɛɴɟɤɬɢɜɧɨ ɨɰɟɧɢɬɶ ɬɟɤɭɳɟɟ ɫɨɫɬɨɹɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɢ ɬɟɧɞɟɧɰɢɢ ɟɝɨ ɢɡɦɟɧɟɧɢɹ. ɉɨɤɚɡɚɧɨ, ɱɬɨ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɦ ɩɨɞɯɨɞɨɦ ɤ ɚɧɚɥɢɡɭ ɪɵɧɤɚ ɬɪɭɞɚ ɹɜɥɹɸɬɫɹ ɦɟɬɨɞɵ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɜɨɣɫɬɜɚ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ, ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɞɥɹ ɟɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ. ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɨɞɧɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ. ɋɮɨɪɦɭɥɢɪɨɜɚɧɨ, ɱɬɨ, ɩɪɚɜɢɥɶɧɨ ɜɵɛɪɚɜ ɩɨɤɚɡɚɬɟɥɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ 10

ɪɚɛɨɬɵ, ɛɢɪɠɭ ɬɪɭɞɚ ɦɨɠɧɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɧɟɤɨɬɨɪɭɸ ɫɢɫɬɟɦɭ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫ ɨɠɢɞɚɧɢɟɦ (ɨɱɟɪɟɞɶɸ), ɚ

ɢɫɩɨɥɶɡɨɜɚɧɢɟ

ɩɨɫɬɪɨɟɧɧɨɣ ɦɨɞɟɥɢ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɫɢɬɭɚɰɢɸ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ, ɫɨɡɞɚɬɶ ɱɟɬɤɭɸ ɫɬɪɭɤɬɭɪɭ, ɨɩɪɟɞɟɥɢɬɶ ɬɟɧɞɟɧɰɢɢ ɢ ɩɪɨɰɟɫɫɵ ɪɚɡɜɢɬɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ. Ɋɚɫɫɦɨɬɪɟɧɨ

ɩɪɢɦɟɧɟɧɢɟ

ɢɦɢɬɚɰɢɨɧɧɨɝɨ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɞɥɹ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɢɦɢɬɚɰɢɨɧɧɵɯ ɦɨɞɟɥɟɣ ɪɵɧɤɚ ɬɪɭɞɚ ɨɬɤɪɵɜɚɟɬ ɧɨɜɵɟ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨ ɤɨɧɰɟɩɬɭɚɥɶɧɨɦɭ ɚɧɚɥɢɡɭ ɩɪɨɛɥɟɦ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ. ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɜɨɫɩɪɨɢɡɜɨɞɢɬɶ

ɯɨɞ

ɫɨɛɵɬɢɣ

ɧɚ

ɛɢɪɠɟ

ɬɪɭɞɚ

ɩɪɢ

ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ

ɮɨɪɦɚɥɢɡɚɰɢɢ ɩɨɜɟɞɟɧɢɹ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɟɟ ɨɛɴɟɤɬɨɜ. ȼɨ ɜɬɨɪɨɣ ɝɥɚɜɟ ɪɚɡɪɚɛɨɬɚɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ, ɩɨɡɜɨɥɹɸɳɚɹ ɩɪɨɫɥɟɞɢɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɚ

ɬɟɧɞɟɧɰɢɢ ɦɟɬɨɞɢɤɚ

ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɨɩɪɟɞɟɥɟɧɢɹ

ɪɵɧɤɚ

ɭɫɬɨɣɱɢɜɨɝɨ

ɪɚɛɨɱɟɣ

ɫɨɫɬɨɹɧɢɹ

ɫɢɥɵ; ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɨɩɢɫɵɜɚɸɳɟɣ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ. ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɜ ɩɨɥɭɱɟɧɧɵɟ ɫɜɟɞɟɧɢɹ ɨɛ ɭɫɬɨɣɱɢɜɵɯ ɢ ɧɟɭɫɬɨɣɱɢɜɵɯ ɫɨɫɬɨɹɧɢɹɯ ɪɵɧɤɚ ɬɪɭɞɚ

ɞɥɹ n ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ ɜɩɨɥɧɟ

ɜɨɡɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɩɪɨɝɧɨɡ ɟɝɨ ɫɨɫɬɨɹɧɢɹ. ɉɨɥɭɱɟɧɧɵɣ ɩɪɨɝɧɨɡ ɩɨɡɜɨɥɢɬ ɢɡɛɟɠɚɬɶ ɤɪɢɡɢɫɨɜ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ. ȼ ɬɪɟɬɶɟɣ ɝɥɚɜɟ ɩɪɟɞɥɨɠɟɧɵ ɦɨɞɟɥɢ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɫɨɫɬɨɹɧɢɣ ɪɵɧɤɚ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɢɟ ɨɩɪɟɞɟɥɢɬɶ ɨɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɵɧɤɚ ɬɪɭɞɚ: ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɪɚɡɥɢɱɧɵɟ ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ; ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɚɯ ɛɢɪɠɢ ɬɪɭɞɚ; ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ; ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɪɟɫɭɪɫɨɜ ɦɟɠɞɭ ɨɬɞɟɥɚɦɢ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɭɧɤɰɢɣ; ɤɨɷɮɮɢɰɢɟɧɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ (ɞɨɥɹ ɜɪɟɦɟɧɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ) ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. ɋ

ɬɨɱɤɢ

ɡɪɟɧɢɹ

ɬɟɨɪɢɢ

ɦɚɫɫɨɜɨɝɨ 11

ɨɛɫɥɭɠɢɜɚɧɢɹ

ɛɢɪɠɚ

ɬɪɭɞɚ

ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɫɢɫɬɟɦɚ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɋɆɈ) ɫ ɨɠɢɞɚɧɢɟɦ (ɨɱɟɪɟɞɶɸ), ɫɨɝɥɚɫɭɸɳɟɣ ɬɚɤɢɟ ɩɪɨɰɟɫɫɵ, ɤɚɤ ɫɩɪɨɫ ɢ ɩɪɟɞɥɨɠɟɧɢɟ ɧɚ ɪɚɛɨɱɭɸ ɫɢɥɭ, ɝɞɟ ɨɬɞɟɥɵ ɛɢɪɠɢ – ɤɚɧɚɥɵ ɋɆɈ, ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ – ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɜ ɋɆɈ, ɨɱɟɪɟɞɶ ɧɚ ɛɢɪɠɟ – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɜ ɋɆɈ ɢ ɬ.ɞ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɫɩɪɨɫ ɢ ɩɪɟɞɥɨɠɟɧɢɟ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ. Ɋɚɡɪɚɛɨɬɚɧɧɚɹ ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɩɨɤɚɡɚɬɟɥɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɪɟɫɭɪɫɨɜ, ɧɚ ɤɨɬɨɪɵɟ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɨɤɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɬɨɤɨɜ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɢ ɩɪɨɜɨɞɢɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ ɚɧɚɥɢɡ ɩɪɨɰɟɫɫɚ ɢ ɪɟɡɭɥɶɬɚɬɨɜ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ. ȼ ɡɚɤɥɸɱɟɧɢɢ ɨɛɨɛɳɟɧɵ ɢɬɨɝɢ ɢ ɪɟɡɭɥɶɬɚɬɵ ɩɪɨɜɟɞɟɧɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ. ɉɪɢɥɨɠɟɧɢɟ ɫɨɞɟɪɠɢɬ ɥɢɫɬɢɧɝ ɤɨɦɩɥɟɤɫɚ ɩɪɨɝɪɚɦɦ, ɪɟɚɥɢɡɭɸɳɢɯ ɚɥɝɨɪɢɬɦ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɧɚ

ɭɫɬɨɣɱɢɜɨɫɬɶ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ

ɦɨɞɟɥɢ

ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ, ɪɚɡɪɚɛɨɬɚɧɧɨɣ ɜ ɞɚɧɧɨɦ ɢɫɫɥɟɞɨɜɚɧɢɢ. Ʉɨɦɩɥɟɤɫ ɩɪɨɝɪɚɦɦ ɪɚɡɪɚɛɨɬɚɧ ɜ ɫɢɫɬɟɦɟ MathCad. ɉɪɢɜɟɞɟɧɵ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɝ. ɋɬɚɜɪɨɩɨɥɹ, Q-ɫɯɟɦɚ ɛɢɪɠɢ ɬɪɭɞɚ, ɛɥɨɤɞɢɚɝɪɚɦɦɚ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ, ɥɢɫɬɢɧɝ ɦɨɞɭɥɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɧɚ ɹɡɵɤɟ GPSS.

12

ȽɅȺȼȺ 1. ȺɇȺɅɂɁ ɗɎɎȿɄɌɂȼɇɈɋɌɂ ɂ ɉɊɈȻɅȿɆ ɆɈȾȿɅɂɊɈȼȺɇɂə ɊɕɇɄȺ ɌɊɍȾȺ 1.1. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɋɪɟɞɢ ɦɧɨɝɢɯ ɩɪɨɛɥɟɦ ɷɤɨɧɨɦɢɤɢ ɜ ɩɨɫɥɟɞɧɢɟ ɝɨɞɵ ɨɫɨɛɭɸ ɨɫɬɪɨɬɭ ɢ ɚɤɬɭɚɥɶɧɨɫɬɶ ɩɪɢɨɛɪɟɬɚɟɬ ɩɪɨɛɥɟɦɚ ɷɮɮɟɤɬɢɜɧɨɝɨ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ. ɍɫɩɟɲɧɨɟ ɪɟɲɟɧɢɟ ɷɬɨɣ ɩɪɨɛɥɟɦɵ ɡɚɜɢɫɢɬ ɨɬ ɝɥɭɛɢɧɵ ɩɨɡɧɚɧɢɹ ɨɛɴɟɤɬɢɜɧɵɯ ɡɚɤɨɧɨɜ ɪɚɡɜɢɬɢɹ ɪɵɧɤɚ ɬɪɭɞɚ. Ɋɵɧɨɤ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ ɨɞɧɨɣ ɢɡ ɧɚɢɛɨɥɟɟ ɩɨɞɜɢɠɧɵɯ ɢ ɞɢɧɚɦɢɱɧɵɯ ɫɢɫɬɟɦ, ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɯ ɜɧɟɲɧɢɦɢ ɮɚɤɬɨɪɚɦɢ, ɝɥɚɜɧɵɦ ɢɡ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ

ɬɟɯɧɢɱɟɫɤɢɣ

ɩɪɨɝɪɟɫɫ.

ɂɡɦɟɧɟɧɢɟ

ɭɫɥɨɜɢɣ

ɨɛɳɟɫɬɜɟɧɧɨɝɨ

ɩɪɨɢɡɜɨɞɫɬɜɚ ɜɫɟɝɞɚ ɨɬɪɚɠɚɟɬɫɹ ɧɚ ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɣ ɫɬɪɭɤɬɭɪɟ ɢ ɦɟɯɚɧɢɡɦɟ ɫɨɰɢɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ. Ɍɚɤ ɛɵɥɨ ɜ ɷɩɨɯɭ ɬɟɯɧɢɱɟɫɤɨɣ ɪɟɜɨɥɸɰɢɢ 20-30-ɯ ɝɝ. ɞɜɚɞɰɚɬɨɝɨ ɫɬɨɥɟɬɢɹ, ɬɚɤ ɩɪɨɢɫɯɨɞɢɬ ɢ ɫɟɝɨɞɧɹ. ɇɌɊ 7080-ɯ ɝɝ. ɨɡɧɚɦɟɧɨɜɚɥɚ ɧɟ ɩɪɨɫɬɨ ɫɦɟɧɭ ɬɟɯɧɢɤɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɭɤɥɚɞɚ, ɚ ɤɚɱɟɫɬɜɟɧɧɵɣ ɩɟɪɟɯɨɞ ɨɬ ɢɧɞɭɫɬɪɢɚɥɶɧɨɣ ɤ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɰɢɜɢɥɢɡɚɰɢɢ, ɜ ɨɫɧɨɜɟ ɤɨɬɨɪɨɣ ɥɟɠɢɬ ɧɚɭɱɧɵɣ ɩɨɬɟɧɰɢɚɥ ɢ ɫɩɨɫɨɛɧɨɫɬɶ ɬɪɚɧɫɮɨɪɦɢɪɨɜɚɬɶ ɧɚɭɱɧɵɟ ɡɧɚɧɢɹ, ɢɧɮɨɪɦɚɰɢɸ ɜ ɤɨɧɟɱɧɵɣ ɩɪɨɞɭɤɬ. "ɂɧɬɟɥɥɟɤɬɭɚɥɶɧɚɹ ɷɤɨɧɨɦɢɤɚ" ɩɪɟɜɪɚɳɚɟɬ ɱɟɥɨɜɟɤɚ ɜ ɝɥɚɜɧɭɸ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɭɸ ɫɢɥɭ ɨɛɳɟɫɬɜɚ, ɚ ɟɝɨ ɫɨɡɢɞɚɬɟɥɶɧɵɣ ɩɨɬɟɧɰɢɚɥ - ɜ ɤɚɩɢɬɚɥ, ɨɬ ɨɛɴɟɦɚ ɢ ɤɚɱɟɫɬɜɚ ɤɨɬɨɪɨɝɨ, ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ, ɡɚɜɢɫɢɬ ɷɤɨɧɨɦɢɱɟɫɤɢɣ ɩɪɨɝɪɟɫɫ. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɧɨɜɵɯ ɤɚɱɟɫɬɜ ɫɨɜɪɟɦɟɧɧɨɝɨ ɪɚɛɨɬɧɢɤɚ ɜɵɡɵɜɚɟɬ ɩɟɪɟɫɬɪɨɣɤɭ ɧɟ ɬɨɥɶɤɨ ɫɬɪɭɤɬɭɪɵ ɢ ɦɟɯɚɧɢɡɦɚ ɪɵɧɤɚ ɬɪɭɞɚ, ɧɨ ɢ ɜɫɟɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɬɪɭɞɨɜɵɯ ɨɬɧɨɲɟɧɢɣ. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɨɫɦɵɫɥɟɧɢɟ ɩɪɨɛɥɟɦ, ɩɪɨɬɢɜɨɪɟɱɢɣ, ɧɨɜɵɯ ɬɟɧɞɟɧɰɢɣ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɯ

ɫɬɚɧɨɜɥɟɧɢɟ

ɫɨɜɪɟɦɟɧɧɨɝɨ

ɪɵɧɤɚ

ɬɪɭɞɚ,

ɬɪɟɛɭɟɬ

ɜɫɟɫɬɨɪɨɧɧɟɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɫɟɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɮɚɤɬɨɪɨɜ, ɩɨɪɨɠɞɚɸɳɢɯ ɫɩɟɰɢɮɢɤɭ ɮɨɪɦ ɟɝɨ ɮɭɧɤɰɢɨɧɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɟɝɨ ɦɨɞɢɮɢɤɚɰɢɢ ɢ ɪɚɡɜɢɬɢɹ. Ɏɭɧɤɰɢɨɧɚɥɶɧɨ - ɨɪɝɚɧɢɡɚɰɢɨɧɧɚɹ ɫɬɪɭɤɬɭɪɚ ɪɵɧɤɚ ɬɪɭɞɚ ɜɤɥɸɱɚɟɬ ɜ 13

ɫɟɛɹ ɜ ɭɫɥɨɜɢɹɯ ɪɚɡɜɢɬɨɣ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: ɩɪɢɧɰɢɩɵ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɣ ɩɨɥɢɬɢɤɢ ɜ ɨɛɥɚɫɬɢ ɡɚɧɹɬɨɫɬɢ ɢ ɛɟɡɪɚɛɨɬɢɰɵ; ɫɢɫɬɟɦɭ ɩɨɞɝɨɬɨɜɤɢ ɤɚɞɪɨɜ; ɫɢɫɬɟɦɭ ɧɚɣɦɚ, ɤɨɧɬɪɚɤɬɧɭɸ ɫɢɫɬɟɦɭ; ɮɨɧɞ ɩɨɞɞɟɪɠɤɢ ɛɟɡɪɚɛɨɬɧɵɯ; ɫɢɫɬɟɦɭ ɩɟɪɟɩɨɞɝɨɬɨɜɤɢ ɢ ɩɟɪɟɤɜɚɥɢɮɢɤɚɰɢɢ; ɛɢɪɠɢ ɬɪɭɞɚ; ɩɪɚɜɨɜɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɡɚɧɹɬɨɫɬɢ [60]. Ɏɚɤɬɨɪɵ ɤɨɧɴɸɧɤɬɭɪɵ ɫɨɜɪɟɦɟɧɧɨɝɨ ɪɵɧɤɚ ɬɪɭɞɚ ɩɨɫɬɨɹɧɧɨ ɢɥɢ ɰɢɤɥɢɱɟɫɤɢ (ɧɚ ɞɨɥɝɨɫɪɨɱɧɵɯ ɜɪɟɦɟɧɧɵɯ ɢɧɬɟɪɜɚɥɚɯ ɢɥɢ ɜ ɤɪɚɬɤɨɫɪɨɱɧɨɦ ɩɟɪɢɨɞɟ),

ɨɬɤɥɨɧɹɸɬ ɪɵɧɨɤ ɨɬ ɪɚɜɧɨɜɟɫɢɹ ɢɥɢ ɩɪɢɛɥɢɠɚɸɬ ɤ ɧɟɦɭ.

Ʉɨɧɴɸɧɤɬɭɪɚ ɪɵɧɤɚ ɬɪɭɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɟɮɢɰɢɬɨɦ ɤɚɞɪɨɜ, ɪɚɜɧɨɜɟɫɧɵɦ ɫɨɫɬɨɹɧɢɟɦ, ɛɟɡɪɚɛɨɬɢɰɟɣ. Ȼɢɪɠɚ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ ɝɥɚɜɧɵɯ ɭɱɪɟɠɞɟɧɢɣ, ɨɪɝɚɧɢɡɭɸɳɢɦ ɪɵɧɨɤ ɬɪɭɞɚ, ɫɨɝɥɚɫɭɸɳɢɦ ɫɩɪɨɫ ɢ ɩɪɟɞɥɨɠɟɧɢɟ ɧɚ ɪɚɛɨɱɭɸ ɫɢɥɭ. Ɂɚɤɨɧɨɞɚɬɟɥɶɧɵɟ ɩɪɚɜɢɥɚ ɩɨɫɬɚɧɨɜɤɢ ɧɚ ɭɱɟɬ ɜ ɤɚɱɟɫɬɜɟ ɛɟɡɪɚɛɨɬɧɨɝɨ, ɚ ɬɚɤɠɟ ɪɚɡɦɟɪ ɩɨɫɨɛɢɹ ɩɨ ɛɟɡɪɚɛɨɬɢɰɟ ɢ ɫɪɨɤɢ ɟɝɨ ɜɵɩɨɥɧɟɧɢɹ ɹɜɥɹɸɬɫɹ ɜɚɠɧɵɦɢ ɞɟɬɟɪɦɢɧɚɧɬɚɦɢ, ɨɩɪɟɞɟɥɹɸɳɢɦɢ ɪɚɡɥɢɱɢɹ ɜ ɫɪɨɤɚɯ ɩɪɟɛɵɜɚɧɢɹ ɧɚ ɭɱɟɬɟ ɜ ɛɢɪɠɟ ɬɪɭɞɚ [1]. Ɉɞɢɧ ɢɡ ɩɨɤɚɡɚɬɟɥɟɣ ɡɞɨɪɨɜɶɹ ɷɤɨɧɨɦɢɤɢ ɫɬɪɚɧɵ - ɷɬɨ ɭɪɨɜɟɧɶ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ. Ɉɫɧɨɜɧɵɦɢ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɡɚɧɹɬɨɫɬɢ ɹɜɥɹɸɬɫɹ, ɤɪɨɦɟ ɫɢɫɬɟɦɵ ɫɨɰɢɚɥɶɧɵɯ ɝɚɪɚɧɬɢɣ: ɫɬɢɦɭɥɢɪɨɜɚɧɢɟ ɫɩɪɨɫɚ ɧɚ ɬɪɭɞ, ɫɬɢɦɭɥɢɪɨɜɚɧɢɟ ɩɪɟɞɥɨɠɟɧɢɹ ɬɪɭɞɚ, ɫɨɝɥɚɫɨɜɚɧɢɟ ɫɩɪɨɫɚ ɢ ɩɪɟɞɥɨɠɟɧɢɹ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ. ɉɪɨɛɥɟɦɵ

ɡɚɧɹɬɨɫɬɢ,

ɛɟɡɪɚɛɨɬɢɰɵ

ɩɪɢɨɛɪɟɬɚɸɬ

ɜɫɟ

ɛɨɥɶɲɭɸ

ɚɤɬɭɚɥɶɧɨɫɬɶ ɧɚ ɫɨɜɪɟɦɟɧɧɨɦ ɷɬɚɩɟ. ɉɪɨɝɧɨɡɢɪɨɜɚɧɢɟ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ ɢ ɟɟ ɫɬɪɭɤɬɭɪɵ

ɡɚɧɢɦɚɟɬ

ɜɚɠɧɨɟ

ɦɟɫɬɨ

ɜ

ɞɟɹɬɟɥɶɧɨɫɬɢ

ɮɟɞɟɪɚɥɶɧɵɯ

ɢ

ɪɟɝɢɨɧɚɥɶɧɵɯ ɨɪɝɚɧɨɜ ɭɩɪɚɜɥɟɧɢɹ [3]. Ɋɟɲɟɧɢɟ ɡɚɞɚɱ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ ɩɨɡɜɨɥɢɬ ɨɩɪɟɞɟɥɢɬɶ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɫɧɨɜɧɵɯ ɫɨɰɢɚɥɶɧɨɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɪɚɡɜɢɬɢɹ, ɞɟɦɨɝɪɚɮɢɱɟɫɤɢɯ ɮɚɤɬɨɪɨɜ, ɜ ɬ. ɱ. ɦɢɝɪɚɰɢɨɧɧɵɯ ɩɪɨɰɟɫɫɨɜ. Ɏɨɪɦɚɥɢɡɚɰɢɹ ɬɟɨɪɢɢ ɦɨɠɟɬ ɛɵɬɶ ɡɚɜɟɪɲɟɧɚ ɪɚɡɪɚɛɨɬɤɨɣ ɤɨɦɩɥɟɤɫɚ ɜɡɚɢɦɨɫɜɹɡɚɧɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɢ ɤɨɦɩɶɸɬɟɪɧɵɯ ɦɨɞɟɥɟɣ, ɩɨɡɜɨɥɹɸɳɢɯ 14

ɝɢɛɤɨ ɢɡɦɟɧɹɬɶ ɩɨɥɢɬɢɤɭ ɝɨɫɭɞɚɪɫɬɜɚ ɜ ɫɮɟɪɟ ɡɚɧɹɬɨɫɬɢ ɢ ɛɟɡɪɚɛɨɬɢɰɵ ɫ ɰɟɥɶɸ ɫɨɝɥɚɫɨɜɚɧɢɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɪɚɡɜɢɬɢɹ ɷɤɨɧɨɦɢɤɢ ɢ ɫɨɰɢɚɥɶɧɨɣ ɡɚɳɢɳɟɧɧɨɫɬɢ ɛɟɡɪɚɛɨɬɧɵɯ. Ɉɬɟɱɟɫɬɜɟɧɧɨɣ

ɧɚɭɤɨɣ ɧɚɤɨɩɥɟɧ

ɨɩɪɟɞɟɥɟɧɧɵɣ ɨɩɵɬ ɫɨɫɬɚɜɥɟɧɢɹ

ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ, ɨɩɢɫɵɜɚɸɳɢɯ ɩɪɨɰɟɫɫɵ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ [13, 47, 65, 76, 100, 101]. Ⱦɥɹ ɩɪɨɝɧɨɡɚ ɫɢɬɭɚɰɢɢ ɜ ɫɮɟɪɟ ɡɚɧɹɬɨɫɬɢ ɢ ɛɟɡɪɚɛɨɬɢɰɵ, ɜ ɨɫɧɨɜɧɨɦ, ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɛɚɥɚɧɫɨɜɵɟ ɦɨɞɟɥɢ ɢ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɚɧɚɥɢɡɚ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɪɟɝɪɟɫɫɢɨɧɧɵɟ ɦɟɬɨɞɵ ɞɚɸɬ ɯɨɪɨɲɢɟ ɪɟɡɭɥɶɬɚɬɵ ɜ ɬɟɯ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɧɟ ɩɪɨɢɫɯɨɞɢɬ ɪɟɡɤɢɯ ɫɬɪɭɤɬɭɪɧɵɯ ɢɡɦɟɧɟɧɢɣ ɫɨɰɢɚɥɶɧɨ-ɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɪɚɡɜɢɬɢɹ ɨɛɳɟɫɬɜɚ. ɉɨɷɬɨɦɭ ɧɢ ɨɞɢɧ ɩɪɨɝɧɨɡ, ɫɨɫɬɚɜɥɟɧɧɵɣ ɩɪɢ ɩɨɦɨɳɢ ɷɬɢɯ ɦɟɬɨɞɨɜ, ɧɟ ɫɦɨɝ ɩɪɟɞɫɤɚɡɚɬɶ ɨɛɨɫɬɪɟɧɢɟ ɫɢɬɭɚɰɢɢ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ ɜ 1998 ɝ. ȼɵɛɨɪ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɟɬɨɞɨɜ ɞɥɹ ɪɟɲɟɧɢɹ ɩɪɨɛɥɟɦɵ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɨɛɭɫɥɨɜɥɟɧ ɫɥɟɞɭɸɳɢɦɢ ɚɫɩɟɤɬɚɦɢ [5, 21, 39, 52, 85, 87]: 1. ɋɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɛɨɪɚ ɢɧɮɨɪɦɚɰɢɢ ɨ ɫɥɨɠɧɨɦ ɨɛɴɟɤɬɟ (ɪɵɧɤɟ ɬɪɭɞɚ). Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɩɨɡɜɨɥɹɸɬ ɭɩɨɪɹɞɨɱɢɬɶ ɫɢɫɬɟɦɭ ɢɧɮɨɪɦɚɰɢɢ, ɜɵɹɜɥɹɬɶ ɧɟɞɨɫɬɚɬɤɢ ɜ ɢɦɟɸɳɟɣɫɹ ɢɧɮɨɪɦɚɰɢɢ ɢ ɜɵɪɚɛɚɬɵɜɚɬɶ ɬɪɟɛɨɜɚɧɢɹ ɞɥɹ ɩɨɞɝɨɬɨɜɤɢ ɧɨɜɨɣ ɢɧɮɨɪɦɚɰɢɢ ɢɥɢ ɟɟ ɤɨɪɪɟɤɬɢɪɨɜɤɢ. Ɋɚɡɪɚɛɨɬɤɚ

ɢ

ɩɪɢɦɟɧɟɧɢɟ

ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ

ɦɨɞɟɥɟɣ

ɭɤɚɡɵɜɚɸɬ

ɩɭɬɢ

ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɫɛɨɪɚ ɢ ɚɧɚɥɢɡɚ ɢɧɮɨɪɦɚɰɢɢ, ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɣ ɧɚ ɪɟɲɟɧɢɟ ɨɩɪɟɞɟɥɟɧɧɵɯ ɡɚɞɚɱ ɩɥɚɧɢɪɨɜɚɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ. ɉɪɨɝɪɟɫɫ ɜ ɢɧɮɨɪɦɚɰɢɨɧɧɨɦ ɨɛɟɫɩɟɱɟɧɢɢ ɩɥɚɧɢɪɨɜɚɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ ɨɩɢɪɚɟɬɫɹ ɧɚ ɛɭɪɧɨ ɪɚɡɜɢɜɚɸɳɢɟɫɹ ɬɟɯɧɢɱɟɫɤɢɟ ɢ ɩɪɨɝɪɚɦɦɧɵɟ ɫɪɟɞɫɬɜɚ ɢɧɮɨɪɦɚɬɢɤɢ. 2. ɂɧɬɟɧɫɢɮɢɤɚɰɢɹ ɢ ɩɨɜɵɲɟɧɢɟ ɬɨɱɧɨɫɬɢ ɬɟɯɧɢɱɟɫɤɢɯ ɢ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ. Ɏɨɪɦɚɥɢɡɚɰɢɹ ɬɟɯɧɢɱɟɫɤɢɯ ɢ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɡɚɞɚɱ ɢ ɩɪɢɦɟɧɟɧɢɟ ɗȼɆ ɦɧɨɝɨɤɪɚɬɧɨ ɭɫɤɨɪɹɸɬ ɬɢɩɨɜɵɟ, ɦɚɫɫɨɜɵɟ ɪɚɫɱɟɬɵ, ɩɨɜɵɲɚɸɬ ɬɨɱɧɨɫɬɶ ɢ ɫɨɤɪɚɳɚɸɬ ɬɪɭɞɨɟɦɤɨɫɬɶ, ɩɨɡɜɨɥɹɸɬ ɩɪɨɜɨɞɢɬɶ ɦɧɨɝɨɜɚɪɢɚɧɬɧɵɟ ɬɟɯɧɢɱɟɫɤɢɟ ɢ ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɨɛɨɫɧɨɜɚɧɢɹ ɫɥɨɠɧɵɯ ɦɟɪɨɩɪɢɹɬɢɣ,

ɧɟɞɨɫɬɭɩɧɵɟ ɩɪɢ

«ɪɭɱɧɨɣ» ɬɟɯɧɨɥɨɝɢɢ. 3.ɍɝɥɭɛɥɟɧɢɟ

ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ

ɚɧɚɥɢɡɚ 15

ɩɪɨɛɥɟɦ

ɜ

ɬɟɯɧɢɱɟɫɤɢɯ,

ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɢ ɞɪɭɝɢɯ ɩɪɢɥɨɠɟɧɢɹɯ. Ȼɥɚɝɨɞɚɪɹ ɩɪɢɦɟɧɟɧɢɸ ɦɟɬɨɞɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɤɨɧɤɪɟɬɧɨɝɨ

ɪɵɧɤɚ

ɬɪɭɞɚ

ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ

ɨɤɚɡɵɜɚɸɳɢɯ ɜɥɢɹɧɢɟ

ɡɧɚɱɢɬɟɥɶɧɨ ɚɧɚɥɢɡɚ:

ɭɫɢɥɢɜɚɸɬɫɹ

ɢɡɭɱɟɧɢɟ

ɧɚ ɩɪɨɰɟɫɫɵ, ɤɨɥɢɱɟɫɬɜɟɧɧɚɹ

ɜɨɡɦɨɠɧɨɫɬɢ

ɦɧɨɝɢɯ

ɮɚɤɬɨɪɨɜ,

ɨɰɟɧɤɚ ɩɨɫɥɟɞɫɬɜɢɣ

ɢɡɦɟɧɟɧɢɹ ɭɫɥɨɜɢɣ ɪɚɡɜɢɬɢɹ ɨɛɴɟɤɬɨɜ ɢ ɬ. ɩ. 4. Ɋɟɲɟɧɢɟ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɯ ɧɚɭɱɧɵɯ ɢ ɩɪɚɤɬɢɱɟɫɤɢɯ ɡɚɞɚɱ ɜ ɥɸɛɨɣ ɫɮɟɪɟ ɩɪɢɥɨɠɟɧɢɣ. ɉɨɫɪɟɞɫɬɜɨɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɭɞɚɟɬɫɹ ɪɟɲɚɬɶ ɬɚɤɢɟ ɡɚɞɚɱɢ, ɤɨɬɨɪɵɟ ɢɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɪɟɲɢɬɶ ɧɟɜɨɡɦɨɠɧɨ, ɧɚɩɪɢɦɟɪ: ɧɚɯɨɠɞɟɧɢɟ ɨɩɬɢɦɚɥɶɧɨɝɨ ɜɚɪɢɚɧɬɚ ɫɬɪɭɤɬɭɪɵ ɛɢɪɠɢ ɬɪɭɞɚ, ɫɨɡɞɚɧɢɟ ɨɛɴɟɤɬɚ ɫ ɡɚɪɚɧɟɟ ɡɚɞɚɧɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ, ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɤɨɧɬɪɨɥɹ ɡɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟɦ ɪɵɧɤɚ ɬɪɭɞɚ ɢ ɬ. ɩ. 1.2. Ɉɛɡɨɪ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɯ ɫɪɟɞɫɬɜ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɂɦɢɬɚɰɢɨɧɧɨɟ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ

ɹɜɥɹɟɬɫɹ

ɫɟɝɨɞɧɹ

ɦɨɳɧɵɦ

ɢ

ɩɟɪɫɩɟɤɬɢɜɧɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ ɢ ɩɨɫɥɟɞɭɸɳɟɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɥɨɠɧɵɯ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɢ ɫɢɫɬɟɦ, ɜ ɤɨɬɨɪɵɯ ɜɟɥɢɤɨ ɱɢɫɥɨ ɩɟɪɟɦɟɧɧɵɯ, ɬɪɭɞɨɟɦɨɤ ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɡɚɜɢɫɢɦɨɫɬɟɣ, ɜɵɫɨɤ ɭɪɨɜɟɧɶ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɢɦɢɬɢɪɭɟɦɵɯ ɫɢɬɭɚɰɢɣ. ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɡɜɨɥɹɟɬ ɨɛɴɟɞɢɧɹɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɫ ɩɪɚɤɬɢɱɟɫɤɢɦ ɢ ɬɟɨɪɟɬɢɱɟɫɤɢɦ ɨɩɵɬɨɦ ɫɩɟɰɢɚɥɢɫɬɨɜ-ɩɪɚɤɬɢɤɨɜ [43, 54, 67]. ɂɦɢɬɚɰɢɨɧɧɨɟ (ɤɨɦɩɶɸɬɟɪɧɨɟ) ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɞɜɭɯ ɫɥɭɱɚɹɯ [34]: • ɞɥɹ ɭɩɪɚɜɥɟɧɢɹ ɫɥɨɠɧɵɦ ɛɢɡɧɟɫ-ɩɪɨɰɟɫɫɨɦ, ɤɨɝɞɚ ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɭɩɪɚɜɥɹɟɦɨɝɨ ɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɨɛɴɟɤɬɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɤɚɱɟɫɬɜɟ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɝɨ ɫɪɟɞɫɬɜɚ ɜ ɤɨɧɬɭɪɟ ɚɞɚɩɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ, ɫɨɡɞɚɜɚɟɦɨɣ ɧɚ ɨɫɧɨɜɟ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ (ɤɨɦɩɶɸɬɟɪɧɵɯ) ɬɟɯɧɨɥɨɝɢɣ; • ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɫ ɞɢɫɤɪɟɬɧɨ-ɧɟɩɪɟɪɵɜɧɵɦɢ ɦɨɞɟɥɹɦɢ 16

ɫɥɨɠɧɵɯ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɢ ɨɬɫɥɟɠɢɜɚɧɢɹ ɢɯ ɞɢɧɚɦɢɤɢ ɜ ɷɤɫɬɪɟɧɧɵɯ ɫɢɬɭɚɰɢɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɪɢɫɤɚɦɢ, ɧɚɬɭɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɤɨɬɨɪɵɯ ɧɟɠɟɥɚɬɟɥɶɧɨ ɢɥɢ ɧɟɜɨɡɦɨɠɧɨ. ȼ [34] ɜɵɞɟɥɟɧɵ ɪɚɡɥɢɱɧɵɟ ɬɢɩɨɜɵɟ ɡɚɞɚɱɢ, ɪɟɲɚɟɦɵɟ ɫɪɟɞɫɬɜɚɦɢ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɪɢ ɭɩɪɚɜɥɟɧɢɢ ɷɤɨɧɨɦɢɱɟɫɤɢɦɢ ɨɛɴɟɤɬɚɦɢ: • ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɥɨɝɢɫɬɢɤɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɧɵɯ ɢ ɫɬɨɢɦɨɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ; • ɭɩɪɚɜɥɟɧɢɟ ɩɪɨɰɟɫɫɨɦ ɪɟɚɥɢɡɚɰɢɢ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ ɧɚ ɪɚɡɥɢɱɧɵɯ ɷɬɚɩɚɯ ɟɝɨ ɠɢɡɧɟɧɧɨɝɨ ɰɢɤɥɚ ɫ ɭɱɟɬɨɦ ɜɨɡɦɨɠɧɵɯ ɪɢɫɤɨɜ ɢ ɬɚɤɬɢɤɢ ɜɵɞɟɥɟɧɢɹ ɞɟɧɟɠɧɵɯ ɫɭɦɦ; • ɚɧɚɥɢɡ ɤɥɢɪɢɧɝɨɜɵɯ ɩɪɨɰɟɫɫɨɜ ɜ ɪɚɛɨɬɟ ɫɟɬɢ ɤɪɟɞɢɬɧɵɯ ɨɪɝɚɧɢɡɚɰɢɣ; • ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɟ ɮɢɧɚɧɫɨɜɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɞɟɹɬɟɥɶɧɨɫɬɢ ɩɪɟɞɩɪɢɹɬɢɹ ɧɚ ɤɨɧɤɪɟɬɧɵɣ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ; • ɛɢɡɧɟɫ-ɪɟɢɧɠɢɧɢɪɢɧɝ ɧɟɫɨɫɬɨɹɬɟɥɶɧɨɝɨ ɩɪɟɞɩɪɢɹɬɢɹ; • ɚɧɚɥɢɡ ɚɞɚɩɬɢɜɧɵɯ ɫɜɨɣɫɬɜ ɢ ɠɢɜɭɱɟɫɬɢ ɤɨɦɩɶɸɬɟɪɧɨɣ ɪɟɝɢɨɧɚɥɶɧɨɣ ɛɚɧɤɨɜɫɤɨɣ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ; • ɨɰɟɧɤɚ ɩɚɪɚɦɟɬɪɨɜ ɧɚɞɟɠɧɨɫɬɢ ɢ ɡɚɞɟɪɠɟɤ ɜ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɣ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɢɫɬɟɦɟ ɫ ɤɨɥɥɟɤɬɢɜɧɵɦ ɞɨɫɬɭɩɨɦ; • ɚɧɚɥɢɡ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɧɨɝɨɭɪɨɜɧɟɜɨɣ ɜɟɞɨɦɫɬɜɟɧɧɨɣ ɧɟɨɞɧɨɪɨɞɧɨɣ

ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɬɪɭɤɬɭɪɵ,

ɭɩɪɚɜɥɹɸɳɟɣ

ɩɪɨɩɭɫɤɧɨɣ

ɫɢɫɬɟɦɵ

ɫɩɨɫɨɛɧɨɫɬɢ

ɤɚɧɚɥɨɜ

ɫ

ɭɱɟɬɨɦ ɫɜɹɡɢ

ɢ

ɧɟɫɨɜɟɪɲɟɧɫɬɜɚ ɮɢɡɢɱɟɫɤɨɣ ɨɪɝɚɧɢɡɚɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɛɚɡɵ ɞɚɧɧɵɯ ɜ ɪɟɝɢɨɧɚɥɶɧɵɯ ɰɟɧɬɪɚɯ; • ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɞɟɣɫɬɜɢɣ ɤɭɪɶɟɪɫɤɨɣ (ɮɟɥɶɞɴɟɝɟɪɫɤɨɣ) ɜɟɪɬɨɥɟɬɧɨɣ ɝɪɭɩɩɵ ɜ ɪɟɝɢɨɧɟ, ɩɨɫɬɪɚɞɚɜɲɟɦ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢɪɨɞɧɨɣ ɤɚɬɚɫɬɪɨɮɵ ɢɥɢ ɤɪɭɩɧɨɣ ɩɪɨɦɵɲɥɟɧɧɨɣ ɚɜɚɪɢɢ; • ɚɧɚɥɢɡ, ɫɟɬɟɜɨɣ ɦɨɞɟɥɢ PERT (Program Evaluation and Review Technique) ɞɥɹ ɩɪɨɟɤɬɨɜ ɡɚɦɟɧɵ ɢ ɧɚɥɚɞɤɢ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɫ ɭɱɟɬɨɦ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɧɟɢɫɩɪɚɜɧɨɫɬɟɣ; •

ɚɧɚɥɢɡ

ɪɚɛɨɬɵ

ɚɜɬɨɬɪɚɧɫɩɨɪɬɧɨɝɨ 17

ɩɪɟɞɩɪɢɹɬɢɹ,

ɡɚɧɢɦɚɸɳɟɝɨɫɹ

ɤɨɦɦɟɪɱɟɫɤɢɦɢ ɩɟɪɟɜɨɡɤɚɦɢ ɝɪɭɡɨɜ, ɫ ɭɱɟɬɨɦ ɫɩɟɰɢɮɢɤɢ ɬɨɜɚɪɧɵɯ ɢ ɞɟɧɟɠɧɵɯ ɩɨɬɨɤɨɜ ɜ ɪɟɝɢɨɧɟ; • ɪɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɧɚɞɟɠɧɨɫɬɢ ɢ ɡɚɞɟɪɠɟɤ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ ɜ ɛɚɧɤɨɜɫɤɨɣ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɢɫɬɟɦɟ. ɉɪɢɦɟɧɟɧɢɟ

ɢɦɢɬɚɰɢɨɧɧɨɝɨ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɧɟ

ɢɦɟɟɬ

ɜɢɞɢɦɵɯ

ɨɝɪɚɧɢɱɟɧɢɣ [56]. ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ ɯɚɪɚɤɬɟɪ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɜɡɚɢɦɨɨɬɧɨɲɟɧɢɣ ɦɟɠɞɭ ɪɚɛɨɬɧɢɤɚɦɢ ɢ ɪɚɛɨɬɨɞɚɬɟɥɹɦɢ.

ɂɧɫɬɪɭɦɟɧɬɨɦ

ɩɨɞɨɛɧɵɯ

ɢɫɫɥɟɞɨɜɚɧɢɣ

ɹɜɥɹɟɬɫɹ

ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɧɨɝɨɚɝɟɧɬɧɚɹ ɦɨɞɟɥɶ. Ɉɛɴɟɤɬɨɦ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɛɢɪɠɚ ɬɪɭɞɚ ɤɚɤ ɨɫɧɨɜɧɨɣ ɷɥɟɦɟɧɬ ɮɭɧɤɰɢɨɧɚɥɶɧɨ - ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɪɵɧɤɚ ɬɪɭɞɚ. ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ: -ɨɬɨɛɪɚɠɚɬɶ ɯɨɞ ɫɨɛɵɬɢɣ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɮɨɪɦɚɥɢɡɚɰɢɢ ɩɨɜɟɞɟɧɢɹ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɟɟ ɨɛɴɟɤɬɨɜ; -ɪɚɫɫɱɢɬɵɜɚɬɶ ɲɢɪɨɤɢɣ ɤɥɚɫɫ ɨɛɨɛɳɟɧɧɵɯ ɩɨɤɚɡɚɬɟɥɟɣ ɦɨɞɟɥɢɪɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ; -ɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɧɚ ɛɭɞɭɳɟɟ ɩɨɜɟɞɟɧɢɟ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɨɛɴɟɤɬɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. ɋɢɫɬɟɦɚ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɫɨɡɞɚɧɢɟ ɦɨɞɟɥɟɣ ɞɥɹ ɪɟɲɟɧɢɹ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɡɚɞɚɱ, ɞɨɥɠɧɚ ɨɛɥɚɞɚɬɶ ɫɥɟɞɭɸɳɢɦɢ ɫɜɨɣɫɬɜɚɦɢ [34]: • ɜɨɡɦɨɠɧɨɫɬɶɸ ɩɪɢɦɟɧɟɧɢɹ ɢɦɢɬɚɰɢɨɧɧɵɯ ɩɪɨɝɪɚɦɦ ɫɨɜɦɟɫɬɧɨ ɫɨ ɫɩɟɰɢɚɥɶɧɵɦɢ

ɷɤɨɧɨɦɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɢ

ɦɨɞɟɥɹɦɢ

ɢ

ɦɟɬɨɞɚɦɢ,

ɨɫɧɨɜɚɧɧɵɦɢ ɧɚ ɬɟɨɪɢɢ ɭɩɪɚɜɥɟɧɢɹ; • ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɦɢ ɦɟɬɨɞɚɦɢ ɩɪɨɜɟɞɟɧɢɹ ɫɬɪɭɤɬɭɪɧɨɝɨ ɚɧɚɥɢɡɚ ɫɥɨɠɧɨɝɨ ɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ; •

ɫɩɨɫɨɛɧɨɫɬɶɸ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɦɚɬɟɪɢɚɥɶɧɵɯ,

ɞɟɧɟɠɧɵɯ

ɢ

ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɩɪɨɰɟɫɫɨɜ ɢ ɩɨɬɨɤɨɜ ɜ ɪɚɦɤɚɯ ɟɞɢɧɨɣ ɦɨɞɟɥɢ, ɜ ɨɛɳɟɦ ɦɨɞɟɥɶɧɨɦ ɜɪɟɦɟɧɢ; • ɜɨɡɦɨɠɧɨɫɬɶɸ ɜɜɟɞɟɧɢɹ ɪɟɠɢɦɚ ɩɨɫɬɨɹɧɧɨɝɨ ɭɬɨɱɧɟɧɢɹ ɩɪɢ ɩɨɥɭɱɟɧɢɢ 18

ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɩɪɨɜɟɞɟɧɢɢ ɷɤɫɬɪɟɦɚɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɵ ɫɥɟɞɭɸɳɢɟ ɩɚɤɟɬɵ ɫɢɫɬɟɦ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ [5, 11, 55, 70, 71]: • GPSS World (General Purpose Simulation System, ɤɨɦɩɚɧɢɹ «Minuteman Software», ɋɒȺ); • Process Charter-1.0.2 (ɤɨɦɩɚɧɢɹ «Scitor», Ɇɟɧɥɨ-ɉɚɪɤ, Ʉɚɥɢɮɨɪɧɢɹ, ɋɒȺ); • Powersim-2.01 (ɤɨɦɩɚɧɢɹ «Modell Data» AS, Ȼɟɪɝɟɧ, ɇɨɪɜɟɝɢɹ), • Ithink-3.0.61 (ɤɨɦɩɚɧɢɹ «High Performance Systems», Ƚɚɧɧɨɜɟɪ, ɇɶɸɏɷɦɩɲɢɪ, ɋɒȺ); • Extend+BPR-3.1 (ɤɨɦɩɚɧɢɹ «Imagine That!», ɋɚɧ-ɏɨɫɟ, Ʉɚɥɢɮɨɪɧɢɹ, ɋɒȺ); • ReThink (ɮɢɪɦɚ «Gensym», Ʉɟɦɛɪɢɞɠ, Ɇɚɫɫɚɱɭɫɟɬɫ, ɋɒȺ); • Micro Saint (ɮɢɪɦɚ «Calspan Advanced Technology Center», Colorado, ɋɒȺ); • Pilgrim (Ɋɨɫɫɢɹ). ȼ

ɩɪɨɰɟɫɫɟ

ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɝɨ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɢɦɢɬɚɰɢɨɧɧɨɟ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɜɨɞɢɥɨɫɶ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɚɤɟɬɨɜ GPSS World [9, 68, 93], Micro Saint [46], Pilgrim [34]. ȼɵɛɨɪ ɜɵɲɟɩɟɪɟɱɢɫɥɟɧɧɵɯ ɩɚɤɟɬɨɜ ɛɵɥ ɨɛɭɫɥɨɜɥɟɧ ɢɯ ɮɭɧɤɰɢɨɧɚɥɶɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ. ɋɢɫɬɟɦɚ GPSS World, ɪɚɡɪɚɛɨɬɚɧɧɚɹ ɤɨɦɩɚɧɢɟɣ Minuteman Software (ɋɒȺ), – ɷɬɨ ɦɨɳɧɚɹ ɫɪɟɞɚ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɨɛɳɟɝɨ ɧɚɡɧɚɱɟɧɢɹ, ɪɚɡɪɚɛɨɬɚɧɧɚɹ ɞɥɹ ɩɪɨɮɟɫɫɢɨɧɚɥɨɜ ɜ ɨɛɥɚɫɬɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɗɬɨ ɤɨɦɩɥɟɤɫɧɵɣ ɦɨɞɟɥɢɪɭɸɳɢɣ ɢɧɫɬɪɭɦɟɧɬ, ɨɯɜɚɬɵɜɚɸɳɢɣ ɨɛɥɚɫɬɢ ɤɚɤ ɞɢɫɤɪɟɬɧɨɝɨ, ɬɚɤ ɢ ɧɟɩɪɟɪɵɜɧɨɝɨ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɨɛɥɚɞɚɸɳɢɣ ɜɵɫɨɱɚɣɲɢɦ ɭɪɨɜɧɟɦ ɢɧɬɟɪɚɤɬɢɜɧɨɫɬɢ ɢ ɜɢɡɭɚɥɶɧɨɝɨ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ

GPSS

World

ɞɚɟɬ

ɜɨɡɦɨɠɧɨɫɬɶ

ɨɰɟɧɢɬɶ

ɷɮɮɟɤɬ

ɤɨɧɫɬɪɭɤɬɨɪɫɤɢɯ ɪɟɲɟɧɢɣ ɜ ɱɪɟɡɜɵɱɚɣɧɨ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦɚɯ ɪɟɚɥɶɧɨɝɨ ɦɢɪɚ. GPSS ɹɜɥɹɟɬɫɹ ɨɛɴɟɤɬɧɨ-ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɦ ɹɡɵɤɨɦ. ȿɝɨ ɜɨɡɦɨɠɧɨɫɬɢ ɜɢɡɭɚɥɶɧɨɝɨ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɩɨɡɜɨɥɹɸɬ ɧɚɛɥɸɞɚɬɶ ɢ ɮɢɤɫɢɪɨɜɚɬɶ 19

ɜɧɭɬɪɟɧɧɢɟ ɦɟɯɚɧɢɡɦɵ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɦɨɞɟɥɟɣ. ȿɝɨ ɢɧɬɟɪɚɤɬɢɜɧɨɫɬɶ ɩɨɡɜɨɥɹɟɬ ɨɞɧɨɜɪɟɦɟɧɧɨ ɢɫɫɥɟɞɨɜɚɬɶ ɢ ɭɩɪɚɜɥɹɬɶ ɩɪɨɰɟɫɫɚɦɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɋ ɩɨɦɨɳɶɸ ɜɫɬɪɨɟɧɧɵɯ ɫɪɟɞɫɬɜ ɚɧɚɥɢɡɚ ɞɚɧɧɵɯ ɦɨɠɧɨ ɥɟɝɤɨ ɜɵɱɢɫɥzɬɶ ɞɨɜɟɪɢɬɟɥɶɧɵɟ ɢɧɬɟɪɜɚɥɵ ɢ ɩɪɨɜɨɞɢɬɶ ɞɢɫɩɟɪɫɢɨɧɧɵɣ ɚɧɚɥɢɡ, ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɫɨɡɞɚɜɚɬɶ

ɢ

ɜɵɩɨɥɧɹɬɶ

ɫɥɨɠɧɵɟ

ɨɬɫɟɢɜɚɸɳɢɟ

ɢ

ɨɩɬɢɦɢɡɢɪɭɸɳɢɟ

ɷɤɫɩɟɪɢɦɟɧɬɵ. ɋɢɫɬɟɦɚ GPSS World ɛɵɥɚ ɪɚɡɪɚɛɨɬɚɧɚ, ɱɬɨɛɵ ɩɨɥɧɨɫɬɶɸ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɨɡɦɨɠɧɨɫɬɢ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɦɟɯɚɧɢɡɦɚ ɜɢɪɬɭɚɥɶɧɨɣ ɩɚɦɹɬɢ ɩɨɡɜɨɥɹɟɬ ɦɨɞɟɥɹɦ ɪɟɚɥɶɧɨ ɞɨɫɬɢɝɚɬɶ ɪɚɡɦɟɪɚ ɦɢɥɥɢɚɪɞɚ ɛɚɣɬ. ȼɵɬɟɫɧɹɸɳɚɹ ɦɧɨɝɨɡɚɞɚɱɧɨɫɬɶ ɢ ɦɧɨɝɨɩɨɬɨɱɧɨɫɬɶ ɨɛɟɫɩɟɱɢɜɚɸɬ ɜɵɫɨɤɭɸ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɧɚ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ ɢ ɞɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ GPSS World ɨɞɧɨɜɪɟɦɟɧɧɨ ɜɵɩɨɥɧɹɬɶ ɦɧɨɠɟɫɬɜɨ ɡɚɞɚɱ. ɉɨɫɥɟɞɧɹɹ ɜɟɪɫɢɹ GPSS World 4.3.2. (ɨɬ 8 ɧɨɹɛɪɹ 2001 ɝɨɞɚ) ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɦɚɫɫɭ ɧɨɜɨɜɜɟɞɟɧɢɣ, ɩɨɡɜɨɥɹɸɳɢɯ ɩɪɨɜɨɞɢɬɶ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɢ ɫɞɟɥɚɬɶ ɪɚɛɨɬɭ ɫ ɫɢɫɬɟɦɨɣ ɦɚɤɫɢɦɚɥɶɧɨ ɩɪɨɫɬɨɣ ɢ ɭɞɨɛɧɨɣ ɞɥɹ ɩɨɥɶɡɨɜɚɬɟɥɹ. Ɏɭɧɤɰɢɨɧɚɥɶɧɨɟ ɧɚɡɧɚɱɟɧɢɟ ɩɚɤɟɬɚ Micro Saint - ɮɭɧɞɚɦɟɧɬɚɥɶɧɨɟ ɩɟɪɟɨɫɦɵɫɥɟɧɢɟ ɢ ɪɚɞɢɤɚɥɶɧɨɟ ɩɟɪɟɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɞɟɥɨɜɵɯ ɩɪɨɰɟɫɫɨɜ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɪɟɡɤɢɯ, ɫɤɚɱɤɨɨɛɪɚɡɧɵɯ ɭɥɭɱɲɟɧɢɣ ɜ ɞɟɹɬɟɥɶɧɨɫɬɢ ɮɢɪɦɵ, ɬ.ɟ. ɜ ɫɬɨɢɦɨɫɬɢ, ɤɚɱɟɫɬɜɟ, ɫɟɪɜɢɫɟ ɢ ɬɟɦɩɚɯ ɪɚɡɜɢɬɢɹ. ɉɚɤɟɬ Micro Saint ɨɛɥɚɞɚɟɬ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɶɸ, ɝɢɛɤɨɫɬɶɸ, ɛɵɫɬɪɨɞɟɣɫɬɜɢɟɦ. ɉɪɨɝɪɚɦɦɧɨɟ ɨɛɟɫɩɟɱɟɧɢɟ Micro Saint - ɝɢɛɤɢɣ ɞɢɫɤɪɟɬɧɨ-ɢɦɢɬɚɰɢɨɧɧɵɣ ɩɚɤɟɬ ɩɪɨɝɪɚɦɦ ɞɥɹ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜɫɟɯ ɬɢɩɨɜ ɩɪɨɰɟɫɫɨɜ. ɂɫɩɨɥɶɡɭɹ Micro Saint ɦɨɠɧɨ ɫɦɨɞɟɥɢɪɨɜɚɬɶ ɥɸɛɨɣ ɩɪɨɰɟɫɫ, ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧ ɛɥɨɤ-ɫɯɟɦɨɣ. ɉɚɤɟɬ Pilgrim ɨɛɥɚɞɚɟɬ ɲɢɪɨɤɢɦ ɫɩɟɤɬɪɨɦ ɜɨɡɦɨɠɧɨɫɬɟɣ ɢɦɢɬɚɰɢɢ ɜɪɟɦɟɧɧɨɣ,

ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ

ɢ

ɮɢɧɚɧɫɨɜɨɣ

ɞɢɧɚɦɢɤɢ

ɦɨɞɟɥɢɪɭɟɦɵɯ

ɨɛɴɟɤɬɨɜ. ɋ ɟɝɨ ɩɨɦɨɳɶɸ ɦɨɠɧɨ ɫɨɡɞɚɜɚɬɶ ɞɢɫɤɪɟɬɧɨ-ɧɟɩɪɟɪɵɜɧɵɟ ɦɨɞɟɥɢ. Ɋɚɡɪɚɛɚɬɵɜɚɟɦɵɟ

ɦɨɞɟɥɢ

ɢɦɟɸɬ

ɫɜɨɣɫɬɜɨ

ɤɨɥɥɟɤɬɢɜɧɨɝɨ

ɭɩɪɚɜɥɟɧɢɹ

ɩɪɨɰɟɫɫɨɦ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ȼ ɬɟɤɫɬ ɦɨɞɟɥɢ ɦɨɠɧɨ ɜɫɬɚɜɥɹɬɶ ɥɸɛɵɟ ɛɥɨɤɢ ɫ 20

ɩɨɦɨɳɶɸ ɫɬɚɧɞɚɪɬɧɨɝɨ ɹɡɵɤɚ C++ [50]. Ɋɚɡɥɢɱɧɵɟ ɜɟɪɫɢɢ ɷɬɨɣ ɫɢɫɬɟɦɵ ɪɚɛɨɬɚɸɬ ɧɚ IBM-ɫɨɜɦɟɫɬɢɦɵɯ ɢ DEC-ɫɨɜɦɟɫɬɢɦɵɯ ɤɨɦɩɶɸɬɟɪɚɯ, ɨɫɧɚɳɟɧɧɵɯ Unix ɢɥɢ Windows. ɉɚɤɟɬ Pilgrim ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɦɨɛɢɥɶɧɨɫɬɢ, ɬ.ɟ. ɩɟɪɟɧɨɫɚ ɧɚ ɥɸɛɭɸ ɞɪɭɝɭɸ ɩɥɚɬɮɨɪɦɭ ɩɪɢ ɧɚɥɢɱɢɢ ɤɨɦɩɢɥɹɬɨɪɚ C++. Ɇɨɞɟɥɢ ɜ ɫɢɫɬɟɦɟ Pilgrim ɤɨɦɩɢɥɢɪɭɸɬɫɹ ɢ ɩɨɷɬɨɦɭ ɢɦɟɸɬ ɜɵɫɨɤɨɟ ɛɵɫɬɪɨɞɟɣɫɬɜɢɟ, ɱɬɨ ɨɱɟɧɶ ɜɚɠɧɨ ɞɥɹ ɨɬɪɚɛɨɬɤɢ ɭɩɪɚɜɥɟɧɱɟɫɤɢɯ ɪɟɲɟɧɢɣ ɢ ɚɞɚɩɬɢɜɧɨɝɨ ɜɵɛɨɪɚ ɜɚɪɢɚɧɬɨɜ

ɜ

ɫɜɟɪɯɭɫɤɨɪɟɧɧɨɦ

ɦɚɫɲɬɚɛɟ

ɜɪɟɦɟɧɢ.

ɉɨɥɭɱɟɧɧɵɣ

ɩɨɫɥɟ

ɤɨɦɩɢɥɹɰɢɢ ɨɛɴɟɤɬɧɵɣ ɤɨɞ ɦɨɠɧɨ ɜɫɬɪɚɢɜɚɬɶ ɜ ɪɚɡɪɚɛɚɬɵɜɚɟɦɵɟ ɩɪɨɝɪɚɦɦɧɵɟ ɤɨɦɩɥɟɤɫɵ ɢɥɢ ɩɟɪɟɞɚɜɚɬɶ (ɩɪɨɞɚɜɚɬɶ) ɡɚɤɚɡɱɢɤɭ, ɬɚɤ ɤɚɤ ɩɪɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɦɨɞɟɥɟɣ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɟ ɫɪɟɞɫɬɜɚ ɩɚɤɟɬɚ Pilgrim ɧɟ ɢɫɩɨɥɶɡɭɸɬɫɹ. ɋɢɫɬɟɦɚ ɢɦɟɟɬ ɫɪɚɜɧɢɬɟɥɶɧɨ ɧɟɜɵɫɨɤɭɸ ɫɬɨɢɦɨɫɬɶ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɢɦɢɬɚɰɢɨɧɧɵɯ ɦɨɞɟɥɟɣ ɪɵɧɤɚ ɬɪɭɞɚ ɨɬɤɪɵɜɚɟɬ ɧɨɜɵɟ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨ ɤɨɧɰɟɩɬɭɚɥɶɧɨɦɭ ɚɧɚɥɢɡɭ ɩɪɨɛɥɟɦ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ, ɫɨɤɪɚɳɟɧɢɸ ɫɪɨɤɨɜ ɪɚɡɪɚɛɨɬɤɢ ɩɟɪɫɩɟɤɬɢɜɧɵɯ ɩɪɨɟɤɬɨɜ ɛɢɪɠɢ ɬɪɭɞɚ, ɨɪɝɚɧɢɡɚɰɢɢ ɟɟ ɷɮɮɟɤɬɢɜɧɨɣ ɪɚɛɨɬɵ. 1.3. Ɉɫɨɛɟɧɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹ

ɹɜɥɹɟɬɫɹ

ɫɜɟɪɯɤɪɢɬɢɱɟɫɤɢɦ

ɹɜɥɟɧɢɟɦ

ɩɪɨɰɟɫɫɚ

(ɫɢɫɬɟɦɵ) [53]. Ɇɧɨɝɢɟ ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɨɛɥɚɞɚɸɬ ɫɜɨɣɫɬɜɚɦɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ, ɚ ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɨɛɴɟɤɬɵ ɹɜɥɹɸɬɫɹ ɩɪɢɦɟɪɚɦɢ ɫɥɨɠɧɵɯ ɫɚɦɨɨɪɝɚɧɢɡɭɸɳɢɯɫɹ ɫɢɫɬɟɦ. Ɏɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɬɚɤɢɯ ɨɛɴɟɤɬɨɜ ɨɛɭɫɥɨɜɥɟɧɨ ɬɟɦ, ɱɬɨ ɨɧɢ ɨɛɥɚɞɚɸɬ ɨɩɪɟɞɟɥɟɧɧɨɣ ɭɫɬɨɣɱɢɜɨɫɬɶɸ ɢ ɩɪɢɫɩɨɫɨɛɥɹɟɦɨɫɬɶɸ ɤ ɜɧɟɲɧɢɦ ɭɫɥɨɜɢɹɦ. Ɂɧɚɧɢɟ ɨɫɧɨɜɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɩɨɡɜɨɥɹɟɬ ɩɟɪɟɣɬɢ ɤ ɰɟɥɟɧɚɩɪɚɜɥɟɧɧɨɦɭ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɸ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɚɤɬɢɜɧɵɯ ɫɪɟɞ, ɩɪɨɰɟɫɫɵ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɜ ɤɨɬɨɪɵɯ ɩɪɢɜɨɞɢɥɢ ɛɵ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɧɭɠɧɵɯ ɫɬɪɭɤɬɭɪ (ɫɬɚɰɢɨɧɚɪɧɵɯ ɢɥɢ ɦɟɧɹɸɳɢɯɫɹ ɫɨ ɜɪɟɦɟɧɟɦ). ɇɚɩɪɢɦɟɪ,

ɟɫɥɢ

ɧɚ

ɪɵɧɤɟ

ɬɪɭɞɚ

ɛɭɞɟɬ

ɩɨɜɵɲɟɧ

ɫɩɪɨɫ

ɧɚ

ɤɜɚɥɢɮɢɰɢɪɨɜɚɧɧɵɣ ɬɪɭɞ, ɩɨɹɜɢɬɫɹ ɫɬɪɟɦɥɟɧɢɟ ɤ ɪɨɫɬɭ ɤɜɚɥɢɮɢɤɚɰɢɢ, ɨɛɪɚɡɨɜɚɧɢɹ, ɱɬɨ ɩɪɢɜɟɞɟɬ ɤ ɩɨɹɜɥɟɧɢɸ ɧɨɜɵɯ ɨɛɪɚɡɨɜɚɬɟɥɶɧɵɯ ɭɫɥɭɝ, 21

ɤɚɱɟɫɬɜɟɧɧɨ ɧɨɜɵɯ ɮɨɪɦ ɩɨɜɵɲɟɧɢɹ ɤɜɚɥɢɮɢɤɚɰɢɢ. Ɋɚɡɜɢɬɢɟ ɮɢɪɦɵ, ɩɨɹɜɥɟɧɢɟ ɫɟɬɢ ɮɢɥɢɚɥɨɜ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɧɨɜɵɦ ɨɪɝɚɧɢɡɚɰɢɨɧɧɵɦ ɮɨɪɦɚɦ, ɜ ɱɚɫɬɧɨɫɬɢ, ɤ ɤɨɦɩɶɸɬɟɪɢɡɨɜɚɧɧɨɦɭ ɨɮɢɫɭ, ɛɨɥɟɟ ɬɨɝɨ, - ɤ ɜɵɫɲɟɣ ɫɬɚɞɢɢ ɪɚɡɜɢɬɢɹ

ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ

ɨɮɢɫɚ

-

ɜɢɪɬɭɚɥɶɧɨɦɭ

ɨɮɢɫɭ

ɢɥɢ

ɠɟ

ɜɢɪɬɭɚɥɶɧɨɣ ɤɨɪɩɨɪɚɰɢɢ. ȼ [43] ɫɜɨɣɫɬɜɨ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ «ɫɜɨɞɢɬɫɹ ɤ ɭɦɟɧɢɸ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɨɛɴɟɤɬɚ ɦɟɧɹɬɶ ɩɨɜɟɞɟɧɢɟ ɢɥɢ ɫɬɪɭɤɬɭɪɭ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɤɪɭɠɚɸɳɟɣ ɨɛɫɬɚɧɨɜɤɢ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɨɬɜɟɱɚɸɳɟɦ ɢɧɬɟɪɟɫɚɦ ɷɬɨɝɨ ɨɛɴɟɤɬɚ». ȼ [75] ɨɬɦɟɱɚɟɬɫɹ, ɱɬɨ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɫɬɪɭɤɬɭɪɵ ɟɫɬɶ ɫɥɟɞɫɬɜɢɟ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ. ɉɨɜɟɞɟɧɢɟ ɫɢɫɬɟɦɵ ɭɩɨɪɹɞɨɱɟɧɧɨ ɢ ɩɟɪɢɨɞɢɱɧɨ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɡɧɚɱɟɧɢɣ ɟɟ ɩɚɪɚɦɟɬɪɚ, ɬ.ɟ. ɨɧɚ ɫɨ ɜɪɟɦɟɧɟɦ ɜɨɫɩɪɨɢɡɜɨɞɢɬɫɹ [75]. ɉɪɨɰɟɫɫ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɜ [29] ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ «ɩɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ ɨɬ ɧɟɭɩɨɪɹɞɨɱɟɧɧɨɫɬɢ ɤ ɩɨɪɹɞɤɭ». ȼ ɮɨɪɦɚɥɢɡɨɜɚɧɧɨɦ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɫɜɨɣɫɬɜɨ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɜ [43] ɨɩɢɫɚɧɨ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ɉɭɫɬɶ ɢɦɟɟɬɫɹ ɧɟɤɨɬɨɪɚɹ ɫɢɫɬɟɦɚ Ⱥ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ

ɛɵɬɶ

ɩɪɟɞɫɬɚɜɥɟɧɚ

ɜ

ɮɨɪɦɟ

ɦɨɞɟɥɢ

ɫɥɨɠɧɨɣ

ɫɢɫɬɟɦɵ

ɫ

ɞɨɩɨɥɧɢɬɟɥɶɧɵɦɢ ɭɩɪɚɜɥɹɸɳɢɦɢ ɜɯɨɞɚɦɢ G = g1, g2, … gp (ɪɢɫ. 1.1). ɂɦɟɟɬɫɹ ɬɚɤɠɟ ɫɢɫɬɟɦɚ Ȼ, ɦɨɞɟɥɶ ɤɨɬɨɪɨɣ ɜɵɪɚɛɚɬɵɜɚɟɬ ɡɧɚɱɟɧɢɹ ɩɨɫɬɭɩɚɸɳɢɯ ɫɢɝɧɚɥɨɜ g1, g2, … gp ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɡɧɚɱɟɧɢɹ ɩɨɤɚɡɚɬɟɥɹ ɤɚɱɟɫɬɜɚ ɭɩɪɚɜɥɟɧɢɹ ɫɢɫɬɟɦɨɣ W, ɬ. ɟ. G = Ȍ(W,Ȝ), ɝɞɟ G – ɦɧɨɠɟɫɬɜɨ ɭɩɪɚɜɥɹɸɳɢɯ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ, ɫɩɨɫɨɛɧɵɯ ɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɭɩɪɚɜɥɟɧɢɹ W ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɚɛɨɪɚ ɡɚɞɚɧɧɵɯ ɩɪɚɜɢɥ Ȝ; Ȍ – ɮɭɧɤɰɢɨɧɚɥ, ɭɜɹɡɵɜɚɸɳɢɣ ɡɚɞɚɧɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ W ɢ Ȝ. ɇɚɛɨɪɵ ɩɪɚɜɢɥ Ȝ ɢ ɜɡɚɢɦɨɫɜɹɡɶ ɢɯ ɫ ɤɚɱɟɫɬɜɨɦ ɭɩɪɚɜɥɟɧɢɹ W, ɮɨɪɦɢɪɭɸɳɢɟ ɭɩɪɚɜɥɹɸɳɢɣ ɜɯɨɞɧɨɣ ɫɢɝɧɚɥ G, ɡɚɞɚɸɬɫɹ ɷɤɫɩɟɪɬɚɦɢ. ɍɩɪɚɜɥɹɸɳɢɣ ɫɢɝɧɚɥ G

ɤɨɪɪɟɤɬɢɪɭɟɬ ɡɧɚɱɟɧɢɟ ɩɨɤɚɡɚɬɟɥɹ ɤɚɱɟɫɬɜɚ

ɭɩɪɚɜɥɟɧɢɹ ɫɢɫɬɟɦɵ Į1, Į2, …, Įk ɜ ɠɟɥɚɟɦɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɉɪɢ ɷɬɨɦ ɤɨɪɪɟɤɬɢɪɨɜɤɚ ɤɚɱɟɫɬɜɚ ɭɩɪɚɜɥɟɧɢɹ ɦɨɠɟɬ ɛɵɬɶ ɫɜɹɡɚɧɚ ɢ ɫ ɢɡɦɟɧɟɧɢɟɦ ɫɬɪɭɤɬɭɪɵ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ, ɬ. ɟ. ɜɫɟɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɟɟ ɚɬɪɢɛɭɬɨɜ. 22

g1

… gp

g2

Y1

X1 Į1, Į2, …, Įk

X2

Y2

Z1, Z2, …, Zl Xn

Yn

Ɋɢɫɭɧɨɤ 1. 1 - Ɇɨɞɟɥɶ ɫɢɫɬɟɦɵ ɫ ɤɨɪɪɟɤɬɢɪɭɟɦɵɦɢ ɰɟɥɹɦɢ ɇɚ ɪɢɫ. 1.2 ɩɪɟɞɫɬɚɜɥɟɧɚ ɦɨɞɟɥɶ ɨɛɴɟɤɬɚ ɜ ɜɢɞɟ ɦɨɞɟɥɢ ɫɥɨɠɧɨɣ ɫɢɫɬɟɦɵ, ɨɛɥɚɞɚɸɳɟɣ ɫɜɨɣɫɬɜɨɦ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ.

g1

…

g2

gp

Y1gA

Ȼ

X1 X2

Į1, Į2, …, Įk

YlAg

Z1, Z2, …, Zl

Y1 Y2

Xn

Ym A Ȝ1 Ȝ2 … Ȝs Ɋɢɫɭɧɨɤ 1.2 - Ɇɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɭɸɳɟɝɨɫɹ ɨɛɴɟɤɬɚ Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɚɦɨɨɪɝɚɧɢɡɭɸɳɢɯɫɹ ɫɢɫɬɟɦ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɫɨɛɵɯ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɩɪɨɛɥɟɦ, ɟɫɥɢ ɩɪɢɦɟɧɹɟɬɫɹ ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ, ɩɨɡɜɨɥɹɸɳɚɹ ɜɜɟɫɬɢ ɥɸɛɨɣ ɧɚɛɨɪ ɩɪɚɜɢɥ Ȝ1, Ȝ 2, …, Ȝ s, ɤɨɪɪɟɤɬɢɪɭɸɳɢɯ ɤɚɱɟɫɬɜɨ ɭɩɪɚɜɥɟɧɢɹ W. ȼɯɨɞɵ, ɜɵɯɨɞɵ ɢ ɫɨɫɬɨɹɧɢɟ ɷɬɨɣ ɦɨɞɟɥɢ (ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ X, Y ɢ Z) ɪɚɛɨɬɚɸɬ ɜ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɜ ɨɛɵɱɧɨɦ ɪɟɠɢɦɟ ɢ ɨɩɢɫɵɜɚɸɬ ɨɛɴɟɤɬ ɢɥɢ ɩɪɨɰɟɫɫ. 23

ȼɵɯɨɞɵ ɫɢɫɬɟɦɵ ɫ ɢɧɞɟɤɫɨɦ «g», ɬ. ɟ. Yg, ɨɬɨɛɪɚɠɚɸɬ ɩɚɪɚɦɟɬɪɵ ɤɚɱɟɫɬɜɚ ɭɩɪɚɜɥɟɧɢɹ W. Ɉɧɢ ɩɨɫɬɭɩɚɸɬ ɜ ɫɢɫɬɟɦɭ Ȼ, ɝɞɟ ɚɧɚɥɢɡɢɪɭɸɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɢɦɟɸɳɢɦɫɹ ɧɚɛɨɪɨɦ ɩɪɚɜɢɥ Ȝ1 Ȝ 2, …, Ȝ s ɢ ɮɨɪɦɢɪɭɸɬ ɭɩɪɚɜɥɹɸɳɢɟ ɫɢɝɧɚɥɵ G. Ɋɵɧɨɤ ɬɪɭɞɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɝɨɦɟɨɫɬɚɬɢɱɟɫɤɭɸ ɫɢɫɬɟɦɭ, ɞɥɹ ɤɨɬɨɪɨɣ ɯɚɪɚɤɬɟɪ ɩɨɞɞɟɪɠɢɜɚɟɬ ɫɜɨɟ ɫɨɫɬɨɹɧɢɟ ɜ ɡɚɞɚɧɧɵɯ ɝɪɚɧɢɰɚɯ [43]. 1.4. Ⱥɧɚɥɢɡ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɨɬɞɟɥɶɧɨɣ ɨɬɪɚɫɥɢ Ɍɟɨɪɟɬɢɱɟɫɤɨɟ

ɢɫɫɥɟɞɨɜɚɧɢɟ

ɪɚɡɥɢɱɧɵɯ

ɷɤɨɧɨɦɢɱɟɫɤɢɯ

ɫɢɫɬɟɦ,

ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɢɞɟɣ ɬɟɨɪɢɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ (ɫɢɧɟɪɝɟɬɢɤɢ), ɹɜɥɹɟɬɫɹ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɦ ɩɨɞɯɨɞɨɦ ɜ ɷɤɨɧɨɦɢɤɟ. Ɉɫɧɨɜɧɵɦ ɩɨɥɨɠɟɧɢɟɦ ɬɚɤɨɝɨ ɩɨɞɯɨɞɚ Ⱥ.ɇ. ȼɚɫɢɥɶɟɜ [12] ɫɱɢɬɚɟɬ ɞɨɫɬɚɬɨɱɧɨ ɨɛɳɢɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɫɚɦɨɪɟɝɭɥɹɰɢɢ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ, ɚ ɜ ɤɚɱɟɫɬɜɟ

ɛɚɡɨɜɨɝɨ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ

ɚɩɩɚɪɚɬɚ

ɛɟɪɟɬ

ɧɟɥɢɧɟɣɧɵɟ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ. ȼ [12] ɩɪɟɞɥɨɠɟɧɚ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ ɨɬɞɟɥɶɧɨɣ ɨɬɪɚɫɥɢ, ɩɨɡɜɨɥɹɸɳɭɸ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ

ɩɪɢɧɹɬɢɹ

ɬɟɯ

ɢɥɢ

ɢɧɵɯ

ɭɩɪɚɜɥɟɧɱɟɫɤɢɯ

ɪɟɲɟɧɢɣ

ɢ

ɫɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɪɚɡɜɢɬɢɹ ɫɨɛɵɬɢɣ ɧɚ ɪɵɧɤɟ. Ⱥ.ɇ. ȼɚɫɢɥɶɟɜ [12] ɫɱɢɬɚɟɬ, ɱɬɨ ɡɚ ɞɚɧɧɵɣ ɩɟɪɢɨɞ ɱɢɫɥɨ ɪɚɛɨɬɚɸɳɢɯ ɢɡɦɟɧɢɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ dN1(t) = (N2(t)W1(t) - N1(t)W2(t))dt,

(1.1)

ɝɞɟ N1(t) – ɨɛɳɟɟ ɱɢɫɥɨ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɡɚɧɹɬɵɯ ɜ ɨɬɪɚɫɥɢ ɧɚ ɞɚɧɧɵɣ ɦɨɦɟɧɬ; N2(t) – ɱɢɫɥɨ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɪɚɛɨɱɢɯ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɜɥɟɱɟɧɵ ɞɥɹ ɪɚɛɨɬɵ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɨɬɪɚɫɥɢ ɢ ɤɨɬɨɪɵɟ ɧɚ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɹɜɥɹɸɬɫɹ ɛɟɡɪɚɛɨɬɧɵɦɢ; N1

= N1(t) + N2(t) = const – ɟɦɤɨɫɬɶ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ

ɨɬɪɚɫɥɢ; W1(t)dt – ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɛɟɡɪɚɛɨɬɧɵɣ ɫɩɟɰɢɚɥɢɫɬ ɦɨɠɟɬ ɧɚɣɬɢ ɪɚɛɨɬɭ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ ɡɚ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt; W2(t)dt – ɜɟɪɨɹɬɧɨɫɬɶ ɭɜɨɥɶɧɟɧɢɹ ɪɚɛɨɬɚɸɳɟɝɨ ɫɩɟɰɢɚɥɢɫɬɚ ɡɚ ɩɟɪɢɨɞ ɫ t ɞɨ t + dt. 1

ȿɦɤɨɫɬɶ ɪɵɧɤɚ – ɩɨɤɚɡɚɬɟɥɶ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɤɨɥɢɱɟɫɬɜɨ ɧɟɨɛɯɨɞɢɦɵɯ ɪɚɛɨɬɧɢɤɨɜ ɢɥɢ ɜɟɥɢɱɢɧɭ ɧɟɨɛɯɨɞɢɦɨɣ ɬɪɭɞɨɟɦɤɨɫɬɢ ɜ ɨɩɪɟɞɟɥɟɧɧɵɣ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɞɥɹ ɞɚɧɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ.

24

Ⱥɜɬɨɪ ɢɫɯɨɞɢɬ ɢɡ ɩɪɟɞɩɨɥɨɠɟɧɢɹ, ɱɬɨ ɜ ɨɬɪɚɫɥɢ ɟɫɬɶ ɜɨɡɦɨɠɧɨɫɬɢ ɞɥɹ ɩɪɟɞɨɫɬɚɜɥɟɧɢɹ ɪɚɛɨɱɢɯ ɦɟɫɬ ɜɫɟɦ ɩɨɬɟɧɰɢɚɥɶɧɵɦ ɪɚɛɨɱɢɦ. ɋ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɞɚɧɧɨɟ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɜɩɨɥɧɟ ɩɪɢɟɦɥɟɦɨ. Ɍɚɤ ɤɚɤ ɨɬɪɚɫɥɶ ɜɵɯɨɞɢɬ ɧɚ ɨɩɬɢɦɚɥɶɧɵɟ ɩɨɤɚɡɚɬɟɥɢ, ɤɨɝɞɚ ɤɨɥɢɱɟɫɬɜɨ ɡɚɧɹɬɵɯ ɪɚɜɧɨ N, ɬɨ N1(t) ɨɩɪɟɞɟɥɹɟɬ ɫɬɟɩɟɧɶ «ɡɚɝɪɭɠɟɧɧɨɫɬɢ» ɨɬɪɚɫɥɢ, ɚ N2(t) – ɱɢɫɥɨ ɫɜɨɛɨɞɧɵɯ ɪɚɛɨɱɢɯ ɦɟɫɬ. ȼɟɪɨɹɬɧɨɫɬɢ W1(t) ɢ W2(t), ɩɪɢ ɞɪɭɝɢɯ ɧɟɢɡɦɟɧɧɵɯ ɭɫɥɨɜɢɹɯ, ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ, ɬɚɤ ɤɚɤ ɜɨ ɜɪɟɦɟɧɢ ɦɟɧɹɸɬɫɹ ɜɟɥɢɱɢɧɵ N1(t) ɢ N2(t), ɬ. ɟ. W1(t) = W1(N1(t),N2(t)) ɢ W2(t) = W2(N1(t),N2(t)). ȼɟɪɨɹɬɧɨɫɬɶ ɧɚɣɬɢ ɪɚɛɨɬɭ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɡɚɜɢɫɢɬ ɨɬ ɧɚɥɢɱɢɹ ɪɚɛɨɱɢɯ ɦɟɫɬ, ɡɧɚɱɢɬ W1(t) = W1(N2(t)). Ɏɭɧɤɰɢɢ W1(N2) ɢ W2(N1, N2) ɦɨɠɧɨ ɪɚɡɥɨɠɢɬɶ ɜ ɪɹɞ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɚɪɝɭɦɟɧɬɚɦ, ɬ. ɟ. W1 | k1N2(t) = k1(N – N1(t)) ɢ W2 | k2N1(t) + k3N2(t) = k2N1(t) + k3(N – N1(t)), ɝɞɟ ki (i = 1, 2, 3) – ɤɨɷɮɮɢɰɢɟɧɬɵ, ɤɨɬɨɪɵɟ ɹɜɧɨ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ t. ɍɪɚɜɧɟɧɢɟ (1.1) ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: dN1 (t ) dt

k1 ( N N 1 (t )) 2 k 2 N 2 (t ) k 3 ( N N 1 (t )) N 1 (t ).

(1.2)

Ɋɚɡɞɟɥɢɜ ɭɪɚɜɧɟɧɢɟ (1.2) ɧɚ N, ɨɛɨɡɧɚɱɢɜ ɯ(t) = N1(t)/N ɢ ɜɜɟɞɹ ɧɨɜɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ Qi = ki N, i = 1, 2, 3, ɭɪɚɜɧɟɧɢɟ (1.2) ɩɪɢɦɟɬ ɜɢɞ:

dx(t ) dt

(v1 v3 v2 ) x 2 (t ) (2v1 v3 ) x(t ) v1 .

(1.3)

Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɫɬɚɰɢɨɧɚɪɧɵɯ ɬɨɱɟɤ ɭɪɚɜɧɟɧɢɹ (1.3) ɚɜɬɨɪ ɩɨɥɚɝɚɟɬ

dx(t ) dt ɢ x2

0 . Ɋɟɲɟɧɢɹɦɢ ɩɨɥɭɱɟɧɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɛɭɞɭɬ x1

2Q 1 Q 3 Q 32 4Q 1Q 2 2(Q 1 Q 3 Q 2 )

2Q 1 Q 3 Q 32 4Q 1Q 2 - ɫɬɚɰɢɨɧɚɪɧɵɟ ɬɨɱɤɢ. Ɍɨɱɧɨɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ 2(Q 1 Q 3 Q 2 )

(1.3) ɜɵɪɚɠɟɧɨ ɱɟɪɟɡ ɫɬɚɰɢɨɧɚɪɧɵɟ ɪɟɲɟɧɢɹ:

x(t )

ɝɞɟ D

x2

x 2 x1 x1 x0 exp(Dt ) 1 x 2 x0

,

(1.4)

v32 4v1v2 , ɚ ɯ0 – ɭɪɨɜɟɧɶ ɡɚɧɹɬɨɫɬɢ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. Ⱥɜɬɨɪ ɢɫɫɥɟɞɭɟɬ ɩɨɥɭɱɟɧɧɵɟ ɫɬɚɰɢɨɧɚɪɧɵɟ ɪɟɲɟɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ. 25

Ⱦɥɹ ɷɬɨɝɨ ɪɚɫɫɦɚɬɪɢɜɚɟɬ ɜɨɡɦɭɳɟɧɢɟ Gɯ(t) – ɧɟɡɧɚɱɢɬɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. ɂɡ (1.3) ɫɥɟɞɭɟɬ:

dGx(t ) dt

(2(v1 v3 v2 ) xɫ 2v1 v3 )Gx(t ),

(1.5)

ɝɞɟ ɯɫ – ɫɬɚɰɢɨɧɚɪɧɚɹ ɬɨɱɤɚ. Ɋɟɲɟɧɢɟɦ (1.5) ɹɜɥɹɸɬɫɹ Gɯ(t) = consteDt ɩɪɢ D = 2(v1 + v3 – v2)xc – 2v1 – v3. 2 ȿɫɥɢ xc = x1, ɬɨ D = 2(v1 + v3 – v2)x1 – 2v1 – v3 = - v3 4v1v 2 0 – ɪɟɲɟɧɢɟ

ɭɫɬɨɣɱɢɜɨɟ. ȼ ɫɥɭɱɚɟ xc = x2, ɬɨ D = 2(v1 + v3 – v2)x2 – 2v1 – v3 =

v32 4v1v 2 ! 0 –

ɪɟɲɟɧɢɟ ɧɟɭɫɬɨɣɱɢɜɨɟ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ,

ɢɡ ɞɜɭɯ ɫɬɚɰɢɨɧɚɪɧɵɯ ɪɟɲɟɧɢɣ ɭɫɬɨɣɱɢɜɵɦ ɹɜɥɹɟɬɫɹ

ɬɨɥɶɤɨ ɨɞɧɨ. ɍɫɬɨɣɱɢɜɨɟ ɫɬɚɰɢɨɧɚɪɧɨɟ ɪɟɲɟɧɢɟ x11, ɚ ɧɟɭɫɬɨɣɱɢɜɨɟ ɫɬɚɰɢɨɧɚɪɧɨɟ ɪɟɲɟɧɢɟ x2 ! 1. ɋ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɭɪɨɜɧɟɦ ɡɚɧɹɬɨɫɬɢ ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɨɬɤɥɨɧɟɧɢɹɯ ɨɬ ɷɬɨɝɨ ɭɪɨɜɧɹ ɡɚɧɹɬɨɫɬɢ ɫɢɫɬɟɦɚ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɫɧɨɜɚ ɜɨɡɜɪɚɬɢɬɶɫɹ ɤ ɧɚɱɚɥɶɧɨɦɭ ɫɨɫɬɨɹɧɢɸ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɭɪɨɜɟɧɶ ɡɚɧɹɬɨɫɬɢ x1 ɹɜɥɹɟɬɫɹ ɪɚɜɧɨɜɟɫɧɵɦ ɫɨɫɬɨɹɧɢɟɦ ɫɢɫɬɟɦɵ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɫɨɫɬɨɹɧɢɟ ɫ ɭɪɨɜɧɟɦ ɡɚɧɹɬɨɫɬɢ x2 ɧɟɪɚɜɧɨɜɟɫɧɨɟ, ɩɨɫɤɨɥɶɤɭ ɞɚɠɟ ɧɟɛɨɥɶɲɨɟ ɨɬɤɥɨɧɟɧɢɟ ɨɬ ɷɬɨɝɨ ɭɪɨɜɧɹ ɩɪɢɜɟɞɟɬ ɤ ɩɟɪɟɯɨɞɭ ɫɢɫɬɟɦɵ ɜ ɞɪɭɝɨɟ ɫɬɚɰɢɨɧɚɪɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɬ. ɟ. ɜ ɫɨɫɬɨɹɧɢɟ x1. Ⱦɚɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɩɨɥɧɨɫɬɶɸ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɢ ɷɤɨɧɨɦɢɱɟɫɤɢɦɢ ɫɨɨɛɪɚɠɟɧɢɹɦɢ, ɬɚɤ ɤɚɤ ɪɟɲɟɧɢɟ x2 ɨɬɜɟɱɚɟɬ ɪɟɠɢɦɭ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɨɬɪɚɫɥɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɪɚɛɨɱɢɯ ɪɟɫɭɪɫɨɜ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɩɪɨɜɟɞɟɧɧɵɯ ɪɚɫɫɭɠɞɟɧɢɣ Ⱥ.ɇ. ȼɚɫɢɥɶɟɜ [12] ɞɟɥɚɟɬ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ: x

ɧɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ ɩɪɟɞɥɨɠɟɧɧɚɹ ɢɦ ɦɨɞɟɥɶ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ

ɭɩɪɨɳɟɧɧɨɣ, ɨɧɚ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɨɫɥɟɞɢɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɬɟɧɞɟɧɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ, x

ɢɫɩɨɥɶɡɨɜɚɧɢɟ

ɫɢɧɟɪɝɟɬɢɱɟɫɤɢɯ

ɩɪɟɞɫɬɚɜɥɟɧɢɣ

ɨ

ɯɚɪɚɤɬɟɪɟ

ɩɪɨɬɟɤɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɫɚɦɨɪɟɝɭɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ 26

ɨɫɨɛɟɧɧɨɫɬɢ ɷɜɨɥɸɰɢɢ ɫɢɫɬɟɦɵ ɢ ɢɫɫɥɟɞɨɜɚɬɶ ɪɵɧɨɤ ɧɚ ɩɪɟɞɦɟɬ ɟɝɨ ɭɫɬɨɣɱɢɜɨɫɬɢ, x

ɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ɦɨɠɟɬ ɢ ɧɟ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ

ɭɫɥɨɜɢɹɦ ɨɩɬɢɦɚɥɶɧɨɝɨ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ. ɇɚɥɢɱɢɟ ɜɬɨɪɨɝɨ ɧɟɭɫɬɨɣɱɢɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɤ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɦ ɩɟɪɟɯɨɞɧɵɦ ɩɪɨɰɟɫɫɚɦ ɢ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɬɶ ɧɚ ɞɢɧɚɦɢɤɭ ɭɪɨɜɧɹ ɡɚɧɹɬɨɫɬɢ, x ɩɚɪɚɦɟɬɪɵ

ɜɯɨɞɹɳɢɟ ɨɬɤɪɵɜɚɸɬ

ɜ

ɪɚɫɫɦɨɬɪɟɧɧɭɸ ɜɨɡɦɨɠɧɨɫɬɢ

ɦɨɞɟɥɶ

ɞɥɹ

ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɟ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɜɥɢɹɧɢɹ

ɧɚ

ɦɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɪɹɞɚ ɫɭɛɴɟɤɬɢɜɧɵɯ ɮɚɤɬɨɪɨɜ, ɱɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɨɡɜɨɥɹɟɬ ɪɚɫɲɢɪɢɬɶ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɭɸ ɛɚɡɭ ɢ ɫɩɨɫɨɛɫɬɜɭɟɬ ɫɢɧɬɟɡɭ ɜɡɝɥɹɞɨɜ ɪɚɡɥɢɱɧɵɯ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɲɤɨɥ ɢ ɬɟɨɪɢɣ. Ɋɢɫɭɧɨɤ 1.3 ɢɥɥɸɫɬɪɢɪɭɟɬ ɞɢɧɚɦɢɤɭ ɡɚɧɹɬɨɫɬɢ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ [12]. Ɂɚɧɹɬɨɫɬɶ (% ɨɬ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɪɨɜɧɹ) 104

100

ȿɫɬɟɫɬɜɟɧɧɵɣ ɭɪɨɜɟɧɶ ɛɟɡɪɚɛɨɬɢɰɵ

96 92 0

5 10 15 20 ȼɪɟɦɹ (ɜ ɭɫɥɨɜɧɵɯ ɟɞɢɧɢɰɚɯ)

Ɋɢɫɭɧɨɤ 1.3 - Ⱦɢɧɚɦɢɤɚ ɭɪɨɜɧɹ ɡɚɧɹɬɨɫɬɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ (ɩɪɢ t=0) ɇɚɯɨɞɹɫɶ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɧɟɭɫɬɨɣɱɢɜɨɣ ɬɨɱɤɢ, ɫɢɫɬɟɦɚ ɜ ɤɚɤɨɣ ɬɨ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɩɟɪɟɣɞɟɬ ɜ ɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ. ɂ ɯɨɬɹ ɜɪɟɦɹ ɢ ɬɟɦɩɵ ɬɚɤɨɝɨ ɩɟɪɟɯɨɞɚ ɡɚɜɢɫɹɬ ɨɬ ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ, ɤɨɧɟɱɧɵɣ ɪɟɡɭɥɶɬɚɬ ɨɫɬɚɟɬɫɹ

ɧɟɢɡɦɟɧɧɵɦ.

n=(1-O1)100%

ȼɟɥɢɱɢɧɭ

ɩɪɢ

ɷɬɨɦ

ɦɨɠɧɨ

ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɟɫɬɟɫɬɜɟɧɧɵɣ ɭɪɨɜɟɧɶ ɛɟɡɪɚɛɨɬɢɰɵ [74]. ɗɤɨɧɨɦɢɤɚ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɣ ɫɬɪɭɤɬɭɪɨɣ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɦɧɨɝɢɯ ɨɬɪɚɫɥɟɣ. 27

Ɂɚɞɚɱɚ ɞɚɧɧɨɣ ɪɚɛɨɬɵ – ɨɛɨɛɳɢɬɶ ɧɚɱɚɬɨɟ ɜ ɷɬɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɢɫɫɥɟɞɨɜɚɧɢɟ ɩɨ

[12]

ɚɧɚɥɢɬɢɱɟɫɤɨɦɭ

ɦɨɞɟɥɢɪɨɜɚɧɢɸ

ɪɵɧɤɚ

ɬɪɭɞɚ,

ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ

ɩɨɫɬɪɨɢɬɶ ɧɟɫɤɨɥɶɤɢɯ

ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ. ɗɬɢ ɨɛɨɛɳɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɜ ɝɥɚɜɟ 2. ɂɫɫɥɟɞɨɜɚɧɢɹ ɜ ɷɬɨɣ ɨɛɥɚɫɬɢ ɜɟɥɢɫɶ ɩɨ ɫɥɟɞɭɸɳɢɦ ɧɚɩɪɚɜɥɟɧɢɹɦ: 1)

ɪɚɡɪɚɛɨɬɤɚ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ

ɦɧɨɝɨɨɬɪɚɫɥɟɜɨɣ ɷɤɨɧɨɦɢɤɢ, 2)

ɢɫɫɥɟɞɨɜɚɧɢɟ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɨɫɬɪɨɟɧɧɨɣ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ

ɦɧɨɝɨɨɬɪɚɫɥɟɜɨɣ ɷɤɨɧɨɦɢɤɢ (ɝɥɚɜɚ 2), 3) ɬɟɨɪɢɢ

ɪɚɡɪɚɛɨɬɤɚ ɜɟɪɨɹɬɧɨɫɬɧɨɣ ɦɨɞɟɥɢ ɪɵɧɤɚ ɬɪɭɞɚ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɨɜ ɦɚɫɫɨɜɨɝɨ

ɨɛɫɥɭɠɢɜɚɧɢɹ,

ɩɨɡɜɨɥɹɸɳɟɣ

ɨɩɪɟɞɟɥɹɬɶ

ɨɫɧɨɜɧɵɟ

ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɟɝɨ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ (ɝɥɚɜɚ 3), 4)

ɪɚɡɪɚɛɨɬɤɚ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ ɤɚɤ ɨɫɧɨɜɧɨɣ ɱɚɫɬɢ

ɮɭɧɤɰɢɨɧɚɥɶɧɨ-ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɪɵɧɤɚ ɬɪɭɞɚ (ɝɥɚɜɚ 3). ɉɪɢɜɟɞɟɦ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɚɦ ɩɨɬɪɟɛɭɸɬɫɹ ɞɥɹ ɩɪɨɜɨɞɢɦɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ. 1.5. ɇɟɤɨɬɨɪɵɟ ɪɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɥɢɧɟɣɧɵɯ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɢɫɬɟɦ Ɋɚɫɫɦɨɬɪɢɦ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ x

x(t)

Ax(t), x Rn .

(1.6)

ɉɪɟɞɩɨɥɨɠɢɦ ɫɧɚɱɚɥɚ, ɱɬɨ ɦɚɬɪɢɰɚ Ⱥ ɢɦɟɟɬ ɬɨɥɶɤɨ ɩɪɨɫɬɵɟ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ Oi ɢ ɫɨɛɫɬɜɟɧɧɵɟ ɜɟɤɬɨɪɵ hi, ɬ.ɟ. Ⱥhi = Oihi (i=1,…n) [6]. Ɉɛɳɟɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (1.6) ɢɦɟɟɬ ɜɢɞ n

x (t )

¦

i 1

ɝɞɟ ɋi – ɩɪɨɢɡɜɨɥɶɧɵɟ ɩɨɫɬɨɹɧɧɵɟ. 28

C ihie O t , i

ɉɪɢɜɟɞɟɦ ɦɚɬɪɢɰɭ Ⱥ ɤ ɠɨɪɞɚɧɨɜɨɣ ɮɨɪɦɟ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɨɛɳɟɝɨ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ (1.6) ɩɪɢ ɧɚɥɢɱɢɢ ɤɪɚɬɧɵɯ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ. ɋɭɳɟɫɬɜɭɸɬ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɩɪɢɜɟɞɟɧɢɹ ɤɜɚɞɪɚɬɧɨɣ ɦɚɬɪɢɰɵ Ⱥ ɪɚɡɦɟɪɧɨɫɬɢ n ɤ ɠɨɪɞɚɧɨɜɨɣ ɮɨɪɦɟ. ɉɪɢɜɟɞɟɦ ɫɩɨɫɨɛ [20], ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɥɟɞɭɸɳɢɦ ɚɥɝɨɪɢɬɦɨɦ: 1. Ⱦɥɹ ɤɚɠɞɨɝɨ k (k=0,…,n) ɧɚɯɨɞɹɬ ɧɚɢɛɨɥɶɲɢɣ ɨɛɳɢɣ ɞɟɥɢɬɟɥɶ Dk(O) ɜɫɟɯ ɦɢɧɨɪɨɜ k ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɣ ɦɚɬɪɢɰɵ OI-A. ɋɬɚɪɲɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɭ ɜɫɟɯ ɩɨɥɢɧɨɦɨɜ Dk(O) ɛɟɪɭɬ ɪɚɜɧɵɦɢ ɟɞɢɧɢɰɟ. ɉɪɢ ɷɬɨɦ Dn(O)=det(OI-A), D0(O)=0. 2. ɇɚɯɨɞɹɬ ɢɧɜɚɪɢɚɧɬɧɵɟ ɦɧɨɝɨɱɥɟɧɵ Lk(O) ɩɨ ɮɨɪɦɭɥɚɦ L1 (O )

Dn (O ) , L2 (O ) Dn1 (O )

Dn1 (O ) ,..., Ln (O ) Dn2 (O )

D1 (O ) D0 (O )

D1 (O ) .

3. Ʉɚɠɞɵɣ ɢɧɜɚɪɢɚɧɬɧɵɣ ɦɧɨɝɨɱɥɟɧ ɪɚɫɤɥɚɞɵɜɚɸɬ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɟ ɞɟɥɢɬɟɥɢ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɣ

ɦɚɬɪɢɰɵ

OI-A ɢɥɢ ɩɪɨɫɬɨ ɦɚɬɪɢɰɵ Ⱥ.

ɗɥɟɦɟɧɬɚɪɧɵɣ ɞɟɥɢɬɟɥɶ ɩɪɟɞɫɬɚɜɥɹɸɬ ɜ ɜɢɞɟ ɫɬɟɩɟɧɢ ɨɞɧɨɣ ɢɡ ɪɚɡɧɨɫɬɟɣ (O-Oi), ɝɞɟ Oi – ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɦɚɬɪɢɰɵ Ⱥ. Ɂɧɚɱɢɬ, Lk(O) ɢɦɟɟɬ ɜɢɞ

Lk (O ) (O O1 ) k (O O2 ) k ...(O O j ) 1

2

kj

. ɉɪɨɢɡɜɟɞɟɧɢɟ ɜɫɟɯ ɷɥɟɦɟɧɬɚɪɧɵɯ ɞɟɥɢɬɟɥɟɣ ɪɚɜɧɨ ɩɪɨɢɡɜɟɞɟɧɢɸ ɜɫɟɯ ɢɧɜɚɪɢɚɧɬɧɵɯ ɦɧɨɠɢɬɟɥɟɣ ɢ ɪɚɜɧɨ Dn(O). k 4. Ʉɚɠɞɨɦɭ ɷɥɟɦɟɧɬɚɪɧɨɦɭ ɞɟɥɢɬɟɥɸ (O O j ) ɫɨɩɨɫɬɚɜɥɹɸɬ ɤɥɟɬɨɱɤɭ j

ɀɨɪɞɚɧɚ ɩɨɪɹɞɤɚ kj c ɱɢɫɥɨɦ Oj ɧɚ ɝɥɚɜɧɨɣ ɞɢɚɝɨɧɚɥɢ. Ʉɥɟɬɨɱɧɨ-ɞɢɚɝɨɧɚɥɶɧɚɹ ɦɚɬɪɢɰɚ – ɠɨɪɞɚɧɨɜɚ ɮɨɪɦɚ ɦɚɬɪɢɰɵ Ⱥ. ɀɨɪɞɚɧɨɜɚ ɮɨɪɦɚ ɦɚɬɪɢɰɵ ɟɞɢɧɫɬɜɟɧɧɚ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɩɨɪɹɞɤɚ ɪɚɫɩɨɥɨɠɟɧɢɹ ɟɟ ɤɥɟɬɨɤ ɀɨɪɞɚɧɚ ɧɚ ɝɥɚɜɧɨɣ ɞɢɚɝɨɧɚɥɢ. Ɋɚɫɫɦɨɬɪɢɦ ɨɛɳɟɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (1.6) ɜ ɫɥɭɱɚɟ ɤɪɚɬɧɵɯ ɤɨɪɧɟɣ. ɉɭɫɬɶ Oi – r-ɤɪɚɬɧɨɟ ɫɨɛɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɦɚɬɪɢɰɵ Ⱥ. ȿɦɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɟɤɨɬɨɪɨɟ

ɤɨɥɢɱɟɫɬɜɨ

ɫɨɛɫɬɜɟɧɧɵɯ

ɜɟɤɬɨɪɨɜ.

ɋɬɟɩɟɧɶ

ɜɵɪɨɠɞɟɧɢɹ

ɫɨɛɫɬɜɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ Oi ɪɚɜɧɚ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɱɢɫɥɭ m(i), ɤɨɬɨɪɨɟ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɪɚɜɧɨ ɬɚɤɠɟ ɱɢɫɥɭ ɤɥɟɬɨɤ ɀɨɪɞɚɧɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ Oi. Ɉɛɨɡɧɚɱɢɜ 29

ɱɟɪɟɡ ȼj ɨɞɧɭ ɢɡ ɷɬɢɯ ɤɥɟɬɨɤ, ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ ɪɚɡɦɟɪɧɨɫɬɶ ɤɥɟɬɤɢ ɀɨɪɞɚɧɚ ȼj ɟɫɬɶ s(j), ɛɭɞɟɦ ɢɦɟɬɶ s(1) + s(2) + … + s(m(i)) = r. Ʉɚɠɞɨɣ ɤɥɟɬɤɟ ɀɨɪɞɚɧɚ ȼj ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɟɪɢɹ ɜɟɤɬɨɪɨɜ hl, l=1, … ,s(j) ɬɚɤɢɯ, ɱɬɨ h1z0, Ⱥh1 = Oih1, Ⱥh2 = Oih2+ h1,… , Ⱥhs(j) = Oihs(j)+ hs(j)-1. ȼɟɤɬɨɪɵ hl, ɝɞɟ l=1, … ,s(j), ɤɚɠɞɨɣ ɫɟɪɢɢ ɥɢɧɟɣɧɨ ɧɟɡɚɜɢɫɢɦɵ ɦɟɠɞɭ ɫɨɛɨɣ. ɉɨɞɩɪɨɫɬɪɚɧɫɬɜɨ, ɧɚɬɹɧɭɬɨɟ ɧɚ ɜɫɟ ɜɟɤɬɨɪɵ hl, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɤɥɟɬɤɟ ȼj, ɹɜɥɹɟɬɫɹ ɢɧɜɚɪɢɚɧɬɧɵɦ, ɰɢɤɥɢɱɟɫɤɢɦ ɢ ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ, ɪɚɜɧɭɸ ɪɚɡɦɟɪɧɨɫɬɢ ɫɟɪɢɢ, ɬ. ɟ. ɪɚɜɧɭɸ s(j). ȼ ɛɚɡɢɫɟ, ɫɨɫɬɚɜɥɟɧɧɨɦ ɢɡ ɜɟɤɬɨɪɨɜ ɜɫɟɯ ɫɟɪɢɣ, ɦɚɬɪɢɰɚ Ⱥ ɢɦɟɟɬ ɠɨɪɞɚɧɨɜɭ ɮɨɪɦɭ. Ɋɟɲɟɧɢɹɦɢ ɭɪɚɜɧɟɧɢɹ (1.6) ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɢ ɜɢɞɚ

xiq (t ) Z q (t )e O t , i

Z q (t )

t q 1 t q2 h1 h2 ... hq , q 1,..., s ( j ) , (q 1)! ( q 2)!

(1.7)

s(1) + s(2) + … + s(m(i)) = ri, r1 + r2 + … + rk = n. ɉɪɢ ɷɬɨɦ ɤɨɥɢɱɟɫɬɜɨ ɥɢɧɟɣɧɨ ɧɟɡɚɜɢɫɢɦɵɯ ɪɟɲɟɧɢɣ ɜɢɞɚ (1.7) ɪɚɜɧɨ n. Ɉɛɳɟɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (1.6) ɟɫɬɶ ɥɢɧɟɣɧɚɹ ɤɨɦɛɢɧɚɰɢɹ ɢɡ ɱɚɫɬɧɵɯ ɪɟɲɟɧɢɣ ɜɢɞɚ (1.7). Ɍɟɨɪɟɦɚ 1.1. [6] Ⱦɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɬɪɢɜɢɚɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ (1.6) ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ, ɱɬɨɛɵ ɜɫɟ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ Oi ɦɚɬɪɢɰɵ Ⱥ ɭɞɨɜɥɟɬɜɨɪɹɥɢ ɭɫɥɨɜɢɸ ReOi d 0, ɩɪɢɱɟɦ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ Oj ɬɚɤɢɟ, ɱɬɨ ReOj = 0, ɢɦɟɸɬ ɩɪɨɫɬɵɟ ɷɥɟɦɟɧɬɚɪɧɵɟ ɞɟɥɢɬɟɥɢ (ɬ. ɟ. ɜ ɮɨɪɦɭɥɟ (1.7) ɜɫɟ s(j)=1). Ⱦɥɹ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ ɭɪɚɜɧɟɧɢɹ (1.6) ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ, ɱɬɨɛɵ ReOi < 0. ɋɥɟɞɨɜɚɬɟɥɶɧɨ,

ɭɫɬɨɣɱɢɜɨɫɬɶ

(ɚɫɢɦɩɬɨɬɢɱɟɫɤɚɹ

ɭɫɬɨɣɱɢɜɨɫɬɶ

ɢɥɢ

ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ) ɭɪɚɜɧɟɧɢɹ (1.6) ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɩɨɥɨɠɟɧɢɟɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɧɢɦɨɣ ɨɫɢ ɤɨɪɧɟɣ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɚɬɪɢɰɵ Ⱥ: det(OI-A) = 0, 30

(1.8)

ɝɞɟ I – ɟɞɢɧɢɱɧɚɹ ɦɚɬɪɢɰɚ (n u n) ɦɚɬɪɢɰɚ. Ɋɚɫɤɪɵɜɚɹ ɨɩɪɟɞɟɥɢɬɟɥɶ, ɭɪɚɜɧɟɧɢɟ (1.8) ɩɪɢɦɟɬ ɜɢɞ Pn(O) = a0 + a1O + … + anOn = 0, an = 1.

(1.9)

Ɇɧɨɝɨɱɥɟɧ Pn(O) ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɵɦ ɦɧɨɝɨɱɥɟɧɨɦ (ɦɧɨɝɨɱɥɟɧɨɦ Ƚɭɪɜɢɰɚ), ɟɫɥɢ ɜɫɟ ɟɝɨ ɤɨɪɧɢ Oj ɢɦɟɸɬ ɨɬɪɢɰɚɬɟɥɶɧɭɸ ɜɟɳɟɫɬɜɟɧɧɭɸ ɱɚɫɬɶ, ɬ. ReOj < 0.

ɟ.

(1.10)

ȿɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ (1.10), ɬɨ ɦɚɬɪɢɰɭ Ⱥ ɧɚɡɵɜɚɸɬ ɭɫɬɨɣɱɢɜɨɣ. Ɍɟɨɪɟɦɚ 1.2 (Ⱥ. ɋɬɨɞɨɥɚ) [6]. ȼɫɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɭɫɬɨɣɱɢɜɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɩɨɥɨɠɢɬɟɥɶɧɵ. ɉɨɥɨɠɢɬɟɥɶɧɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɟɫɬɶ ɧɟɨɛɯɨɞɢɦɨɟ, ɧɨ ɧɟ ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɟ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɧɟɪɚɜɟɧɫɬɜ (1.10). Ɇɚɬɪɢɰɟɣ Ƚɭɪɜɢɰɚ

MP

n

ɦɧɨɝɨɱɥɟɧɚ (1.9) ɧɚɡɵɜɚɸɬ ɦɚɬɪɢɰɭ ɜɢɞɚ

§ a1 ¨ ¨ a3 ¨ ... ¨ ¨a © 2 n 1

M Pn

a0 a2 ... a2 n2

... ...

0· ¸ 0¸ ... ... ¸ . ¸ ... a n ¸¹

(1.11)

ȼ ɦɚɬɪɢɰɟ (1.11) ɜɫɟ ɚs=0 ɩɪɢ s<0 ɢ s>n. Ʉɪɢɬɟɪɢɣ

Ɋɚɭɫɚ-Ƚɭɪɜɢɰɚ

(ɧɟɨɛɯɨɞɢɦɵɣ

ɢ

ɞɨɫɬɚɬɨɱɧɵɣ

ɩɪɢɡɧɚɤ

ɭɫɬɨɣɱɢɜɨɫɬɢ) [6]. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɧɨɝɨɱɥɟɧ Pn(O) ɫ ɚj>0 ɢ ɚnz0 ɛɵɥ ɭɫɬɨɣɱɢɜɵɦ, ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ, ɱɬɨɛɵ ɛɵɥɢ ɩɨɥɨɠɢɬɟɥɶɧɵ ɜɫɟ ɝɥɚɜɧɵɟ ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɢɧɨɪɵ

' 1 = ɚ 1, ǻ 2 ɟɝɨ ɦɚɬɪɢɰɵ Ƚɭɪɜɢɰɚ Ʉɪɢɬɟɪɢɣ

MP

n

a1 a 0

ǻ a3 a 2 , …, n

ɚn ǻ n 1

(1.12)

.

Ʌɶɟɧɚɪɚ-ɒɢɩɚɪɚ

[6].

Ⱦɥɹ

ɬɨɝɨ

ɱɬɨɛɵ

ɦɧɨɝɨɱɥɟɧ

ɫ

ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɛɵɥ ɭɫɬɨɣɱɢɜɵɦ, ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ ɜɵɩɨɥɧɟɧɢɟ ɨɞɧɨɝɨ ɢɡ ɞɜɭɯ ɭɫɥɨɜɢɣ: ɚ) '1>0, '3>0, …, ɛ) '2>0, '4>0, … ȿɫɥɢ ɫɬɟɩɟɧɶ ɩɨɥɢɧɨɦɚ Pn(O) ɫɪɚɜɧɢɬɟɥɶɧɨ ɛɨɥɶɲɚɹ, ɬɨ ɩɪɢɦɟɧɟɧɢɟ 31

ɤɪɢɬɟɪɢɹ Ƚɭɪɜɢɰɚ ɫɬɚɧɨɜɢɬɫɹ ɡɚɬɪɭɞɧɢɬɟɥɶɧɵɦ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɩɨɥɨɠɟɧɢɹ ɤɨɪɧɟɣ ɩɨɥɢɧɨɦɚ Pn(O) ɧɚ ɤɨɦɩɥɟɤɫɧɨɣ ɩɥɨɫɤɨɫɬɢ ɢɧɨɝɞɚ ɨɤɚɡɵɜɚɟɬɫɹ ɛɨɥɟɟ ɭɞɨɛɧɵɦ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɱɚɫɬɨɬɧɨɝɨ ɤɪɢɬɟɪɢɹ Ɇɢɯɚɣɥɨɜɚ. Ɉɩɪɟɞɟɥɟɧɢɟ 1.1. ɉɭɫɬɶ Pn(O) = a0 + a1O + … + anOn, ɝɞɟ a0 ! 0, an z 0 ,

ai R , O = iZ (i2=-1), O C . Ʉɪɢɜɚɹ w

Pn (i Z ) , Z t 0, ɧɚɡɵɜɚɟɬɫɹ

ɝɨɞɨɝɪɚɮɨɦ Ɇɢɯɚɣɥɨɜɚ ɮɭɧɤɰɢɢ Pn (O). Ʉɪɢɬɟɪɢɣ Ɇɢɯɚɣɥɨɜɚ [6]. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɩɨɥɢɧɨɦ Pn(O), ɧɟ ɢɦɟɸɳɢɣ ɱɢɫɬɨ ɦɧɢɦɵɯ ɤɨɪɧɟɣ, ɹɜɥɹɥɫɹ ɩɨɥɢɧɨɦɨɦ Ƚɭɪɜɢɰɚ, ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ, ɱɬɨɛɵ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɜɟɤɬɨɪɚ Pn (i Z ) ɩɪɢ 0 d Z f ɛɵɥ ɛɵ ɪɚɜɟɧ

S n. 2

Ɂɚɦɟɱɚɧɢɟ. ȿɫɥɢ ɩɨɥɢɧɨɦ Pn(O) ɟɫɬɶ ɩɨɥɢɧɨɦ Ƚɭɪɜɢɰɚ ɫɬɟɩɟɧɢ n, ɬɨ ɜɟɤɬɨɪ f (i Z) ɦɨɧɨɬɨɧɧɨ ɩɨɜɨɪɚɱɢɜɚɟɬɫɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɧɚ ɭɝɨɥ S n , ɬɨ ɟɫɬɶ ɝɨɞɨɝɪɚɮ Ɇɢɯɚɣɥɨɜɚ, ɜɵɯɨɞɹ ɢɡ ɬɨɱɤɢ a0 ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɨɥɭɨɫɢ 2 Re O ! 0 ,

ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ

ɩɟɪɟɫɟɤɚɟɬ

ɩɨɥɭɨɫɢ

Im O ! 0, Re O 0, Im O 0, ... ,

ɩɪɨɯɨɞɹ n ɤɜɚɞɪɚɧɬɨɜ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɧɨɝɨɱɥɟɧɚ Pn(O) ɦɨɠɧɨ ɩɪɨɜɨɞɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɩɚɤɟɬɵ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɩɚɤɟɬɨɜ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ ɩɨɡɜɨɥɹɟɬ ɢɡɛɟɠɚɬɶ ɬɪɭɞɨɟɦɤɢɯ ɜɵɱɢɫɥɟɧɢɣ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɦɧɨɝɨɱɥɟɧɚ Pn(O) (ɚj>0, ɚnz0) ɥɸɛɨɣ ɫɬɟɩɟɧɢ. 1.6. ɇɟɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢɦɵɟ ɫɜɟɞɟɧɢɹ ɢɡ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ 1.6.1. ɍɪɚɜɧɟɧɢɹ Ʉɨɥɦɨɝɨɪɨɜɚ ɞɥɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɣ t

Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ s k ɫɥɭɱɚɣɧɨɟ ɫɨɛɵɬɢɟ, ɫɨɫɬɨɹɳɟɟ ɜ ɬɨɦ, ɱɬɨ ɜ ɦɨɦɟɧɬ t

ɜɪɟɦɟɧɢ tɌ=[a, b] ɫɢɫɬɟɦɚ S ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ Sk; pk(t) P[ s k ], tT ɜɟɪɨɹɬɧɨɫɬɶ ɪɟɚɥɢɡɚɰɢɢ ɷɬɨɝɨ ɫɨɛɵɬɢɹ, ɝɞɟ ɩɨɜɟɞɟɧɢɟ ɫɢɫɬɟɦɵ S ɫ ɦɧɨɠɟɫɬɜɨɦ 32

ɜɨɡɦɨɠɧɵɯ ɫɨɫɬɨɹɧɢɣ

^S k `nk 1

ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɚɪɤɨɜɫɤɢɣ ɩɪɨɰɟɫɫ ɫ

ɞɢɫɤɪɟɬɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ, ɬɨɝɞɚ ɜɟɤɬɨɪ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɣ P(t) = (p1(t)p2(t) … pn(t))T ɨɩɪɟɞɟɥɹɟɬ ɜɟɪɨɹɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ S ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ tɌ. Ɍɚɤ ɤɚɤ ɜ ɥɸɛɨɣ ɮɢɤɫɢɪɨɜɚɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɥɭɱɚɣɧɵɯ ɫɨɛɵɬɢɣ

^s `

t n k k 1

- ɩɨɥɧɚɹ ɝɪɭɩɩɚ, ɬɨ n

Ip(t) =

¦p

k

(t ) = 1, t T,

(1.13)

k 1

ɝɞɟ I = (1 … 1) Ɇ1n(R). Ɉɩɪɟɞɟɥɟɧɢɟ 1.2. [19] ɉɭɫɬɶ S – ɧɟɤɨɬɨɪɚɹ ɫɢɫɬɟɦɚ ɫ ɜɨɡɦɨɠɧɵɦ ɞɢɫɤɪɟɬɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ ^S k `k 1 . ɉɨɞ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɢ ɩɟɪɟɯɨɞɚ ɷɬɨɣ n

ɫɢɫɬɟɦɵ ɢɡ ɫɨɫɬɨɹɧɢɹ Si ɜ ɫɨɫɬɨɹɧɢɟ Sj ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɩɨɧɢɦɚɸɬ ɱɢɫɥɨ Ȝij(t)

lim 't o 0

Pij (t ; 't ) 't

,

ɝɞɟ Ɋij(t; ¨t) – ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɢɫɬɟɦɚ S, ɧɚɯɨɞɹɳɚɹɫɹ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ Si, ɡɚ ɜɪɟɦɹ ¨t > 0 ɩɟɪɟɣɞɟɬ ɜ ɫɨɫɬɨɹɧɢɟ Sj. ɉɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɩɟɪɟɯɨɞɚ ɫɢɫɬɟɦɵ ɢɡ ɨɞɧɨɝɨ ɜɨɡɦɨɠɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ ɨɛɥɚɞɚɸɬ ɨɛɵɱɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ ɭɫɥɨɜɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ, ɜ ɱɚɫɬɧɨɫɬɢ, ɹɜɥɹɸɬɫɹ ɧɟɨɬɪɢɰɚɬɟɥɶɧɵɦɢ. Ɉɩɪɟɞɟɥɟɧɢɟ 1.3. [19] ɋɤɚɥɹɪɧɵɣ Ɇɚɪɤɨɜɫɤɢɣ ɩɪɨɰɟɫɫ ɫ ɞɢɫɤɪɟɬɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ, ɨɩɢɫɵɜɚɸɳɢɣ ɩɨɜɟɞɟɧɢɟ ɫɢɫɬɟɦɵ S, ɧɚɡɵɜɚɸɬ ɨɞɧɨɪɨɞɧɵɦ, ɟɫɥɢ ɞɥɹ ɥɸɛɵɯ i, j = 1, n Ȝij(t) Ł Ȝij = ɫonst,

t T.

ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɧɚɡɵɜɚɸɬ ɧɟɨɞɧɨɪɨɞɧɵɦ. Ɍɟɨɪɟɦɚ 1.3. [19]

ɉɭɫɬɶ ɫɢɫɬɟɦɚ S ɢɦɟɟɬ ɦɧɨɠɟɫɬɜɨ ɜɨɡɦɨɠɧɵɯ

ɫɨɫɬɨɹɧɢɣ ^S k `k 1 , ɚ ɩɪɨɰɟɫɫ ɢɡɦɟɧɟɧɢɹ ɫɨɫɬɨɹɧɢɣ ɷɬɨɣ ɫɢɫɬɟɦɵ ɩɪɟɞɫɬɚɜɥɹɟɬ n

ɫɨɛɨɣ Ɇɚɪɤɨɜɫɤɢɣ ɩɪɨɰɟɫɫ, ɩɪɢɱɟɦ ɞɥɹ ɜɫɟɯ ɩɚɪ ɜɨɡɦɨɠɧɵɯ ɫɨɫɬɨɹɧɢɣ Si ɢ Sj ɨɩɪɟɞɟɥɟɧɵ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɩɟɪɟɯɨɞɨɜ Ȝij(t) ɢ Ȝji (t). Ɍɨɝɞɚ ɜɟɪɨɹɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ Ɋk(t) ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɫɢɫɬɟɦɟ ɭɪɚɜɧɟɧɢɣ Ʉɨɥɦɨɝɨɪɨɜɚ: 33

dp k (t ) dt

n

n

i 1 i zk

i 1 i zk

¦ Oik (t ) pi (t ) (¦ Oki (t )) pk (t ) , k = 1, n , t T.

(1.14)

ɋɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ Ʉɨɥɦɨɝɨɪɨɜɚ (1.14) ɧɟ ɹɜɥɹɟɬɫɹ ɥɢɧɟɣɧɨ ɧɟɡɚɜɢɫɢɦɨɣ, ɬ. ɟ. ɨɧɚ ɹɜɥɹɟɬɫɹ ɢɡɛɵɬɨɱɧɨɣ, ɱɬɨ ɫɥɟɞɭɟɬ ɢɡ ɪɚɜɟɧɫɬɜɚ (1.13). Ʉɨɦɩɨɧɟɧɬɵ ɪk(t) ɜɟɤɬɨɪɚ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ S ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ, ɬ. ɟ. ɪk(t) t 0, k = 1, n , t T = [a, b].

(1.15)

ɍɫɥɨɜɢɹ (1.15) ɧɚɤɥɚɞɵɜɚɸɬ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ ɧɚ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɩɟɪɟɯɨɞɨɜ ɫɢɫɬɟɦɵ S ɢɡ ɨɞɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ. ɗɬɢ ɨɝɪɚɧɢɱɟɧɢɹ ɢɦɟɸɬ ɜɚɠɧɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢ ɢɡɭɱɟɧɢɢ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ ɩɪɟɞɟɥɶɧɵɯ ɪɟɠɢɦɨɜ ɨɞɧɨɪɨɞɧɵɯ Ɇɚɪɤɨɜɫɤɢɯ ɫɥɭɱɚɣɧɵɯ ɞɢɫɤɪɟɬɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ, ɢɝɪɚɸɳɢɯ

ɩɪɨɰɟɫɫɨɜ ɫ

ɫɭɳɟɫɬɜɟɧɧɭɸ ɪɨɥɶ ɜ ɪɚɡɥɢɱɧɵɯ

ɩɪɢɥɨɠɟɧɢɹɯ. Ɉɩɪɟɞɟɥɟɧɢɟ 1.4. [19] ɉɭɫɬɶ ^S k `k

n 1

- ɦɧɨɠɟɫɬɜɨ ɜɨɡɦɨɠɧɵɯ ɫɨɫɬɨɹɧɢɣ

ɫɢɫɬɟɦɵ S, ɚ ɩɪɨɰɟɫɫ ɟɟ ɩɟɪɟɯɨɞɚ ɢɡ ɨɞɧɨɝɨ ɜɨɡɦɨɠɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ ɩɪɟɞɫɬɚɜɥɹɟɬ

ɫɨɛɨɣ

ɨɞɧɨɪɨɞɧɵɣ

ɦɚɪɤɨɜɫɤɢɣ

ɩɪɨɰɟɫɫ

ɫ

ɞɢɫɤɪɟɬɧɵɦɢ

ɫɨɫɬɨɹɧɢɹɦɢ, ɨɩɪɟɞɟɥɟɧɧɵɣ ɧɚ ɦɧɨɠɟɫɬɜɟ Ɍ = [ɚ,f). ȿɫɥɢ ɪ(t) = (ɪ1(t) … ɪn(t))T – ɜɟɤɬɨɪ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ S ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ tɌ ɢ ɫɭɳɟɫɬɜɭɟɬ ɩɪɟɞɟɥ lim p(t ) , ɬɨ ɜɟɤɬɨɪ ɪ ɧɚɡɵɜɚɸɬ ɜɟɤɬɨɪɨɦ ɩɪɟɞɟɥɶɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ t of

ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ. ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɜɟɤɬɨɪɚ ɩɪɟɞɟɥɶɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɣ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɜ ɫɢɫɬɟɦɟ S ɧɚɫɬɭɩɚɟɬ ɧɟɤɨɬɨɪɵɣ ɫɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ. Ɉɧ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɫɢɫɬɟɦɚ ɫɥɭɱɚɣɧɵɦ ɨɛɪɚɡɨɦ ɦɟɧɹɟɬ ɫɜɨɢ ɫɨɫɬɨɹɧɢɹ, ɧɨ ɜɟɪɨɹɬɧɨɫɬɶ ɤɚɠɞɨɝɨ ɢɡ ɧɢɯ ɭɠɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɪɟɦɟɧɢ. Ʉɚɠɞɨɟ ɢɡ ɫɨɫɬɨɹɧɢɣ ɪɟɚɥɢɡɭɟɬɫɹ ɫ ɧɟɤɨɬɨɪɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ, ɢɧɬɟɪɩɪɟɬɚɰɢɹ ɤɨɬɨɪɨɣ ɦɨɠɟɬ ɛɵɬɶ ɫɜɹɡɚɧɚ ɫɨ ɫɪɟɞɧɢɦ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɜɪɟɦɟɧɟɦ ɩɪɟɛɵɜɚɧɢɹ ɫɢɫɬɟɦɵ S ɜ ɞɚɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ȼɟɤɬɨɪ ɪ ɩɪɟɞɟɥɶɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ S ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɭɫɬɨɣɱɢɜɭɸ ɬɨɱɤɭ ɩɨɤɨɹ ɞɥɹ ɧɨɪɦɚɥɶɧɨɣ ɨɞɧɨɪɨɞɧɨɣ 34

ɫɢɫɬɟɦɵ

ɨɛɵɤɧɨɜɟɧɧɵɯ

ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɪc(t )

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

Op(t ) ,

ɢɦɟɸɳɭɸ

ɭɪɚɜɧɟɧɢɣ

ɫ

ɩɨɫɬɨɹɧɧɵɦɢ

ɧɟɨɬɪɢɰɚɬɟɥɶɧɵɟ

ɤɨɨɪɞɢɧɚɬɵ

ɪɚɫɩɨɥɨɠɟɧɧɭɸ ɧɚ ɝɢɩɟɪɩɥɨɫɤɨɫɬɢ ɪ1+ … + ɪn = 1. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɟɤɬɨɪ ɪ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɦɚɬɪɢɱɧɨɣ ɫɢɫɬɟɦɟ [19]

Op 0, ® ¯ Iɪ 1. ɉɭɫɬɶ ^S i `i

n 0

(1.16)

- ɦɧɨɠɟɫɬɜɨ ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ɉɛɨɡɧɚɱɢɦ

ɚi ( i 0, n ) - ɫɥɭɱɚɣɧɨɟ ɫɨɛɵɬɢɟ, ɡɚɤɥɸɱɚɸɳɟɟɫɹ ɜ ɬɨɦ, ɱɬɨ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t t 0 ɫɢɫɬɟɦɚ ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ Si, Pi(t) - ɜɟɪɨɹɬɧɨɫɬɶ ɟɝɨ ɪɟɚɥɢɡɚɰɢɢ,

^ai `in 1

- ɩɨɥɧɚɹ ɝɪɭɩɩɚ ɫɨɛɵɬɢɣ, ɬɚɤ ɤɚɤ ɫɢɫɬɟɦɚ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ

ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɥɢɲɶ ɜ ɨɞɧɨɦ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɨɫɬɨɹɧɢɣ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ [19], n

¦ p (t ) { 1 . i

(1.17)

i o

ȼ ɧɚɱɚɥɟ ɩɨɫɥɟ ɜɤɥɸɱɟɧɢɹ ɫɢɫɬɟɦɵ ɜ ɪɚɛɨɬɭ, ɩɪɨɬɟɤɚɸɳɢɣ ɜ ɧɟɣ ɩɪɨɰɟɫɫ ɟɳɟ ɧɟ ɛɭɞɟɬ ɫɬɚɰɢɨɧɚɪɧɵɦ, ɫɩɭɫɬɹ ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɫɢɫɬɟɦɚ ɩɟɪɟɣɞɟɬ ɜ ɫɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ. ȼ ɫɬɚɰɢɨɧɚɪɧɨɦ ɪɟɠɢɦɟ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɢɡɭɱɚɟɦɚɹ ɫɢɫɬɟɦɚ ɬɚɤɠɟ ɦɟɧɹɟɬ ɫɜɨɟ ɫɨɫɬɨɹɧɢɟ ɫɥɭɱɚɣɧɵɦ ɨɛɪɚɡɨɦ, ɧɨ ɜɟɪɨɹɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ ɭɠɟ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ. Ʉɚɠɞɚɹ ɢɡ ɧɢɯ, ɹɜɥɹɹɫɶ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɫɢɫɬɟɦɵ ɜ ɞɚɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɪɟɠɢɦɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɥɸɛɨɣ ɫɢɫɬɟɦɵ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɟɝɨ ɫɭɳɟɫɬɜɨɜɚɧɢɹ, ɮɨɪɦɚɥɶɧɨ ɹɜɥɹɟɬɫɹ ɩɪɟɞɟɥɶɧɵɦ (t ĺ ) ɫɥɭɱɚɟɦ ɟɟ ɨɛɳɟɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ. 1.6.2. ɉɪɨɫɬɟɣɲɢɣ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ Ɉɩɪɟɞɟɥɟɧɢɟ 1.5. [24] ɉɨɬɨɤɨɦ ɨɞɧɨɪɨɞɧɵɯ ɫɨɛɵɬɢɣ ɧɚɡɵɜɚɟɬɫɹ ɤɨɧɟɱɧɚɹ ɢɥɢ ɫɱɟɬɧɚɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ^W n ` ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ, ɨɩɪɟɞɟɥɟɧɧɵɯ ɧɚ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɜɟɪɨɹɬɧɨɫɬɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɜ ɥɸɛɨɣ 35

ɮɢɤɫɢɪɨɜɚɧɧɵɣ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ (ɚ, b) ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ 1 ɩɨɩɚɞɚɟɬ ɤɨɧɟɱɧɨɟ ɱɢɫɥɨ ɷɬɢɯ ɜɟɥɢɱɢɧ. ȿɫɥɢ ɞɚɧɧɨɟ t ɫɨɜɩɚɞɚɟɬ ɫ r ɷɥɟɦɟɧɬɚɦɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ^W n `, ɬɨ ɜ ɦɨɦɟɧɬ t ɩɪɨɢɫɯɨɞɢɬ r ɫɨɛɵɬɢɣ ɩɨɬɨɤɚ. ȿɫɥɢ Wn ɭɩɨɪɹɞɨɱɟɧɵ ɬɚɤ, ɱɬɨ Wn ɚ d

Wn+1 d Wn+2 d … d Wn+k b d Wn+k +1, ɬɨ Wn+i ɧɚɡɵɜɚɟɬɫɹ ɦɨɦɟɧɬɨɦ ɧɚɫɬɭɩɥɟɧɢɹ i-ɝɨ ɫɨɛɵɬɢɹ ɩɨɬɨɤɚ ɨɞɧɨɪɨɞɧɵɯ ɫɨɛɵɬɢɣ ɜ ɩɨɥɭɢɧɬɟɪɜɚɥɟ [ɚ, b). ɉɨɬɨɤ

ɨɞɧɨɪɨɞɧɵɯ

ɫɨɛɵɬɢɣ,

ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ

ɭɫɥɨɜɢɹɦ

ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ, ɨɬɫɭɬɫɬɜɢɹ ɩɨɫɥɟɞɟɣɫɬɜɢɹ ɢ ɨɪɞɢɧɚɪɧɨɫɬɢ ɩɨɬɨɤɚ ɨɞɧɨɪɨɞɧɵɯ ɫɨɛɵɬɢɣ ɧɚɡɵɜɚɟɬɫɹ ɩɪɨɫɬɟɣɲɢɦ ɩɨɬɨɤɨɦ. ɋɬɚɰɢɨɧɚɪɧɨɫɬɶ ɩɨɬɨɤɚ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɞɥɹ ɥɸɛɨɣ ɝɪɭɩɩɵ ɢɡ ɤɨɧɟɱɧɨɝɨ ɱɢɫɥɚ ɧɟɩɟɪɟɫɟɤɚɸɳɢɯɫɹ ɨɬɪɟɡɤɨɜ ɜɪɟɦɟɧɢ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɹɜɥɟɧɢɹ ɜ ɧɢɯ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ k1, k2, …, kn ɬɪɟɛɨɜɚɧɢɣ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɷɬɢɯ ɱɢɫɟɥ ɢ ɨɬ ɞɥɢɧ ɭɤɚɡɚɧɧɵɯ ɩɪɨɦɟɠɭɬɤɨɜ ɜɪɟɦɟɧɢ, ɧɨ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɪɚɫɩɨɥɨɠɟɧɢɹ ɧɚ ɨɫɢ ɜɪɟɦɟɧɢ, ɬ. ɟ. ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɩɨɫɬɨɹɧɧɨ. Ɉɬɫɭɬɫɬɜɢɟ ɩɨɫɥɟɞɫɬɜɢɹ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɫɬɭɩɥɟɧɢɹ ɜ ɬɟɱɟɧɢɟ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ (Ɍ, Ɍ + t) ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɫɤɨɥɶɤɨ ɬɪɟɛɨɜɚɧɢɣ ɢ ɤɚɤ ɩɨɫɬɭɩɚɥɢ ɞɨ ɷɬɨɝɨ ɩɪɨɦɟɠɭɬɤɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɬɨ ɩɪɟɞɥɨɠɟɧɢɟ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɭɫɥɨɜɧɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɫɬɭɩɥɟɧɢɹ k ɬɪɟɛɨɜɚɧɢɣ ɡɚ ɩɪɨɦɟɠɭɬɨɤ (T, T + t), ɜɵɱɢɫɥɟɧɧɚɹ ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɦ ɩɪɟɞɥɨɠɟɧɢɢ ɨ ɩɨɫɬɭɩɥɟɧɢɹɯ ɬɪɟɛɨɜɚɧɢɣ ɞɨ ɷɬɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ, ɫɨɜɩɚɞɚɟɬ ɫ ɛɟɡɭɫɥɨɜɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɬɨɝɨ ɠɟ ɫɨɛɵɬɢɹ, ɬ. ɟ. ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɧɟɤɨɬɨɪɵɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ, ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɫɤɨɥɶɤɨ ɬɪɟɛɨɜɚɧɢɣ ɭɠɟ ɩɨɫɬɭɩɢɥɨ ɜ ɫɢɫɬɟɦɭ. Ɉɪɞɢɧɚɪɧɨɫɬɶ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɜɵɪɚɠɚɟɬ ɫɨɛɨɣ ɭɫɥɨɜɢɟ ɩɪɚɤɬɢɱɟɫɤɨɣ ɧɟɜɨɡɦɨɠɧɨɫɬɢ ɩɨɹɜɥɟɧɢɹ ɞɜɭɯ ɢɥɢ ɧɟɫɤɨɥɶɤɢɯ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. ɍɫɥɨɜɢɟ ɨɪɞɢɧɚɪɧɨɫɬɢ ɩɨɬɨɤɚ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɩɪɢ h o 0 P!1(h) o 0, h

ɢɥɢ, P!1(h) = 0(h), ɝɞɟ Ɋ!1(h)

(1.18)

ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɹɜɥɟɧɢɹ ɜ ɩɪɨɦɟɠɭɬɤɟ ɞɥɢɧɵ h ɞɜɭɯ ɢɥɢ ɛɨɥɟɟ 36

ɬɪɟɛɨɜɚɧɢɣ. ɉɪɨɫɬɟɣɲɢɣ

ɫɥɭɱɚɣ

ɩɨɬɨɤɨɜ,

ɤɨɝɞɚ

ɜɟɪɨɹɬɧɨɫɬɶ

ɩɨɫɬɭɩɥɟɧɢɹ

ɜ

ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ t ɪɨɜɧɨ k ɬɪɟɛɨɜɚɧɢɣ ɡɚɞɚɟɬɫɹ ɮɨɪɦɭɥɨɣ

Pk (t )

( O t ) k Ot e , k!

(1.19)

ɝɞɟ Ȝ ! 0 – ɩɨɫɬɨɹɧɧɨɟ ɱɢɫɥɨ. ɉɪɢ ɷɬɨɦ ɩɨɫɬɭɩɚɸɳɢɣ ɩɨɬɨɤ ɫɱɢɬɚɟɬɫɹ ɬɚɤɢɦ, ɱɬɨ ɞɥɹ ɥɸɛɨɣ ɤɨɧɟɱɧɨɣ ɝɪɭɩɩɵ ɧɟɩɟɪɟɫɟɤɚɸɳɢɯɫɹ ɨɬɪɟɡɤɨɜ ɜɪɟɦɟɧɢ ɱɢɫɥɚ ɩɨɹɜɢɜɲɢɯɫɹ ɧɚ ɢɯ ɩɪɨɬɹɠɟɧɢɢ ɬɪɟɛɨɜɚɧɢɣ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɜɡɚɢɦɧɨ ɧɟɡɚɜɢɫɢɦɵɟ ɫɥɭɱɚɣɧɵɟ ɜɟɥɢɱɢɧɵ. Ɍɚɤ ɤɚɤ ɩɚɪɚɦɟɬɪ O ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɩɨɷɬɨɦɭ ɟɝɨ ɧɚɡɵɜɚɸɬ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ, ɢɥɢ ɩɥɨɬɧɨɫɬɶɸ ɩɪɨɫɬɟɣɲɟɝɨ ɩɨɬɨɤɚ. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɚɹ ɩɪɨɜɟɪɤɚ ɧɚɥɢɱɢɹ ɬɪɟɯ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɭɫɥɨɜɢɣ – ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ, ɨɬɫɭɬɫɬɜɢɹ ɩɨɫɥɟɞɫɬɜɢɹ ɢ ɨɪɞɢɧɚɪɧɨɫɬɢ – ɧɟɪɟɞɤɨ ɬɪɭɞɧɨ ɜɵɩɨɥɧɢɦɚ, ɩɨɷɬɨɦɭ ɨɱɟɧɶ ɜɚɠɧɨ ɧɚɣɬɢ ɢɧɵɟ ɭɫɥɨɜɢɹ, ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɢɥɢ ɛɵ ɢɡ ɢɧɵɯ ɨɫɧɨɜɚɧɢɣ ɞɟɥɚɬɶ ɜɵɜɨɞ ɨ ɬɨɦ, ɱɬɨ ɩɨɬɨɤ ɫɨɛɵɬɢɣ ɨɤɚɠɟɬɫɹ ɩɪɨɫɬɟɣɲɢɦ ɢɥɢ ɛɥɢɡɤɢɦ ɤ ɩɪɨɫɬɟɣɲɟɦɭ. Ɍɟɨɪɟɦɚ, ɞɨɤɚɡɚɧɧɚɹ ɜ ɨɛɳɟɣ ɮɨɪɦɟ ɨɞɧɢɦ ɢɡ ɫɨɡɞɚɬɟɥɟɣ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɨɪɢɢ ɜɟɪɨɹɬɧɨɫɬɟɣ Ⱥ. ə. ɏɢɧɱɢɧɵɦ [26], ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɪɢɧɰɢɩɢɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɩɪɢɥɨɠɟɧɢɣ. ɂɡ ɩɪɟɞɩɨɥɨɠɟɧɢɹ, ɱɬɨ ɞɚɧɧɵɣ ɩɨɬɨɤ ɹɜɥɹɟɬɫɹ ɫɭɦɦɨɣ ɨɱɟɧɶ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɧɟɡɚɜɢɫɢɦɵɯ ɦɟɠɞɭ ɫɨɛɨɣ ɫɬɚɰɢɨɧɚɪɧɵɯ ɩɨɬɨɤɨɜ, ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɥɢɲɶ ɦɚɥɨ ɜɥɢɹɟɬ ɧɚ ɫɭɦɦɭ, ɫɥɟɞɭɟɬ, ɱɬɨ ɫɭɦɦɢɪɨɜɚɧɧɵɣ ɩɨɬɨɤ ɩɪɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦ ɨɝɪɚɧɢɱɟɧɢɢ ɚɪɢɮɦɟɬɢɱɟɫɤɨɝɨ ɯɚɪɚɤɬɟɪɚ, ɝɚɪɚɧɬɢɪɭɸɳɟɦ ɨɪɞɢɧɚɪɧɨɫɬɶ ɫɭɦɦɚɪɧɨɝɨ

ɩɨɬɨɤɚ, ɨɤɚɡɵɜɚɟɬɫɹ

ɛɥɢɡɤɢɦ ɤ ɩɪɨɫɬɟɣɲɟɦɭ. ɇɚɡɜɚɧɢɟ «ɩɪɨɫɬɟɣɲɢɣ» ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɫɨɛɵɬɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɨɫɬɟɣɲɢɦɢ ɩɨɬɨɤɚɦɢ, ɨɤɚɡɵɜɚɟɬɫɹ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɵɦ. ɋɚɦɵɣ ɩɪɨɫɬɨɣ, ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ, ɪɟɝɭɥɹɪɧɵɣ ɩɨɬɨɤ ɫɨ ɫɬɪɨɝɨ ɩɨɫɬɨɹɧɧɵɦɢ ɢɧɬɟɪɜɚɥɚɦɢ ɦɟɠɞɭ ɫɨɛɵɬɢɹɦɢ ɨɬɧɸɞɶ ɧɟ ɹɜɥɹɟɬɫɹ «ɩɪɨɫɬɟɣɲɢɦ» ɜ ɜɵɲɟɧɚɡɜɚɧɧɨɦ ɫɦɵɫɥɟ ɫɥɨɜɚ: ɨɧ ɨɛɥɚɞɚɟɬ ɹɪɤɨ ɜɵɪɚɠɟɧɧɵɦ ɩɨɫɥɟɞɟɣɫɬɜɢɟɦ, 37

ɬɚɤ ɤɚɤ ɦɨɦɟɧɬɵ ɩɨɹɜɥɟɧɢɹ ɫɨɛɵɬɢɣ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɠɟɫɬɤɨɣ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ. ɉɪɨɫɬɟɣɲɢɣ ɩɨɬɨɤ ɜ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɢɝɪɚɟɬ ɬɚɤɭɸ ɠɟ ɪɨɥɶ, ɤɚɤ ɧɨɪɦɚɥɶɧɵɣ ɡɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ ɜ ɬɟɨɪɢɢ ɜɟɪɨɹɬɧɨɫɬɟɣ: ɫɬɚɰɢɨɧɚɪɧɵɯ

ɩɪɢ

ɫɥɨɠɟɧɢɢ

ɫɥɭɱɚɣɧɵɯ

ɧɟɫɤɨɥɶɤɢɯ

ɩɨɬɨɤɨɜ

ɧɟɡɚɜɢɫɢɦɵɯ,

ɨɛɪɚɡɭɟɬɫɹ

ɨɪɞɢɧɚɪɧɵɯ,

ɫɭɦɦɚɪɧɵɣ

ɩɨɬɨɤ,

ɩɪɢɛɥɢɠɚɸɳɢɣɫɹ ɩɨ ɫɜɨɢɦ ɫɜɨɣɫɬɜɚɦ ɤ ɩɪɨɫɬɟɣɲɟɦɭ [59]. ɉɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɧɚ ɛɢɪɠɭ ɬɪɭɞɚ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɩɪɨɫɬɟɣɲɢɣ, ɬ. ɤ. ɢɦɟɟɬ ɦɟɫɬɨ ɫɬɚɰɢɨɧɚɪɧɨɫɬɶ ɩɪɨɰɟɫɫɚ, ɫɭɳɟɫɬɜɭɟɬ ɬɚɤɠɟ ɨɬɫɭɬɫɬɜɢɟ ɩɨɫɥɟɞɟɣɫɬɜɢɹ, ɤɨɝɞɚ ɤɨɥɢɱɟɫɬɜɨ ɬɪɟɛɨɜɚɧɢɣ ɩɨɫɬɭɩɢɜɲɢɯ ɜ ɤɨɧɰɟ ɦɟɫɹɰɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɭɞɨɜɥɟɬɜɨɪɟɧɢɹ ɜ ɧɚɱɚɥɟ ɦɟɫɹɰɚ. ɇɚɛɥɸɞɚɟɬɫɹ ɢ ɹɜɥɟɧɢɟ ɨɞɧɨɪɨɞɧɨɫɬɢ. ɉɭɫɬɶ Pk(t) ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜ ɬɟɱɟɧɢɟ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ ɞɥɢɬɟɥɶɧɨɫɬɢ t ɤ ɨɛɫɥɭɠɢɜɚɧɢɸ ɛɭɞɭɬ ɩɪɟɞɴɹɜɥɟɧɵ k ɬɪɟɛɨɜɚɧɢɣ. ȼ ɫɢɥɭ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ ɩɨɬɨɤɚ ɷɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɧɟ ɡɚɜɢɫɢɬ ɧɢ ɨɬ ɜɵɛɨɪɚ ɧɚɱɚɥɚ ɨɬɫɱɟɬɚ, ɧɢ ɨɬ ɜɫɟɣ ɟɝɨ ɩɪɟɞɵɫɬɨɪɢɢ. ɍɫɥɨɜɢɹ, ɨɩɪɟɞɟɥɹɸɳɢɟ ɩɪɨɫɬɟɣɲɢɣ ɩɨɬɨɤ, ɩɨɡɜɨɥɹɸɬ ɨɞɧɨɡɧɚɱɧɨ, ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɨɞɧɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɧɚɣɬɢ ɮɨɪɦɭɥɵ ɞɥɹ ɜɟɪɨɹɬɧɨɫɬɟɣ Pk(t). Ɏɨɪɦɭɥɚ ɩɨɥɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ ɜ ɬɟɱɟɧɢɟ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ t + h ɩɨɫɬɭɩɢɬ ɪɨɜɧɨ k ɬɪɟɛɨɜɚɧɢɣ ɩɪɢ ɭɱɟɬɟ ɨɬɫɭɬɫɬɜɢɹ ɩɨɫɥɟɞɫɬɜɢɣ ɢɦɟɟɬ ɜɢɞ: k

Pk (t h)

¦

Pj (t ) Pk j (h).

j 0

ɋɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ ɨɪɞɢɧɚɪɧɨɫɬɢ ɩɨɬɨɤɚ, ɩɨɥɭɱɢɦ ɪɚɜɟɧɫɬɜɨ Pk (t h)

Pk (t ) P0 (h) Pk 1 (t ) P1 (h) 0(h).

(1.20)

ȼ ɪɚɜɟɧɫɬɜɟ (1.20) ɡɚɦɟɧɢɦ P1(h) ɧɚ Ȝh + 0(h) ɫɨɝɥɚɫɧɨ (1.17). ȿɫɥɢ ɩɪɟɞɟɥ ɩɪɚɜɨɣ ɱɚɫɬɢ ɫɭɳɟɫɬɜɭɟɬ, ɬɨ ɫɭɳɟɫɬɜɭɟɬ ɢ ɩɪɟɞɟɥ ɥɟɜɨɣ ɱɚɫɬɢ ɩɨɫɥɟɞɧɟɝɨ ɪɚɜɟɧɫɬɜɚ. Ɍɨɝɞɚ ɩɪɢ h o 0, ɩɨɥɭɱɢɦ: dPk (t ) dt

OPk (t ) OPk 1 (t ). 38

(1.21)

ɍɪɚɜɧɟɧɢɟ

(1.21)

ɩɪɟɞɫɬɚɜɥɹɟɬ

ɫɨɛɨɣ

ɛɟɫɤɨɧɟɱɧɭɸ

ɫɢɫɬɟɦɭ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨ-ɪɚɡɧɨɫɬɧɵɯ ɭɪɚɜɧɟɧɢɣ. ɍɪɚɜɧɟɧɢɟ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ P0(t) ɢɦɟɟɬ ɜɢɞ:

dP0 (t ) dt

OP0 (t ).

(1.22)

Ce Ot .

(1.23)

ɍɪɚɜɧɟɧɢɟ (1.22) ɢɦɟɟɬ ɪɟɲɟɧɢɟ

P0 (t ) Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɟɪɨɹɬɧɨɫɬɶ Pk(t)

ɫ ɩɪɨɢɡɜɨɥɶɧɵɦɢ

ɢɧɞɟɤɫɚɦɢ ɩɪɢ

ɥɸɛɨɦ k 0 ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ (1.19). Ɍɟɨɪɟɦɚ 1.4. [19] Ⱦɢɫɤɪɟɬɧɚɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ Wn, ɩɪɢɧɢɦɚɸɳɚɹ ɡɧɚɱɟɧɢɹ 0, 1, 2, ... ɢ ɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɩɪɢ ɩɪɨɫɬɟɣɲɟɦ ɜɯɨɞɧɨɦ ɩɨɬɨɤɟ ɱɢɫɥɨ ɡɚɹɜɨɤ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɫɢɫɬɟɦɭ ɨɛɫɥɭɠɢɜɚɧɢɹ ɧɚ ɜɪɟɦɟɧɧɨɦ ɢɧɬɟɪɜɚɥɟ ɞɥɢɬɟɥɶɧɨɫɬɢ t, ɪɚɫɩɪɟɞɟɥɟɧɚ ɩɨ ɡɚɤɨɧɭ ɉɭɚɫɫɨɧɚ ɫ ɩɚɪɚɦɟɬɪɨɦ Ot. ɋɥɟɞɫɬɜɢɟ 1.1. [19] ȿɫɥɢ ɜɯɨɞɧɨɣ ɩɨɬɨɤ ɹɜɥɹɟɬɫɹ ɩɪɨɫɬɟɣɲɢɦ, ɬɨ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɫɢɫɬɟɦɭ ɨɛɫɥɭɠɢɜɚɧɢɹ ɧɚ ɜɪɟɦɟɧɧɨɦ ɢɧɬɟɪɜɚɥɟ ɞɥɢɬɟɥɶɧɨɫɬɢ t, ɪɚɜɧɨ Ot. ɋɥɟɞɫɬɜɢɟ 1.2. [19] ȿɫɥɢ ɜɯɨɞɧɨɣ ɩɨɬɨɤ ɡɚɹɜɨɤ ɹɜɥɹɟɬɫɹ ɩɪɨɫɬɟɣɲɢɦ, ɬɨ ɞɢɫɩɟɪɫɢɹ ɫɤɚɥɹɪɧɨɣ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ Wn, ɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɪɚɫɫɟɢɜɚɧɢɟ ɱɢɫɥɚ ɡɚɹɜɨɤ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɫɢɫɬɟɦɭ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɧɚ ɜɪɟɦɟɧɧɨɦ ɢɧɬɟɪɜɚɥɟ ɞɥɢɬɟɥɶɧɨɫɬɢ t, ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɯ ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ, ɪɚɜɧɨ Ot. Ⱦɥɹ ɩɪɨɫɬɟɣɲɟɝɨ ɩɨɬɨɤɚ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɡɚ ɜɪɟɦɹ t, ɪɚɜɧɨ f

ɆP (t )

¦

f

kPk (t )

k 1

e Ot ¦ k k 1

(Ot ) k k!

Ot ,

ɝɞɟ ȝ(t) - ɢɫɬɢɧɧɨɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɢɜɲɢɯ ɡɚ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ t. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɱɢɫɥɚ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɧɚɡɵɜɚɟɬɫɹ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɩɨɬɨɤɚ. Ɉɛɨɡɧɚɱɢɦ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɛɭɤɜɨɣ ȝ. Ⱦɥɹ ɩɪɨɫɬɟɣɲɟɝɨ ɩɨɬɨɤɚ ȝ = Ȝ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ, ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɩɨ ɡɚɤɨɧɭ 39

ɉɭɚɫɫɨɧɚ, ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɢ ɞɢɫɩɟɪɫɢɹ ɫɨɜɩɚɞɚɸɬ. Ɍɟɨɪɟɦɚ 1.5. [19]

ȼ ɫɥɭɱɚɟ ɩɪɨɫɬɟɣɲɟɝɨ ɜɯɨɞɧɨɝɨ ɩɨɬɨɤɚ ɫ

ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ O ɞɥɢɬɟɥɶɧɨɫɬɶ t(n) ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɦɟɠɞɭ ɞɜɭɦɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦɢ ɡɚɹɜɤɚɦɢ ɢɦɟɟɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫ ɩɚɪɚɦɟɬɪɨɦ O. ɋɥɟɞɫɬɜɢɟ 1.3. [19] ȼ ɫɥɭɱɚɟ ɩɪɨɫɬɟɣɲɟɝɨ

ɜɯɨɞɧɨɝɨ ɩɨɬɨɤɚ ɫ

ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ O ɞɥɢɬɟɥɶɧɨɫɬɶ t(n) ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɦɟɠɞɭ ɞɜɭɦɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨɫɬɭɩɚɸɳɢɦɢ ɡɚɹɜɤɚɦɢ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɨɣ ɫ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɜɟɪɨɹɬɧɨɫɬɟɣ) f t (T )

Oe OT , T ! 0; ® ¯ 0, T d 0,

ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɢ ɞɢɫɩɟɪɫɢɹ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɪɚɜɟɧɫɬɜɚɦɢ M [t (n)] M [t (n)]

1

O 1

O2

,

(1.24)

.

(1.25)

1.6.3. ɋɢɫɬɟɦɵ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ

ɉɨɞ ɫɢɫɬɟɦɨɣ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɋɆɈ) ɩɨɧɢɦɚɸɬ ɞɢɧɚɦɢɱɟɫɤɭɸ ɫɢɫɬɟɦɭ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɭɸ ɞɥɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ ɩɪɢ ɨɝɪɚɧɢɱɟɧɢɹɯ ɧɚ ɪɟɫɭɪɫɵ ɫɢɫɬɟɦɵ. ȼ ɬɟɨɪɢɢ ɋɆɈ ɨɛɫɥɭɠɢɜɚɟɦɵɣ ɨɛɴɟɤɬ ɧɚɡɵɜɚɸɬ ɬɪɟɛɨɜɚɧɢɟɦ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɩɨɞ ɬɪɟɛɨɜɚɧɢɟɦ ɨɛɵɱɧɨ ɩɨɧɢɦɚɸɬ ɡɚɩɪɨɫ ɧɚ ɭɞɨɜɥɟɬɜɨɪɟɧɢɟ ɧɟɤɨɬɨɪɨɣ ɩɨɬɪɟɛɧɨɫɬɢ, ɧɚɩɪɢɦɟɪ, ɬɪɟɛɨɜɚɧɢɟ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ. ɋɪɟɞɫɬɜɚ, ɨɛɫɥɭɠɢɜɚɸɳɢɟ ɬɪɟɛɨɜɚɧɢɹ, ɧɚɡɵɜɚɸɬɫɹ ɨɛɫɥɭɠɢɜɚɸɳɢɦɢ ɭɫɬɪɨɣɫɬɜɚɦɢ ɢɥɢ ɤɚɧɚɥɚɦɢ ɨɛɫɥɭɠɢɜɚɧɢɹ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɛɢɪɠɢ ɬɪɭɞɚ ɤɚɧɚɥɚɦɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɹɜɥɹɸɬɫɹ ɫɩɟɰɢɚɥɢɫɬɵ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɨɬɞɟɥɚ ɛɢɪɠɢ. Ɉɫɧɨɜɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɋɆɈ ɹɜɥɹɸɬɫɹ: ɜɯɨɞɹɳɢɣ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ, ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ, ɨɛɫɥɭɠɢɜɚɸɳɢɟ ɭɫɬɪɨɣɫɬɜɚ (ɤɚɧɚɥɵ) ɢ ɜɵɯɨɞɹɳɢɣ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ (ɪɢɫ. 1.4). 40

Ɉɱɟɪɟɞɢ ɬɪɟɛɨɜɚɧɢɣ ɢ ɤɚɧɚɥɵ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɛɪɚɡɭɸɬ ɨɛɫɥɭɠɢɜɚɸɳɭɸ ɫɢɫɬɟɦɭ. ɂɫɬɨɱɧɢɤɢ ɬɪɟɛɨɜɚɧɢɣ ɜ ɫɢɫɬɟɦɭ ɧɟ ɜɤɥɸɱɚɸɬɫɹ. ȼɨɡɦɨɠɧɵ ɫɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɵɯ ɨɱɟɪɟɞɢ ɨɬɫɭɬɫɬɜɭɸɬ. ȼɯɨɞɹɳɢɣ ɩɨɬɨɤ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɱɢɫɥɨɦ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɫɢɫɬɟɦɭ ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ. Ɍɪɟɛɨɜɚɧɢɹ ɦɨɝɭɬ ɩɨɫɬɭɩɚɬɶ ɪɚɜɧɨɦɟɪɧɨ ɢ ɧɟɪɚɜɧɨɦɟɪɧɨ. ɉɪɢɦɟɪɨɦ ɜɯɨɞɹɳɟɝɨ ɩɨɬɨɤɚ ɧɚ ɪɵɧɤɟ ɢɥɢ ɛɢɪɠɟ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ

ɂɫɬɨɱɧɢɤ ɬɪɟɛɨɜɚɧɢɣ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ

ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. ȼɯɨɞɹɳɢɣ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ

ɋɂɋɌȿɆȺ ɆȺɋɋɈȼɈȽɈ ɈȻɋɅɍɀɂȼȺɇɂə Ɉɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ, ɨɠɢɞɚɸɳɢɯ ɨɛɫɥɭɠɢɜɚɧɢɹ

Ɉɛɫɥɭɠɢɜɚɸɳɢɟ ɤɚɧɚɥɵ ɉɨɬɨɤ ɨɬɤɚɡɨɜ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ

ɉɨɬɨɤ ɨɛɫɥɭɠɟɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ

Ɋɢɫɭɧɨɤ 1.4 - Ɉɫɧɨɜɧɵɟ ɷɥɟɦɟɧɬɵ ɫɢɫɬɟɦɵ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ

ȼ ɤɚɠɞɨɣ ɫɢɫɬɟɦɟ ɨɛɫɥɭɠɢɜɚɧɢɹ ɢɦɟɸɬɫɹ ɨɛɫɥɭɠɢɜɚɸɳɢɟ ɷɥɟɦɟɧɬɵ, ɢɯ ɧɚɡɵɜɚɸɬ ɤɚɧɚɥɚɦɢ ɨɛɫɥɭɠɢɜɚɧɢɹ. ɂɦɢ ɦɨɝɭɬ ɛɵɬɶ ɪɚɛɨɬɧɢɤɢ ɛɢɪɠɢ ɬɪɭɞɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɡɚɩɪɨɫ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɢɥɢ ɬɟɯɧɢɱɟɫɤɢɟ ɭɫɬɪɨɣɫɬɜɚ. ȼɵɯɨɞɹɳɢɣ ɩɨɬɨɤ - ɷɬɨ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɤɢɞɚɸɳɢɯ ɫɢɫɬɟɦɭ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɜ ɜɵɯɨɞɹɳɟɦ ɩɨɬɨɤɟ ɩɨ ɜɪɟɦɟɧɢ ɡɚɜɢɫɢɬ ɨɬ ɩɥɨɬɧɨɫɬɢ ɜɯɨɞɹɳɟɝɨ ɩɨɬɨɤɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɪɚɛɨɬɵ ɤɚɧɚɥɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫɢɫɬɟɦɵ. ȼ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹɯ ɜɵɯɨɞɹɳɢɣ ɩɨɬɨɤ ɫɥɭɠɢɬ ɜɯɨɞɹɳɢɦ ɩɨɬɨɤɨɦ ɞɥɹ ɞɪɭɝɢɯ ɤɚɧɚɥɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɬɪɟɛɨɜɚɧɢɟ 41

ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ, ɩɪɨɣɞɹ ɨɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɟ ɩɟɪɜɢɱɧɨɝɨ ɩɪɢɟɦɚ, ɩɨɩɚɞɚɟɬ ɜ ɨɬɞɟɥ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɚ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ⱦɥɹ ɨɛɴɟɤɬɢɜɧɨɣ ɨɰɟɧɤɢ ɤɚɱɟɫɬɜɚ ɪɚɛɨɬɵ ɫɢɫɬɟɦ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜɚɠɧɨ ɩɪɚɜɢɥɶɧɨ

ɜɵɛɪɚɬɶ

ɩɨɤɚɡɚɬɟɥɢ

ɷɮɮɟɤɬɢɜɧɨɫɬɢ

ɟɺ

ɪɚɛɨɬɵ.

Ɉɫɧɨɜɧɵɦ

ɩɨɤɚɡɚɬɟɥɟɦ ɪɚɛɨɬɵ ɨɛɫɥɭɠɢɜɚɸɳɟɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɟɺ ɩɪɨɩɭɫɤɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ. Ʉɪɨɦɟ ɬɨɝɨ, ɪɚɛɨɬɚ ɫɢɫɬɟɦ ɱɚɫɬɨ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɬɚɤɢɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ, ɤɚɤ ɫɪɟɞɧɢɣ ɩɪɨɰɟɧɬ ɨɬɤɚɡɨɜ, ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɩɪɨɫɬɨɹ ɤɚɧɚɥɨɜ, ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɨɱɟɪɟɞɢ, ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɜ ɨɱɟɪɟɞɢ ɢ ɬ. ɞ. Ʉɚɠɞɨɣ ɢɡ ɫɢɫɬɟɦ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫɜɨɣɫɬɜɟɧɧɚ ɨɩɪɟɞɟɥɺɧɧɚɹ ɨɪɝɚɧɢɡɚɰɢɹ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɟ ɫ ɷɬɨɣ ɨɪɝɚɧɢɡɚɰɢɟɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢ ɯɚɪɚɤɬɟɪ ɡɚɞɚɱ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ. ɑɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ. ȿɺ ɩɨɥɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɫɥɭɠɢɬ ɡɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɟ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɦɧɨɝɨɤɪɚɬɧɨ

ɩɨɜɬɨɪɹɸɳɢɯɫɹ

ɩɪɨɰɟɫɫɨɜ

ɩɨɡɜɨɥɹɸɬ ɭɫɬɚɧɨɜɢɬɶ ɨɩɪɟɞɟɥɺɧɧɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɧɚɛɥɸɞɚɟɦɵɯ ɹɜɥɟɧɢɣ, ɜ ɱɚɫɬɧɨɫɬɢ, ɜɵɹɜɢɬɶ ɡɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ [27, 92]. Ɂɚɤɨɧɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ

ɫɥɭɱɚɣɧɨɣ

ɩɨɥɨɠɢɬɟɥɶɧɨɣ

ɜɟɥɢɱɢɧɵ

ɨɩɪɟɞɟɥɹɸɬɫɹ

ɜ

ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɚɪɢɚɰɢɢ [7]. ȼ ɱɚɫɬɧɨɫɬɢ, ɩɨɫɬɭɩɥɟɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɩɨɞɱɢɧɟɧɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ, ɚ ɨɛɫɥɭɠɢɜɚɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɫɩɟɰɢɚɥɢɫɬɚɦɢ ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ ɪɚɫɩɪɟɞɟɥɟɧɨ ɪɚɜɧɨɦɟɪɧɨ. Ɋɚɜɧɨɦɟɪɧɵɦ ɹɜɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɟɣ ɧɟɩɪɟɪɵɜɧɨɣ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ X, ɤɨɬɨɪɨɦɭ ɩɪɢɧɚɞɥɟɠɚɬ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ X ɧɚ ɢɧɬɟɪɜɚɥɟ (a, b), ɚ ɩɥɨɬɧɨɫɬɶ ɫɨɯɪɚɧɹɟɬ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ, ɬ. ɟ. f ( x )

1 ; ɜɧɟ ɷɬɨɝɨ ba

ɢɧɬɟɪɜɚɥɚ f(x)=0 [23]. Ɉɞɧɨɣ ɢɡ ɜɚɠɧɟɣɲɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɛɫɥɭɠɢɜɚɸɳɢɯ ɭɫɬɪɨɣɫɬɜ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬ

ɩɪɨɩɭɫɤɧɭɸ

ɫɩɨɫɨɛɧɨɫɬɶ

ɜɫɟɣ

ɫɢɫɬɟɦɵ,

ɹɜɥɹɟɬɫɹ

ɜɪɟɦɹ

ɨɛɫɥɭɠɢɜɚɧɢɹ [45]. ȼɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɜ ɤɚɧɚɥɟ 42

ɨɛɫɥɭɠɢɜɚɧɢɹ)

ɹɜɥɹɟɬɫɹ

ɫɥɭɱɚɣɧɨɣ

ɜɟɥɢɱɢɧɨɣ,

ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ

ɩɨ

ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɜɟɪɨɹɬɧɨɫɬɟɣ) [19] g (t )

Pe Pt , t ! 0; ® t d 0. ¯0,

(1.26)

ȼɟɥɢɱɢɧɭ P ɧɚɡɵɜɚɸɬ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ɂɧɚɱɟɧɢɟ G(t) ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ 1 e Pt , t ! 0; g x dx ( ) ® ³ t d 0, ¯0, f t

G (t )

(1.27)

ɪɚɜɧɨ ɜɟɪɨɹɬɧɨɫɬɢ ɬɨɝɨ, ɱɬɨ ɤ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ t ɨɛɫɥɭɠɢɜɚɧɢɟ ɬɪɟɛɨɜɚɧɢɹ ɛɭɞɟɬ ɡɚɜɟɪɲɟɧɨ (ɤɚɧɚɥ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɫɜɨɛɨɞɢɬɫɹ). ȼɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ - ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɢɡɦɟɧɹɬɶɫɹ ɜ ɛɨɥɶɲɨɦ ɞɢɚɩɚɡɨɧɟ. Ɉɧɚ ɡɚɜɢɫɢɬ ɤɚɤ ɨɬ ɫɬɚɛɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɫɚɦɢɯ ɨɛɫɥɭɠɢɜɚɸɳɢɯ ɭɫɬɪɨɣɫɬɜ, ɬɚɤ ɢ ɨɬ ɪɚɡɥɢɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ, ɩɨɫɬɭɩɚɸɳɢɯ ɜ ɫɢɫɬɟɦɭ, ɬɪɟɛɨɜɚɧɢɣ. ȼɪɟɦɹ ɨɠɢɞɚɧɢɹ (ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɱɟɪɟɞɢ, ɟɫɥɢ ɩɨɫɥɟɞɧɹɹ ɫɭɳɟɫɬɜɭɟɬ) ɫɱɢɬɚɸɬ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɜɟɪɨɹɬɧɨɫɬɟɣ) [19] h(t )

Qe Qt , t ! 0; ® t d 0. ¯0,

(1.28)

ɝɞɟ Q - ɜɟɥɢɱɢɧɚ, ɨɛɪɚɬɧɚɹ ɫɪɟɞɧɟɦɭ ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ. Ɂɧɚɱɟɧɢɟ H(t) ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ 1 e Qt , t ! 0; h x dx ( ) ® ³ t d 0, ¯0, f t

H (t )

(1.29)

ɪɚɜɧɨ ɜɟɪɨɹɬɧɨɫɬɢ ɬɨɝɨ, ɱɬɨ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɧɚɱɧɟɬɫɹ ɨɛɫɥɭɠɢɜɚɧɢɟ ɬɪɟɛɨɜɚɧɢɹ. ɉɪɢQ o ɫɢɫɬɟɦɚ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫ ɨɠɢɞɚɧɢɟɦ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɱɢɫɬɭɸ ɫɢɫɬɟɦɭ ɫ ɨɬɤɚɡɚɦɢ, ɚ ɩɪɢ Q o 0 ɫɢɫɬɟɦɚ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫ ɨɠɢɞɚɧɢɟɦ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɱɢɫɬɭɸ ɫɢɫɬɟɦɭ ɫ ɨɠɢɞɚɧɢɟɦ. ȼ ɤɚɱɟɫɬɜɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɋɆɈ ɦɨɠɧɨ, ɜɵɛɪɚɬɶ ɬɪɢ ɨɫɧɨɜɧɵɟ ɝɪɭɩɩɵ (ɨɛɵɱɧɨ ɫɪɟɞɧɢɯ) ɩɨɤɚɡɚɬɟɥɟɣ: 43

1. ɉɨɤɚɡɚɬɟɥɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɋɆɈ • Ⱥɛɫɨɥɸɬɧɚɹ

ɩɪɨɩɭɫɤɧɚɹ

ɫɩɨɫɨɛɧɨɫɬɶ

ɋɆɈ —

ɫɪɟɞɧɟɟ

ɱɢɫɥɨ

ɬɪɟɛɨɜɚɧɢɣ, ɤɨɬɨɪɵɟ ɦɨɠɟɬ ɨɛɫɥɭɠɢɬɶ ɋɆɈ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ. • Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɩɭɫɤɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɋɆɈ — ɨɬɧɨɲɟɧɢɟ ɫɪɟɞɧɟɝɨ ɱɢɫɥɚ ɬɪɟɛɨɜɚɧɢɣ, ɨɛɫɥɭɠɢɜɚɟɦɵɯ ɋɆɈ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɤ ɫɪɟɞɧɟɦɭ ɱɢɫɥɭ ɩɨɫɬɭɩɢɜɲɢɯ ɬɪɟɛɨɜɚɧɢɣ ɡɚ ɷɬɨ ɠɟ ɜɪɟɦɹ. • ɋɪɟɞɧɹɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɟɪɢɨɞɚ ɡɚɧɹɬɨɫɬɢ ɋɆɈ. • Ʉɨɷɮɮɢɰɢɟɧɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɋɆɈ — ɫɪɟɞɧɹɹ ɞɨɥɹ ɜɪɟɦɟɧɢ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɋɆɈ ɡɚɧɹɬɚ ɨɛɫɥɭɠɢɜɚɧɢɟɦ ɬɪɟɛɨɜɚɧɢɣ, ɢ ɬ.ɩ. 2. ɉɨɤɚɡɚɬɟɥɢ ɤɚɱɟɫɬɜɚ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ • ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɱɟɪɟɞɢ. • ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɋɆɈ. • ȼɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɬɪɟɛɨɜɚɧɢɸ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɛɟɡ ɨɠɢɞɚɧɢɹ. • ȼɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɨɫɬɭɩɢɜɲɟɟ ɬɪɟɛɨɜɚɧɢɟ ɧɟɦɟɞɥɟɧɧɨ ɛɭɞɟɬ ɩɪɢɧɹɬɨ ɤ ɨɛɫɥɭɠɢɜɚɧɢɸ. • Ɂɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɱɟɪɟɞɢ. • Ɂɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɢ ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɋɆɈ. • ɋɪɟɞɧɟɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɱɟɪɟɞɢ. • ɋɪɟɞɧɟɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɋɆɈ, ɢ ɬ.ɩ. 3.

ɉɨɤɚɡɚɬɟɥɢ

ɷɮɮɟɤɬɢɜɧɨɫɬɢ

ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ

ɩɚɪɵ

«ɋɆɈ

-

ɩɨɬɪɟɛɢɬɟɥɶ», ɝɞɟ ɩɨɞ ɩɨɬɪɟɛɢɬɟɥɟɦ ɩɨɧɢɦɚɸɬ ɜɫɸ ɫɨɜɨɤɭɩɧɨɫɬɶ ɬɪɟɛɨɜɚɧɢɣ ɢɥɢ ɧɟɤɢɣ ɢɯ ɢɫɬɨɱɧɢɤ (ɧɚɩɪɢɦɟɪ, ɫɪɟɞɧɢɣ ɞɨɯɨɞ, ɩɪɢɧɨɫɢɦɵɣ ɋɆɈ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɢ ɬ.ɩ.) Ɍɪɟɬɶɹ ɝɪɭɩɩɚ ɩɨɤɚɡɚɬɟɥɟɣ ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɥɟɡɧɨɣ ɜ ɬɟɯ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɧɟɤɨɬɨɪɵɣ ɞɨɯɨɞ, ɩɨɥɭɱɚɟɦɵɣ ɨɬ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ, ɢ ɡɚɬɪɚɬɵ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ ɢɡɦɟɪɹɸɬɫɹ ɜ ɨɞɧɢɯ ɢ ɬɟɯ ɠɟ ɟɞɢɧɢɰɚɯ. ɗɬɢ ɩɨɤɚɡɚɬɟɥɢ ɨɛɵɱɧɨ ɧɨɫɹɬ ɜɩɨɥɧɟ ɤɨɧɤɪɟɬɧɵɣ ɯɚɪɚɤɬɟɪ ɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɩɟɰɢɮɢɤɨɣ ɋɆɈ, ɨɛɫɥɭɠɢɜɚɟɦɵɯ ɬɪɟɛɨɜɚɧɢɣ ɢ ɞɢɫɰɢɩɥɢɧɨɣ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɷɬɨɬ ɫɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ ɢɡɭɱɢɬɶ, ɬ. ɟ. ɩɨɫɬɪɨɢɬɶ ɢ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɟɝɨ 44

ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ. ɋɆɈ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɬɢɩɵ ɢɥɢ ɤɥɚɫɫɵ ɩɨ ɪɹɞɭ ɩɪɢɡɧɚɤɨɜ (ɪɢɫ. 1.5). ɋɆɈ Ɉɞɧɨɤɚɧɚɥɶɧɵɟ

Ɇɧɨɝɨɤɚɧɚɥɶɧɵɟ

Ɉɬɤɪɵɬɵɟ

Ɂɚɦɤɧɭɬɵɟ

ɋ ɨɬɤɚɡɚɦɢ

ɋ ɨɱɟɪɟɞɹɦɢ

ɋ ɨɝɪɚɧɢɱɟɧɧɵɦ ɜɪɟɦɟɧɟɦ ɨɠɢɞɚɧɢɹ

ɋ ɨɝɪɚɧɢɱɟɧɧɨɣ ɞɥɢɧɨɣ ɨɱɟɪɟɞɢ

Ȼɟɡ ɩɪɢɨɪɢɬɟɬɨɜ

ɋ ɩɪɢɨɪɢɬɟɬɚɦɢ

ɋ ɚɛɫɨɥɸɬɧɵɦɢ ɩɪɢɨɪɢɬɟɬɚɦɢ

ɋ ɧɟɨɝɪɚɧɢɱɟɧɧɨɣ ɞɥɢɧɨɣ ɨɱɟɪɟɞɢ

ɋ ɨɬɧɨɫɢɬɟɥɶɧɵɦɢ ɩɪɢɨɪɢɬɟɬɚɦɢ

Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɩɨɪɹɞɤɟ ɩɨɫɬɭɩɥɟɧɢɹ

Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɫɥɭɱɚɣɧɨɦ ɩɨɪɹɞɤɟ

Ɋɢɫɭɧɨɤ 1.5 - Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɫɢɫɬɟɦ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ

ȼ ɋɆɈ ɫ ɨɱɟɪɟɞɶɸ ɬɪɟɛɨɜɚɧɢɟ, ɩɪɢɲɟɞɲɟɟ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɤɨɝɞɚ ɜɫɟ ɤɚɧɚɥɵ ɨɛɫɥɭɠɢɜɚɧɢɹ ɡɚɧɹɬɵ, ɧɟ ɭɯɨɞɢɬ ɧɟ ɨɛɫɥɭɠɟɧɧɨɣ, ɚ ɫɬɚɧɨɜɢɬɫɹ ɜ ɨɱɟɪɟɞɶ ɢ ɨɠɢɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɢ ɛɵɬɶ ɨɛɫɥɭɠɟɧɧɨɣ. ȼ ɩɪɚɤɬɢɱɟɫɤɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɵ ɋɆɈ ɫ ɨɱɟɪɟɞɹɦɢ. ȼ ɱɚɫɬɧɨɫɬɢ, ɛɢɪɠɭ ɬɪɭɞɚ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɋɆɈ ɫ ɨɱɟɪɟɞɶɸ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɪɝɚɧɢɡɚɰɢɢ ɨɱɟɪɟɞɢ - ɨɝɪɚɧɢɱɟɧɚ ɨɧɚ ɢɥɢ ɧɟ ɨɝɪɚɧɢɱɟɧɚ - ɋɆɈ ɫ ɨɱɟɪɟɞɶɸ ɩɨɞɪɚɡɞɟɥɹɸɬɫɹ ɧɚ ɪɚɡɧɵɟ ɜɢɞɵ. Ɉɝɪɚɧɢɱɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɩɨ ɞɥɢɧɟ ɨɱɟɪɟɞɢ ɢɥɢ ɩɨ ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ. ɋɆɈ

ɤɥɚɫɫɢɮɢɰɢɪɭɸɬɫɹ

ɬɚɤɠɟ

ɩɨ

ɞɢɫɰɢɩɥɢɧɟ

ɨɛɫɥɭɠɢɜɚɧɢɹ

–

ɬɪɟɛɨɜɚɧɢɹ ɦɨɝɭɬ ɨɛɫɥɭɠɢɜɚɬɶɫɹ ɛɟɡ ɩɪɢɨɪɢɬɟɬɨɜ ɜ ɩɨɪɹɞɤɟ ɩɨɫɬɭɩɥɟɧɢɹ, ɥɢɛɨ ɜ ɫɥɭɱɚɣɧɨɦ ɩɨɪɹɞɤɟ. ɑɚɫɬɨ ɜɫɬɪɟɱɚɟɬɫɹ ɨɛɫɥɭɠɢɜɚɧɢɟ ɫ ɩɪɢɨɪɢɬɟɬɚɦɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɩɨɪɹɞɨɤ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɡɚɜɢɫɢɬ ɤɚɤ ɨɬ ɜɪɟɦɟɧɢ ɢɯ 45

ɩɨɫɬɭɩɥɟɧɢɹ, ɬɚɤ ɢ ɨɬ ɢɯ ɤɚɬɟɝɨɪɢɢ. ɉɪɢɨɪɢɬɟɬ ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɚɛɫɨɥɸɬɧɵɦ, ɬɚɤ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɦ. ɉɪɢ ɚɛɫɨɥɸɬɧɵɯ ɩɪɢɨɪɢɬɟɬɚɯ ɬɪɟɛɨɜɚɧɢɣ ɜ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɞɥɹ ɧɟɦɟɞɥɟɧɧɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɨɫɬɭɩɢɜɲɟɝɨ ɬɪɟɛɨɜɚɧɢɹ ɜɵɫɨɤɨɝɨ ɩɪɢɨɪɢɬɟɬɚ ɧɟɬ ɫɜɨɛɨɞɧɨɝɨ ɨɛɫɥɭɠɢɜɚɸɳɟɝɨ ɤɚɧɚɥɚ ɩɪɨɢɫɯɨɞɢɬ ɨɫɜɨɛɨɠɞɟɧɢɟ ɨɞɧɨɝɨ ɢɡ ɤɚɧɚɥɨɜ ɋɆɈ, ɡɚɧɹɬɵɯ ɨɛɫɥɭɠɢɜɚɧɢɟɦ ɬɪɟɛɨɜɚɧɢɹ ɛɨɥɟɟ ɧɢɡɤɨɝɨ ɩɪɢɨɪɢɬɟɬɚ, ɢ ɷɬɨɬ ɤɚɧɚɥ ɩɪɟɞɨɫɬɚɜɥɹɟɬɫɹ ɩɨɫɬɭɩɢɜɲɟɦɭ ɬɪɟɛɨɜɚɧɢɸ ɫ ɛɨɥɟɟ ɜɵɫɨɤɢɦ ɩɪɢɨɪɢɬɟɬɨɦ. ɉɪɟɪɜɚɜɲɟɟɫɹ

ɨɛɫɥɭɠɢɜɚɧɢɟ

ɬɪɟɛɨɜɚɧɢɹ

ɧɢɡɤɨɝɨ

ɩɪɢɨɪɢɬɟɬɚ

ɩɨɫɥɟ

ɨɫɜɨɛɨɠɞɟɧɢɹ ɨɞɧɨɝɨ ɢɡ ɨɛɫɥɭɠɢɜɚɸɳɢɯ ɤɚɧɚɥɨɜ ɋɆɈ ɦɨɠɟɬ ɛɵɬɶ ɧɚɱɚɬɨ ɫ ɧɚɱɚɥɚ ɢɥɢ ɫ ɬɨɝɨ ɦɟɫɬɚ, ɧɚ ɤɨɬɨɪɨɦ ɩɪɟɪɜɚɥɨɫɶ ɟɟ ɨɛɫɥɭɠɢɜɚɧɢɟ. ɋɭɬɶ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɩɪɢɨɪɢɬɟɬɨɜ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɩɨɫɬɭɩɢɜɲɟɦɭ ɬɪɟɛɨɜɚɧɢɸ, ɭ ɤɨɬɨɪɨɝɨ ɩɪɢɨɪɢɬɟɬ ɜɵɲɟ, ɱɟɦ ɭ ɬɪɟɛɨɜɚɧɢɣ ɭɠɟ ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɱɟɪɟɞɢ, ɩɪɟɞɨɫɬɚɜɥɹɟɬɫɹ ɩɟɪɜɨɟ ɦɟɫɬɨ ɜ ɨɱɟɪɟɞɢ ɩɟɪɟɞ ɬɪɟɛɨɜɚɧɢɹɦɢ ɛɨɥɟɟ ɧɢɡɤɨɝɨ ɩɪɢɨɪɢɬɟɬɚ ɢ ɩɪɢɧɭɞɢɬɟɥɶɧɨɝɨ ɨɫɜɨɛɨɠɞɟɧɢɹ ɨɛɫɥɭɠɢɜɚɸɳɟɝɨ ɤɚɧɚɥɚ ɞɥɹ ɧɟɦɟɞɥɟɧɧɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɪɢɲɟɞɲɟɝɨ ɬɪɟɛɨɜɚɧɢɹ ɜɵɫɨɤɨɣ ɤɚɬɟɝɨɪɢɢ ɧɟ ɞɟɥɚɟɬɫɹ. ɉɪɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɩɪɢɨɪɢɬɟɬɚɯ ɨɛɫɥɭɠɢɜɚɧɢɟ ɜɫɹɤɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɩɨɫɥɟ ɟɝɨ ɧɚɱɚɥɚ ɜɫɟɝɞɚ ɞɨɜɨɞɢɬɫɹ ɞɨ ɤɨɧɰɚ ɛɟɡ ɩɪɟɪɵɜɚɧɢɹ. ɋɢɫɬɟɦɵ

ɦɚɫɫɨɜɨɝɨ

ɨɛɫɥɭɠɢɜɚɧɢɹ

ɦɨɠɧɨ

ɤɥɚɫɫɢɮɢɰɢɪɨɜɚɬɶ

ɩɨ

ɥɨɝɢɱɟɫɤɨɣ ɫɬɪɭɤɬɭɪɟ ɩɪɨɰɟɫɫɚ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɱɢɫɥɨ ɩɪɢɛɨɪɨɜ, ɩɨɪɹɞɨɤ ɩɪɢɨɪɢɬɟɬɨɜ, ɜɨɡɦɨɠɧɨɫɬɶ ɨɠɢɞɚɧɢɹ ɢ ɬ. ɩ.), ɚ ɬɚɤɠɟ ɩɨ ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɩɪɟɞɩɨɫɵɥɤɚɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɯɨɞɹɳɟɝɨ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ɉɛɳɟɩɪɢɧɹɬɨɣ ɹɜɥɹɟɬɫɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɤɥɚɫɫɢɱɟɫɤɢɯ ɫɢɫɬɟɦ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɩɪɟɞɥɨɠɟɧɧɚɹ Ⱦ. Ʉɟɧɞɚɥɥɨɦ [24]. 1.7. ȼɵɜɨɞɵ

ȼ ɞɚɧɧɨɣ ɝɥɚɜɟ: 1. ɉɪɨɜɟɞɟɧ ɚɧɚɥɢɡ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɨɞɧɨɣ ɨɬɪɚɫɥɢ, ɜ ɤɚɱɟɫɬɜɟ ɛɚɡɨɜɨɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ ɤɨɬɨɪɨɣ ɜɵɫɬɭɩɚɸɬ ɧɟɥɢɧɟɣɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ. 46

2.

Ɉɛɨɫɧɨɜɚɧɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɩɨɫɬɪɨɟɧɢɹ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ

ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ, ɩɨɡɜɨɥɹɸɳɟɣ ɨɰɟɧɢɬɶ ɫɢɬɭɚɰɢɸ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɛɭɞɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɟɧɞɟɧɰɢɢ ɪɚɡɜɢɬɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ. 3. ɉɪɢɜɟɞɟɧɵ

ɧɟɨɛɯɨɞɢɦɵɟ

ɬɟɨɪɟɬɢɱɟɫɤɢɟ

ɫɜɟɞɟɧɢɹ

ɢɡ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɬɟɨɪɢɢ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ.

47

ɬɟɨɪɢɢ

ȽɅȺȼȺ 2. ɆȺɌȿɆȺɌɂɑȿɋɄȺə ɆɈȾȿɅɖ ɋȺɆɈɈɊȽȺɇɂɁȺɐɂɂ ɊɕɇɄȺ ɌɊɍȾȺ 2.1. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ

ɉɪɟɞɥɨɠɟɧɧɚɹ Ⱥ.ɇ. ȼɚɫɢɥɶɟɜɵɦ [12] ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ ɨɬɞɟɥɶɧɨɣ ɨɬɪɚɫɥɢ ɩɨɡɜɨɥɹɟɬ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɩɪɢɧɹɬɢɹ ɬɟɯ ɢɥɢ ɢɧɵɯ ɭɩɪɚɜɥɟɧɱɟɫɤɢɯ ɪɟɲɟɧɢɣ ɢ ɫɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɪɚɡɜɢɬɢɹ ɫɨɛɵɬɢɣ ɧɚ ɪɵɧɤɟ ɞɥɹ ɨɬɞɟɥɶɧɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ. ȼɯɨɞɹɳɢɟ ɜ ɞɚɧɧɭɸ ɦɨɞɟɥɶ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ ɨɬɤɪɵɜɚɸɬ ɜɨɡɦɨɠɧɨɫɬɢ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɥɢɹɧɢɹ ɧɚ ɦɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɪɹɞɚ ɫɭɛɴɟɤɬɢɜɧɵɯ ɮɚɤɬɨɪɨɜ. Ɉɛɨɛɳɢɦ ɪɟɡɭɥɶɬɚɬɵ [12] ɧɚ ɫɥɭɱɚɣ n ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ [38, 83, 84]. i Ɉɛɨɡɧɚɱɢɦ N 1 ( t ) - ɨɛɳɟɟ ɱɢɫɥɨ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɡɚɧɹɬɵɯ ɜ i-ɨɣ ɨɬɪɚɫɥɢ i ɷɤɨɧɨɦɢɤɢ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t; N 2 ( t ) - ɱɢɫɥɨ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɪɚɛɨɱɢɯ,

ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɜɥɟɱɟɧɵ ɞɥɹ ɪɚɛɨɬɵ ɜ i-ɨɣ ɨɬɪɚɫɥɢ ɢ ɤɨɬɨɪɵɟ ɜ ɦɨɦɟɧɬ n

ɜɪɟɦɟɧɢ t ɹɜɥɹɸɬɫɹ ɛɟɡɪɚɛɨɬɧɵɦɢ;

2

¦¦ N

(i ) k

N

const - ɟɦɤɨɫɬɶ ɪɵɧɤɚ

i 1 k 1

(i , j ) - ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɛɟɡɪɚɛɨɬɧɵɣ ɪɚɛɨɱɟɣ ɫɢɥɵ n ɨɬɪɚɫɥɟɣ; W1

ɫɩɟɰɢɚɥɢɫɬ i-ɨɣ ɨɬɪɚɫɥɢ ɦɨɠɟɬ ɧɚɣɬɢ ɪɚɛɨɬɭ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ ɜ j-ɨɣ ɨɬɪɚɫɥɢ (i ) ɡɚ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt; W2 - ɜɟɪɨɹɬɧɨɫɬɶ ɭɜɨɥɶɧɟɧɢɹ ɪɚɛɨɬɚɸɳɟɝɨ

ɫɩɟɰɢɚɥɢɫɬɚ i-ɨɣ ɨɬɪɚɫɥɢ ɡɚ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt; i,j =1,…,n, t [0;f) . n

Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ

¦W

(i, j ) 1

z 1 , i, j = 1,…,n.

i 1

ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t=0 ɱɢɫɥɨ ɫɩɟɰɢɚɥɢɫɬɨɜ, (i ) , ɚ ɱɢɫɥɨ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɪɚɛɨɱɢɯ, ɡɚɧɹɬɵɯ ɜ i-ɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ, ɪɚɜɧɨ N10

48

ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɜɥɟɱɟɧɵ ɞɥɹ ɪɚɛɨɬɵ ɜ j-ɨɣ ɨɬɪɚɫɥɢ ɢ ɤɨɬɨɪɵɟ ɜ ɦɨɦɟɧɬ (j) ɜɪɟɦɟɧɢ t ɹɜɥɹɸɬɫɹ ɛɟɡɪɚɛɨɬɧɵɦɢ ɪɚɜɧɨ N 20 ,

(j) N1(i)( 0 ) N10(i) , N 2(j)( 0 ) N 20 , i,j=1,…,n.

ɬ. ɟ.

(2.1)

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɜɜɟɞɟɧɧɵɦɢ ɜɵɲɟ ɨɛɨɡɧɚɱɟɧɢɹɦɢ ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɫ ɡɚɞɚɧɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (2.1), ɨɩɢɫɵɜɚɸɳɭɸ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ n ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ: n n dN1(1) (t) (1,1) (1) (1) (1) (i ) (i ) N t W N t W N t W N2(i ) (t)W1(i,1) , ( ) ( ) ( ) ¦ ¦ 1 2 1 2 1 2 ° dt i 2 i 2 ° ( 2) n n °dN1 (t) (1) (1) ( 2) ( 2) (i ) (i ) (1) (1,2) ( 2) ( 2,2) N t W N t W N t W N t W N t W N2(i ) (t)W1(i,2) , ( ) ( ) ( ) ( ) ( ) ¦ ¦ ° 1 2 1 2 1 2 2 1 2 1 i 3 i 3 ° dt °....................................................................................................................................................., ° ( n) n1 n1 (i ) (i ) (n) ( n) °dN1 (t) N1 (t)W2 N1 (t)W2 ¦N2(i ) (t)W1(i,n) N2(n) (t)W1(n,n) , ¦ °° dt i 1 i 1 ® (1) n n n (i ) (i ) (1) (1,i ) °dN2 (t) N1 (t)W2 N2 (t)¦W1 ¦N2(i ) (t)W1(i,1) , ¦ ° dt i 1 i 1 i 2 ° ( 2) n n n (i ) (i ) (1) (1,2) ( 2) ( 2,i ) °dN2 (t) N1 (t)W2 N2 (t)W1 N2 (t)¦W1 ¦N2(i ) (t)W1(i,2) , ¦ ° dt i 1 i 1 i 3 ° °................................................................................................................., °dN(n) (t) n n1 n (i ) (i ) (i ) (i ,n) ° 2 N1 (t)W2 ¦N2 (t)W1 ¦N2(n) (t)W1(n,i ) . ¦ °¯ dt i 1 i 1 i 1

(2.2) Ȼɭɞɟɦ ɫɱɢɬɚɬɶ ɜɟɪɨɹɬɧɨɫɬɢ W2( i ) , W1( i , j )

ɩɨɫɬɨɹɧɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ,

i,j =1,…,n. (k ) ɍɱɢɬɵɜɚɹ, ɱɬɨ ɜɟɪɨɹɬɧɨɫɬɢ W2 ɩɪɢɧɢɦɚɸɬ ɧɭɥɟɜɵɟ ɡɧɚɱɟɧɢɹ ɜɨ ɜɫɟɯ

ɫɥɭɱɚɹɯ, ɤɪɨɦɟ k-ɨɝɨ ɡɚ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt ɞɥɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɢɡɦɟɧɟɧɢɹ N 1i ( t ) (i,k =1,…,n); ɚ ɜɟɪɨɹɬɧɨɫɬɢ W1(i , j ) ɩɪɢɧɢɦɚɸɬ ɧɭɥɟɜɵɟ ɡɧɚɱɟɧɢɹ ɜɨ ɜɫɟɯ ɫɥɭɱɚɹɯ, ɤɪɨɦɟ i = j ɡɚ ɩɟɪɢɨɞ

ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt ɞɥɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɢɡɦɟɧɟɧɢɹ N 2i ( t ) (i, j, k =1,…,n) ɫɢɫɬɟɦɚ (2.2) ɩɪɢɦɟɬ ɜɢɞ:

49

n dN 1(1) ( t ) (1) (1 ) (1 ) ( 1,1 ) ( ) ( ) N t W N t W N 2( i ) ( t )W1( i ,1) , ¦ 1 2 2 1 ° dt i 2 ° n ° dN 1( 2 ) ( t ) ( 2,2 ) (2) (2) (1) ( 1, 2 ) (2) ( ) ( ) ( ) N t W N t W N t W N 2( i ) ( t )W1( i , 2 ) , ¦ ° 1 1 2 2 1 2 i 3 ° dt °.......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ....., ° (n) n 1 ° dN 1 ( t ) N ( n ) ( t )W ( n ) N 2( i ) ( t )W1( i ,n ) N 2( n ) ( t )W1( n ,n ) , ¦ 1 2 °° dt i 1 ® (1 ) n n (i ) (i ) (1 ) ° dN 2 ( t ) (2.2ɚ) N 1 ( t )W 2 N 2 ( t ) ¦ W1(1,i ) , ¦ ° dt i 1 i 1 ° (2) n n (i ) (i ) (2) ° dN 2 ( t ) N ( t ) W N ( t ) W1( 2 ,i ) , ¦ ¦ 1 2 2 ° dt i 1 i 1 ° °.......... .......... .......... .......... .......... .......... .......... ., n ° dN ( n ) ( t ) n (i ) (i ) 2 ° N ( t ) W N 2( n ) ( t )W1( n ,i ) . ¦ ¦ 1 2 °¯ dt i 1 i 1

Ɍɚɤ ɤɚɤ ɥɸɛɚɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɡɚɜɟɞɨɦɨ ɧɟɫɟɬ ɜ ɫɟɛɟ ɩɨɝɪɟɲɧɨɫɬɶ (ɧɟɥɶɡɹ ɭɱɟɫɬɶ ɜɫɟ ɭɫɥɨɜɢɹ ɪɚɛɨɬɵ), ɬɨ ɢɫɫɥɟɞɨɜɚɧɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ ɹɜɥɹɟɬɫɹ ɨɞɧɨɣ ɢɡ ɜɚɠɧɵɯ ɩɪɨɰɟɞɭɪ ɜ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. ɍɫɬɨɣɱɢɜɨɫɬɶ (ɚɫɢɦɩɬɨɬɢɱɟɫɤɚɹ ɭɫɬɨɣɱɢɜɨɫɬɶ ɢɥɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ) ɫɢɫɬɟɦɵ

ɥɢɧɟɣɧɵɯ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ

ɫ

ɩɨɫɬɨɹɧɧɵɦɢ

ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ (2.2) ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɩɨɥɨɠɟɧɢɟɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɧɢɦɨɣ ɨɫɢ ɤɨɪɧɟɣ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ (2.2). ɋɨɝɥɚɫɧɨ ɬɟɪɦɢɧɨɥɨɝɢɢ [6] ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ (2.2) ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɵɦ ɬɨɝɞɚ ɢ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɟɝɨ ɤɨɪɧɢ Oj (j = 1,…,n) ɢɦɟɸɬ ɨɬɪɢɰɚɬɟɥɶɧɭɸ ɜɟɳɟɫɬɜɟɧɧɭɸ ɱɚɫɬɶ, ɬ. ɟ. ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɫɥɨɜɢɸ ReOj < 0, (ɚ ɡɧɚɱɢɬ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ (2.1), (2.2) ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɭɫɬɨɣɱɢɜɚ). ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ

ɜɵɱɢɫɥɟɧɢɟ

ɫɨɛɫɬɜɟɧɧɵɯ

ɡɧɚɱɟɧɢɣ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ (2.2) ɞɥɹ ɛɨɥɶɲɢɯ ɫɬɟɩɟɧɟɣ ɦɧɨɝɨɱɥɟɧɚ ɜɟɫɶɦɚ ɬɪɭɞɨɟɦɤɢɣ ɩɪɨɰɟɫɫ, ɬɪɟɛɭɸɳɢɣ ɡɧɚɱɢɬɟɥɶɧɵɯ

ɡɚɬɪɚɬ

ɜɪɟɦɟɧɢ.

ɉɪɢ

ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ. 50

ɷɬɨɦ

ɭɜɟɥɢɱɢɜɚɟɬɫɹ

ɩɨɝɪɟɲɧɨɫɬɶ

ɇɚ ɪɢɫɭɧɤɟ 2.1 ɩɪɟɞɫɬɚɜɥɟɧɚ ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɢɧɬɟɪɩɪɟɬɚɰɢɹ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ

ɥɢɧɟɣɧɵɯ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ

ɫ

ɩɨɫɬɨɹɧɧɵɦɢ

ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ.

O(t) İ

O1(t) O2(t)

0

t01

t02

t a)

O(t) İ

O1(t) O2(t)

0

t01

t02

t ɛ)

Ɋɢɫɭɧɨɤ 2.1 - Ɏɚɡɨɜɵɟ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ: ɚ) ɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ, ɛ) ɧɟɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ 2.2. Ɇɟɬɨɞɢɤɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ

ɍɤɚɠɟɦ ɭɫɥɨɜɢɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɡɚɞɚɱɢ (2.1), (2.2). ɉɪɟɞɩɨɥɨɠɟɧɢɟ, ɱɬɨ (i , j ) (i ) ɜɟɪɨɹɬɧɨɫɬɢ W2 , W1 ɹɜɥɹɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ, i,j =1,…,n, ɜɩɨɥɧɟ

ɩɪɢɟɦɥɟɦɨ ɫ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ [49]. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ W – ɦɚɬɪɢɰɭ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ (2.2). 51

Ɇɚɬɪɢɰɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ W ɢɦɟɟɬ ɜɢɞ:

W

· § W2( 1 ) 0 ... 0 W1( 2 ,1 ) W1(n,1) ... W1( 1,1 ) ¸ ¨ (2) ( 1,2 ) ( 2 ,2 ) (n,2) ¸ ¨0 -W2 ... 0 W1 W1 ... W1 ¸ ¨ ¸ ¨ .............................................................................................................. (n) ( 1,n) ( 2 ,n) (n,n) ¨0 ¸ 0 ... ... W2 W1 W1 W1 ¨ ¸ ... 0 ¨W2( 1 ) W2( 2 ) ... W2(n) -W1( 1,1 )-... W1( 1,n) 0 ¸ .(2.3) ¨ (1) ¸ (2) (n) 0 0 W1( 2 ,1 ) ... W1( 2 ,n) ... ¨W2 W2 ... W2 ¸ ¨ .............................................................................................................. ¸ ¨¨ ( 1 ) ¸ (2) (n) (n,1 ) (n,n) ¸ W W ... W 0 0 ... W ...-W 2 2 1 1 ¹ © 2

ɋɨɫɬɚɜɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɦɚɬɪɢɰɵ W: det (W–OI) = 0,

(2.4)

ɝɞɟ I – ɟɞɢɧɢɱɧɚɹ ɦɚɬɪɢɰɚ ɪɚɡɦɟɪɚ n x n. ɍɪɚɜɧɟɧɢɟ (2.4) ɷɤɜɢɜɚɥɟɧɬɧɨ ɭɪɚɜɧɟɧɢɸ [6] Pn(O) = a0 + a1O + … + anOn = 0, an = 1.

(2.5)

Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɩɪɢɛɥɢɠɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɨɥɢɧɨɦɨɜ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɢɯ ɩɨɪɹɞɤɨɜ ɦɨɠɟɬ ɩɨɬɪɟɛɨɜɚɬɶɫɹ ɝɪɨɦɚɞɧɵɣ ɡɚɩɚɫ ɡɧɚɤɨɜ ɜ ɡɧɚɱɟɧɢɹɯ ɮɭɧɤɰɢɢ, ɱɬɨ ɧɚ ɩɪɚɤɬɢɤɟ ɬɪɭɞɧɨ ɨɛɟɫɩɟɱɢɬɶ. ɇɟɨɫɬɨɪɨɠɧɨɟ ɨɤɪɭɝɥɟɧɢɟ ɜ ɩɪɨɰɟɫɫɟ ɢɯ ɜɵɱɢɫɥɟɧɢɹ ɦɨɠɟɬ ɧɚɪɭɲɢɬɶ ɢɯ ɜɡɚɢɦɧɭɸ

ɫɜɹɡɚɧɧɨɫɬɶ

ɢ

ɩɪɢɜɟɫɬɢ

ɡɚɬɟɦ

ɤ ɧɟɩɪɚɜɢɥɶɧɵɦ

ɡɧɚɱɟɧɢɹɦ

ɫɨɛɫɬɜɟɧɧɵɯ ɱɢɫɟɥ. ɍɫɬɨɣɱɢɜɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɧɟ ɜɵɱɢɫɥɹɹ ɟɝɨ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ. Ɂɧɚɹ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɦɚɬɪɢɰɵ W ɧɚ ɨɫɧɨɜɚɧɢɢ ɬɟɨɪɟɦɵ Ⱥ. ɋɬɨɞɨɥɚ (ɫɦ. ɩ. 1.5), ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ ɨɛ ɭɫɬɨɣɱɢɜɨɫɬɢ ɦɧɨɝɨɱɥɟɧɚ. ɉɨɥɨɠɢɬɟɥɶɧɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɟɫɬɶ ɧɟɨɛɯɨɞɢɦɨɟ, ɧɨ ɧɟ ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ. Ⱦɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ (2.5) ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ (ɤɪɢɬɟɪɢɣ ɊɚɭɫɚȽɭɪɜɢɰɚ (ɫɦ. ɩ. 1.5)), ɱɬɨɛɵ ɛɵɥɢ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ: '1 = ɚ1>0, ǻ 2

a1 a 0 a3 a 2

>0, …, ǻ n

ɚn ǻ n 1 >0.

ɗɬɨɬ ɤɪɢɬɟɪɢɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɢɡɭɱɟɧɢɹ ɚɫɢɦɩɬɨɬɢɱɟɫɤɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ 52

(2.1), (2.2). ɋ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɶ (2.1), (2.2) ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɭɪɨɜɧɟɦ ɡɚɧɹɬɨɫɬɢ (2.1) ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɨɬɤɥɨɧɟɧɢɹɯ ɨɬ (2.2) ɫɢɫɬɟɦɚ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɫɧɨɜɚ ɜɨɡɜɪɚɬɢɬɫɹ ɤ ɧɚɱɚɥɶɧɨɦɭ ɫɨɫɬɨɹɧɢɸ [74]. ȿɫɥɢ ɠɟ ɡɚɞɚɱɚ (2.1), (2.2)

ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɣ, ɬɨ ɞɚɠɟ ɧɟɛɨɥɶɲɢɟ

ɨɬɤɥɨɧɟɧɢɹ (2.1) ɨɛɹɡɚɬɟɥɶɧɨ ɩɪɢɜɟɞɭɬ ɤ ɞɪɭɝɨɦɭ ɫɨɨɬɧɨɲɟɧɢɸ ɱɢɫɥɚ ɛɟɡɪɚɛɨɬɧɵɯ ɢ ɡɚɧɹɬɵɯ ɧɚ ɩɪɨɢɡɜɨɞɫɬɜɟ ɜ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ. ɇɚ ɪɢɫ. 2.2 ɩɨɤɚɡɚɧɵ ɮɚɡɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɦɚɬɪɢɰɵ W. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɞɚɧɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ ɮɚɡɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɩɨɡɜɨɥɹɸɬ ɩɨɤɚɡɚɬɶ ɭɫɬɨɣɱɢɜɵɟ ɫɨɫɬɨɹɧɢɹ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ ɞɥɹ n ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ. dO(t)/dt

dO(t)/dt

3

3

2

2

1

1

-1

0

On

-1

O(t)

0

-1

-1

-2

-2

On

O(t)

ɛ)

a)

Ɋɢɫɭɧɨɤ 2.2 - Ɏɚɡɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɥɹ

ɦɚɬɪɢɰɵ W: ɚ) ɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɛ) ɧɟɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ ȿɫɥɢ ɫɢɫɬɟɦɚ ɧɚɯɨɞɢɬɫɹ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɭɫɬɨɣɱɢɜɨɣ ɫɬɚɰɢɨɧɚɪɧɨɣ ɬɨɱɤɢ, ɬɨ ɢɦɟɟɬ ɦɟɫɬɨ ɫɧɢɠɟɧɢɟ ɬɟɦɩɨɜ ɪɨɫɬɚ ɛɟɡɪɚɛɨɬɢɰɵ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ – ɬɟɦɩɵ ɪɨɫɬɚ ɛɟɡɪɚɛɨɬɢɰɵ ɩɪɨɝɪɟɫɫɢɪɭɸɬ. ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɜ ɩɨɥɭɱɟɧɧɵɟ ɫɜɟɞɟɧɢɹ ɨɛ ɭɫɬɨɣɱɢɜɵɯ ɢ ɧɟɭɫɬɨɣɱɢɜɵɯ ɫɨɫɬɨɹɧɢɹɯ ɪɵɧɤɚ ɬɪɭɞɚ

ɞɥɹ n ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ ɜɩɨɥɧɟ

ɜɨɡɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɩɪɨɝɧɨɡ. ɉɨɥɭɱɟɧɧɵɣ 53

ɩɪɨɝɧɨɡ ɩɨɡɜɨɥɢɬ ɢɡɛɟɠɚɬɶ

ɤɪɢɡɢɫɧɵɯ ɫɨɫɬɨɹɧɢɣ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ. 2.3. ɉɪɢɦɟɪɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɞɜɭɯ ɢ ɬɪɟɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ

Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɧɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɧɚ ɫɥɭɱɚɣ ɞɜɭɯ ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ [81, 82]. Ɉɛɨɡɧɚɱɢɦ N 1i ( t ) - ɨɛɳɟɟ ɱɢɫɥɨ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɡɚɧɹɬɵɯ ɜ i-ɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t; N 2i ( t ) - ɱɢɫɥɨ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɪɚɛɨɱɢɯ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɜɥɟɱɟɧɵ ɞɥɹ ɪɚɛɨɬɵ ɜ i-ɨɣ ɨɬɪɚɫɥɢ ɢ ɤɨɬɨɪɵɟ ɜ ɦɨɦɟɧɬ 2

ɜɪɟɦɟɧɢ t ɹɜɥɹɸɬɫɹ ɛɟɡɪɚɛɨɬɧɵɦɢ;

2

¦¦ N

(i ) j

N

const - ɟɦɤɨɫɬɶ ɪɵɧɤɚ

i 1 j 1

(i , j ) ɪɚɛɨɱɟɣ ɫɢɥɵ ɞɜɭɯ ɨɬɪɚɫɥɟɣ; W1 - ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɛɟɡɪɚɛɨɬɧɵɣ

ɫɩɟɰɢɚɥɢɫɬ i-ɨɣ ɨɬɪɚɫɥɢ ɦɨɠɟɬ ɧɚɣɬɢ ɪɚɛɨɬɭ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ ɜ j-ɨɣ ɨɬɪɚɫɥɢ (k )

ɡɚ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt; W2 - ɜɟɪɨɹɬɧɨɫɬɶ ɭɜɨɥɶɧɟɧɢɹ ɪɚɛɨɬɚɸɳɟɝɨ ɫɩɟɰɢɚɥɢɫɬɚ k-ɨɣ ɨɬɪɚɫɥɢ ɡɚ ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ ɫ t ɞɨ t + dt; i,j,k =1,2, t [0;f) . 2

Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ

¦ W1(i , j ) z 1 , j = 1,2. i 1

Ɍɚɤɠɟ ɤɚɤ ɜ ɩ. 2.1 ɛɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ (i) t=0 ɱɢɫɥɨ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɡɚɧɹɬɵɯ ɜ i-ɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ, ɪɚɜɧɨ N10 , ɚ ɱɢɫɥɨ

ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɪɚɛɨɱɢɯ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɜɥɟɱɟɧɵ ɞɥɹ ɪɚɛɨɬɵ ɜ i-ɨɣ (i) ɨɬɪɚɫɥɢ ɢ ɤɨɬɨɪɵɟ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɹɜɥɹɸɬɫɹ ɛɟɡɪɚɛɨɬɧɵɦɢ ɪɚɜɧɨ N20 , (i) (i) N1(i)( 0 ) N10 , N2(i)( 0 ) N20 , i=1,2

ɬ. ɟ.

(2.6)

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɜɜɟɞɟɧɧɵɦɢ ɜɵɲɟ ɨɛɨɡɧɚɱɟɧɢɹɦɢ ɩɨɫɥɟ ɧɟɫɥɨɠɧɵɯ ɪɚɫɫɭɠɞɟɧɢɣ

ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɫ ɡɚɞɚɧɧɵɦɢ

ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (2.6), ɨɩɢɫɵɜɚɸɳɭɸ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ ɞɜɭɯ ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ: 54

dN1(1) (t ) ° dt ° ( 2) ° dN1 (t ) °° dt ® (1) ° dN 2 (t ) ° dt ° ( 2) ° dN 2 (t ) °¯ dt

N1(1) (t )W2(1) N1( 2 ) (t )W2( 2 ) N 2(1) (t )W1(1,1) N 2( 2 ) (t )W1( 2,1) , N1(1) (t )W2(1) N1( 2 ) (t )W2( 2 ) N 2(1) (t )W1(1, 2 ) N 2( 2 ) (t )W1( 2, 2 ) , N1(1) (t )W2(1) N1( 2 ) (t )W2( 2 ) N 2(1) (t )(W1(1,1) W1(1, 2 ) ) N 2( 2 ) (t )W1( 2,1) ,

(2.7)

N1(1) (t )W2(1) N1( 2 ) (t )W2( 2 ) N 2(1) (t )W1(1, 2 ) N 2( 2 ) (t )(W1( 2,1) W1( 2, 2 ) ).

(i , j ) (i ) Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɟɪɨɹɬɧɨɫɬɢ W2 , W1 ɹɜɥɹɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ

ɜɟɥɢɱɢɧɚɦɢ, i,j=1,2. Ɍɚɤɨɟ ɞɨɩɭɳɟɧɢɟ ɜɩɨɥɧɟ ɩɪɢɟɦɥɟɦɨ ɫ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɛɟɡɪɚɛɨɬɧɵɣ i-ɨɣ ɨɬɪɚɫɥɢ ɦɨɠɟɬ ɩɪɟɬɟɧɞɨɜɚɬɶ ɧɚ ɦɟɫɬɨ ɪɚɛɨɬɚɸɳɟɝɨ ɫɩɟɰɢɚɥɢɫɬɚ ɞɚɧɧɨɣ ɨɬɪɚɫɥɢ ɩɪɢ ɭɫɥɨɜɢɢ ɨɫɜɨɛɨɠɞɟɧɢɹ ɪɚɛɨɱɟɝɨ ɦɟɫɬɚ, ɬ. ɟ. ɭɜɨɥɶɧɟɧɢɹ ɪɚɛɨɱɟɝɨ i-ɨɣ ɨɬɪɚɫɥɢ, ɫɢɫɬɟɦɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (2.7) ɩɪɢɦɟɬ ɜɢɞ: dN 1(1) (t ) ° dt ° (2) ° dN 1 (t ) °° dt ® (1) ° dN 2 (t ) ° dt ° (2) ° dN 2 (t ) °¯ dt

N 1(1) (t )W2(1) N 2(1) (t )W1(1,1) N 2( 2 ) (t )W1( 2,1) , N 1( 2 ) (t )W2( 2 ) N 2(1) (t )W1(1, 2 ) N 2( 2 ) (t )W1( 2, 2 ) , N 1(1) (t )W2(1) N1( 2 ) (t )W2( 2 ) N 2(1) (t )(W1(1,1) W1(1, 2 ) ),

(2.8)

N1(1) (t )W2(1) N 1( 2 ) (t )W2( 2 ) N 2( 2 ) (t )(W1( 2,1) W1( 2, 2 ) ).

Ɉɛɨɡɧɚɱɢɦ

W

§ -W2( 1 ) · W1( 1,1 ) 0 W1( 2 ,1 ) ¨ ¸ (2) ( 1,2 ) ( 2 ,2 ) ¨ 0 ¸ W1 -W2 W1 ¨ ¸ . (1) W2( 2 ) -W1( 1,1 ) W1( 1,2 ) 0 ¨ W2 ¸ ¨ W (1) W ( 2 ) W1( 2 ,1 ) W1( 2 ,2 ) ¸¹ 0 2 © 2

(2.9)

ɂɡ [99] ɢɡɜɟɫɬɧɨ, ɱɬɨ ɜɚɠɧɵɦ ɚɫɩɟɤɬɨɦ ɥɸɛɨɣ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɟɟ ɭɫɬɨɣɱɢɜɨɫɬɶ. ɋɢɫɬɟɦɚ ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɨɣ, ɟɫɥɢ ɨɧɚ ɫɨɯɪɚɧɹɟɬ ɬɟɧɞɟɧɰɢɸ ɫɬɪɟɦɥɟɧɢɹ ɤ ɬɨɦɭ ɫɨɫɬɨɹɧɢɸ, ɤɨɬɨɪɚɹ ɧɚɢɛɨɥɟɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɰɟɥɹɦ ɫɢɫɬɟɦɵ, ɰɟɥɹɦ ɫɨɯɪɚɧɟɧɢɹ ɤɚɱɟɫɬɜɚ ɛɟɡ ɢɡɦɟɧɟɧɢɹ ɫɬɪɭɤɬɭɪɵ ɢɥɢ ɧɟ 55

ɩɪɢɜɨɞɹɳɢɦ ɤ ɫɢɥɶɧɵɦ ɢɡɦɟɧɟɧɢɹɦ ɫɬɪɭɤɬɭɪɵ ɫɢɫɬɟɦɵ ɧɚ ɧɟɤɨɬɨɪɨɦ ɡɚɞɚɧɧɨɦ ɦɧɨɠɟɫɬɜɟ ɪɟɫɭɪɫɨɜ (ɧɚɩɪɢɦɟɪ, ɧɚ ɜɪɟɦɟɧɧɨɦ ɢɧɬɟɪɜɚɥɟ). ɉɨɧɹɬɢɟ “ɫɢɥɶɧɨɟ

ɢɡɦɟɧɟɧɢɟ”

ɤɚɠɞɵɣ

ɪɚɡ

ɞɨɥɠɧɨ

ɛɵɬɶ

ɤɨɧɤɪɟɬɢɡɢɪɨɜɚɧɨ,

ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɨ. ɂɡ ɩ. 2.3 ɢɡɜɟɫɬɧɨ, ɱɬɨ ɫ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɶ (2.7) ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɭɪɨɜɧɟɦ ɡɚɧɹɬɨɫɬɢ (2.6) ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɨɬɤɥɨɧɟɧɢɹɯ ɨɬ (2.6) ɫɢɫɬɟɦɚ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɫɧɨɜɚ ɜɨɡɜɪɚɬɢɬɫɹ ɤ ɧɚɱɚɥɶɧɨɦɭ ɫɨɫɬɨɹɧɢɸ. ȿɫɥɢ ɠɟ ɡɚɞɚɱɚ (2.6), (2.7) ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɣ, ɬɨ ɞɚɠɟ

ɧɟɛɨɥɶɲɢɟ

ɨɬɤɥɨɧɟɧɢɹ

(2.6)

ɨɛɹɡɚɬɟɥɶɧɨ

ɩɪɢɜɟɞɭɬ

ɤ

ɞɪɭɝɨɦɭ

ɫɨɨɬɧɨɲɟɧɢɸ ɱɢɫɥɚ ɛɟɡɪɚɛɨɬɧɵɯ ɢ ɡɚɧɹɬɵɯ ɧɚ ɩɪɨɢɡɜɨɞɫɬɜɟ ɜ ɞɜɭɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ. ɂɫɫɥɟɞɭɟɦ

ɡɚɞɚɱɭ

(2.6),

(2.7)

ɧɚ

ɭɫɬɨɣɱɢɜɨɫɬɶ

[6].

Ɋɚɫɫɦɨɬɪɢɦ

0 .

(2.10)

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ - W2( 1 )- O 0

- W1( 1,1 )

W1( 2 ,1 )

W1( 1,2 )

W1( 2 ,2 )

0 -W2( 2 )- O

W2( 1 )

W2( 2 ) -W1( 1,1 ) W1( 1,2 )- O

W2( 1 )

W2( 2 )

0

W1( 2 ,1 ) W1( 2 ,2 ) Ȝ

0

Ɉɛɨɡɧɚɱɢɦ W2(1)W 2( 2 )W1(1, 2 )W1( 2 , 2 ) 3W 2(1)W 2( 2 )W1(1, 2 )W1( 2,1) W 2(1)W 2( 2 )W1(1,1)W1( 2,1) W 2(1)W 2( 2 )W1(1,1)W1( 2, 2 )

ɚ0 ,

W2(1)W1(1, 2)W1( 2, 2) W2( 2)W1(1, 2)W1( 2, 2) 2W2( 2)W1(1, 2)W1( 2,1) W2( 2)W1(1,1)W1( 2,1) 2W2(1)W1(1, 2)W1( 2,1) W2(1)W1(1,1)W1( 2,1) 2W2(1)W2( 2)W1( 2,1) 2W2(1)W2( 2)W1(1, 2)

ɚ1 ,

W1(1,1)W1( 2, 2) W1(1, 2)W1( 2, 2) W1(1, 2)W1( 2,1) W2(1)W2( 2) W2(1)W1(1, 2) W2( 2)W1( 2,1) W1(1,1)W1( 2,1) W2( 2)W1(1, 2) W2( 2)W1(1,1) W2(1)W1( 2, 2) 2W2(1)W1( 2,1)

W2(1) W2( 2 ) W1(1,1) W1(1, 2 ) W1( 2,1) W1( 2, 2 )

ɚ2 ,

ɚ3 .

Ɍɨɝɞɚ (2.10) ɩɪɢɦɟɬ ɜɢɞ: P4(O) =O4+ ɚ3O3 + ɚ2O2+ ɚ1O + ɚ0 = 0, a4=1. Ɂɚɩɢɲɟɦ ɦɚɬɪɢɰɭ Ƚɭɪɜɢɰɚ:

56

§ ɚ1 ¨ ¨ ɚ3 Mp = ¨ 0 ¨ ¨0 © 4

ɚ0

0

ɚ2 1

ɚ1 ɚ3

0

0

0· ¸ ɚ0 ¸ ɚ2 ¸ ¸ 1 ¸¹

(2.11)

ɋɨɝɥɚɫɧɨ ɤɪɢɬɟɪɢɸ Ɋɚɭɫɚ-Ƚɭɪɜɢɰɚ ɦɧɨɝɨɱɥɟɧ P4(O) ɭɫɬɨɣɱɢɜ (ɚ ɡɧɚɱɢɬ ɢ ɡɚɞɚɱɚ (2.6), (2.7) ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɭɫɬɨɣɱɢɜɚ) ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɜɫɟ ɝɥɚɜɧɵɟ

ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɢɧɨɪɵ '1 = ɚ1,

'2

ɚ1 ɚ3

ɚ0

' ɚ2 , 3

ɚ1 ɚ 0 0 ɚ 3 ɚ 2 ɚ1

ɦɚɬɪɢɰɵ

0 1 ɚ3

Ƚɭɪɜɢɰɚ Mp 4 ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɫɥɨɜɢɹɦ [6]:

'1 > 0, '2 > 0, '3 > 0, ɬ. ɟ. ɚ1 > 0, ɚ1 ɚ2 – ɚ0 ɚ3 > 0, ɚ1 ɚ2 ɚ3 – ɚ12 – ɚ0 ɚ32 > 0, ɢɥɢ

W2(1)W1(1, 2)W1( 2, 2) W2( 2)W1(1, 2)W1( 2, 2) 2W2( 2)W1(1, 2)W1( 2,1) W2( 2)W1(1,1)W1( 2,1) 2W2(1)W1(1, 2)W1( 2,1) W2(1)W1(1,1)W1( 2,1) 2W2(1)W2( 2)W1( 2,1) 2W2(1)W2( 2)W1(1, 2) ! 0, (W2(1)W1(1, 2)W1( 2, 2) W2( 2)W1(1, 2)W1( 2, 2) 2W2( 2)W1(1, 2)W1( 2,1) W2( 2)W1(1,1)W1( 2,1) 2W2(1)W1(1, 2)W1( 2,1) W2(1)W1(1,1)W1( 2,1) 2W2(1)W2( 2)W1( 2,1) 2W2(1)W2( 2)W1(1, 2) ) * * (W1(1,1)W1( 2, 2) W1(1, 2)W1( 2, 2) W1(1, 2)W1( 2,1) W2(1)W2( 2) W2(1)W1(1, 2) W2( 2)W1( 2,1) W1(1,1)W1( 2,1) W2( 2)W1(1, 2) W2( 2)W1(1,1) W2(1)W1( 2, 2) 2W2(1)W1( 2,1) ) (W2(1) W2( 2) W1(1,1) W1(1, 2) W1( 2,1) W1( 2, 2) ) * (W2(1)W2( 2)W1(1, 2)W1( 2, 2) 3W2(1)W2( 2)W1(1, 2)W1( 2,1) W2(1)W2( 2)W1(1,1)W1( 2,1) W2(1)W2( 2)W1(1,1)W1( 2, 2) ) ! 0,

(W2(1)W1(1, 2)W1( 2, 2) W2( 2)W1(1, 2)W1( 2, 2) 2W2( 2)W1(1, 2)W1( 2,1) W2( 2)W1(1,1)W1( 2,1) 2W2(1)W1(1, 2)W1( 2,1) W2(1)W1(1,1)W1( 2,1) 2W2(1)W2( 2)W1( 2,1) 2W2(1)W2( 2)W1(1, 2) ) * * (W1(1,1)W1( 2, 2) W1(1, 2)W1( 2, 2) W1(1, 2)W1( 2,1) W2(1)W2( 2) W2(1)W1(1, 2) W2( 2)W1( 2,1) W1(1,1)W1( 2,1) W2( 2)W1(1, 2) W2( 2)W1(1,1) W2(1)W1( 2, 2) 2W2(1)W1( 2,1) ) * * (W2(1) W2( 2) W1(1,1) W1(1, 2) W1( 2,1) W1( 2, 2) ) (W2(1)W1(1, 2)W1( 2, 2) W2( 2)W1(1, 2)W1( 2, 2) 2W2( 2)W1(1, 2)W1( 2,1) W2( 2)W1(1,1)W1( 2,1) 2W2(1)W1(1, 2)W1( 2,1) W2(1)W1(1,1)W1( 2,1) 2W2(1)W2( 2)W1( 2,1) 2W2(1)W2( 2)W1(1, 2) ) 2 (W2(1) W2( 2) W1(1,1) W1(1, 2) W1( 2,1) W1( 2, 2) ) 2 * (W2(1)W2( 2)W1(1, 2)W1( 2, 2) 3W2(1)W2( 2)W1(1, 2)W1( 2,1) W2(1)W2( 2)W1(1,1)W1( 2,1) W2(1)W2( 2)W1(1,1)W1( 2, 2) ) ! 0, 57

(2.12)

ɉɭɫɬɶ W1( 1,2 )

ɜ

ɫɢɫɬɟɦɟ

0.2 , W1( 2 ,1 )

0.4 , W1( 2 ,2 )

(2.6),

(2.7)

W2( 1 )

0.8, W2( 2 )

0.2, W1( 1,1 )

0.3,

0.1 . Ɍɨɝɞɚ '1 = 0.328 > 0, '2 = 0.382 > 0, '3 =

0.656 > 0. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɞɚɧɧɵɯ ɜɟɪɨɹɬɧɨɫɬɹɯ ɦɧɨɝɨɱɥɟɧ P4(O) ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɵɦ. Ⱥ ɡɧɚɱɢɬ, ɡɚɞɚɱɚ (2.6), (2.7) ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɭɫɬɨɣɱɢɜɚ, ɬ. ɟ. ɞɥɹ ɞɚɧɧɵɯ ɡɧɚɱɟɧɢɣ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɢɫɬɟɦɚ ɛɭɞɟɬ ɜɨɡɜɪɚɳɚɬɶɫɹ ɤ ɪɚɜɧɨɜɟɫɧɨɦɭ ɫɨɫɬɨɹɧɢɸ ɩɪɢ t ɫɬɪɟɦɹɳɟɦɫɹ ɤ ɛɟɫɤɨɧɟɱɧɨɫɬɢ ɢɡ ɥɸɛɨɝɨ ɧɟɪɚɜɧɨɜɟɫɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. ɉɭɫɬɶ

W1( 2 ,1 )

ɜ

ɫɢɫɬɟɦɟ

W1( 2 ,2 )

(2.6),

(2.7)

W2( 1 )

W2( 2 )

W1( 1,1 )

W1( 1,2 )

0.9 . Ɍɨɝɞɚ '1 = 41.69 > 0, '2 = 412.92 > 0, '3 = -2 175 < 0.

ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɞɚɧɧɵɯ ɜɟɪɨɹɬɧɨɫɬɹɯ ɦɧɨɝɨɱɥɟɧ P4(O) ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɵɦ, ɱɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɡɚɞɚɱɚ (2.6), (2.7) ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɧɟɭɫɬɨɣɱɢɜɚ. ɋɢɫɬɟɦɚ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ

ɫ

ɡɚɞɚɧɧɵɦɢ

ɧɚɱɚɥɶɧɵɦɢ

ɭɫɥɨɜɢɹɦɢ (2.1), ɨɩɢɫɵɜɚɸɳɚɹ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ 3 ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ, ɢɦɟɟɬ ɜɢɞ: 3 dN1(1) (t) (1) (1) N1 (t)W2 ¦N1(i ) (t)W2(i ) N2(1) (t)W1(1,1) N2(2) (t)W1(2,1) N2(3) (t)W1(3,1) , ° dt i 2 ° ( 2) °dN1 (t) N1(1) (t)W2(1) N1(2) (t)W2(2) N1(3) (t)W2(3) N2(1) (t)W1(1,2) N2(2) (t)W1(2,2) N2(3) (t)W1(3,2) , ° ° dt °dN1(3) (t) N1(1) (t)W2(1) N1(2) (t)W2(2) N1(3) (t)W2(3) N2(1) (t)W1(1,3) N2(2) (t)W1(2,3) N2(3) (t)W1(3,3) , ° dt ° ® (1) 3 3 3 °dN2 (t) ¦N1(3) (t)W2(3) N2(1) (t)¦W1(1,i ) ¦N2(i ) (t)W1(i,1) , ° dt i 1 i 1 i 2 ° (2) 3 3 °dN2 (t) ¦N (i ) (t)W (i ) N (1) (t)W (1,2) N (2) (t)¦W (2,i ) N (3) (t)W (3,2) , 1 2 2 1 2 1 2 1 ° dt i 1 i 1 ° (3) 3 2 3 (i ) (i ) (i ) (i ,3) °dN2 (t) N1 (t)W2 ¦N2 (t)W1 ¦N2(3) (t)W1(3,i ) . ¦ °¯ dt i 1 i 1 i 1

Ɍɨɝɞɚ W – ɦɚɬɪɢɰɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ (i ) (i , j ) ɭɪɚɜɧɟɧɢɣ ɫ ɭɱɟɬɨɦ ɧɭɥɟɜɵɯ ɡɧɚɱɟɧɢɣ ɜɟɪɨɹɬɧɨɫɬɟɣ W1 , W2 , i,j =1,…,3

ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ: 58

W

§ W2( 1 ) 0 · W1( 1,1 ) 0 W1( 2 ,1 ) W1( 3 ,1 ) ¨ ¸ ¨0 ¸ W1( 2 ,2 ) -W 2( 2 ) 0 W1( 1,2 ) W1( 3 ,2 ) ¨ ¸ ( 3) ( 1,3 ) ( 2 ,3 ) ( 3 ,3 ) 0 0 W W W W ¨ ¸ 2 1 1 1 ¨W ( 1 ) W ( 2 ) W ( 3 ) -W ( 1,1 )-W ( 1,2 ) W ( 1,3 ) ¸. 0 0 2 2 1 1 1 ¨ 2 ¸ ( 2 ,1 ) ( 2 ,2 ) ( 2 ,3 ) ¨W2( 1 ) W2( 2 ) W2( 3 ) ¸ W1 W1 W1 0 0 ¨¨ ( 1 ) ¸ (2) ( 3) ( 1 ,3 ) ( 2 ,3 ) ( 3 ,3 ) ¸ W W W 0 0 W W -W 2 2 1 1 1 © 2 ¹

ɉɭɫɬɶ ɜ ɫɢɫɬɟɦɟ (2.1), (2.2) W2( 1 )

0.1, W2( 2 )

0.2 , W2( 3 )

0.3,

W1( 1,1 )

0.3, W1( 1,2 )

0.2 , W1( 1,3 )

0.1,

W1( 2 ,1 )

0.4 , W1( 2 ,2 )

0.1, W1( 2 ,3 )

0.5, .

W1( 3 ,1 )

0.6 , W1( 3,2 )

0.2, W1( 3 ,3 )

0.3

Ɇɚɬɪɢɰɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ W ɩɪɢɦɟɬ ɜɢɞ: 0 0.3 0.4 0.6 · § -0.1 0 ¸ ¨ 0.2 0.1 0.2 ¸ ¨ 0 -0.2 0 ¨ 0 0 -0.3 0.1 0.5 0.3 ¸ ¸ W= ¨¨ 0.1 0.2 0.3 0.6 0 0 ¸. ¨ 0.1 0.2 0.3 0 -1 0 ¸ ¨ ¸ ¨ 0.1 0.2 0.3 0 ¸ 0 -1 .1 ¹ ©

Ɍɨɝɞɚ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ W ɩɪɢɦɟɬ ɜɢɞ: -0.1 Ȝ 0 0 0.3 0 -0.2 -Ȝ 0 0.2 0 0 -0.3-Ȝ 0.1 0.1 0.2 0.3 0.6 -Ȝ 0.1 0.1

0.2 0.2

0.3 0.3

0 0

0.4 0.6 0.1 0.2 0.5 0.3 0 0

0

.

-1 -Ȝ 0 0 -1.1 Ȝ

ɉɨɥɭɱɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ: P6(O) =O6+3.3O5+3.87O4+ 1.904O3 + 0.354O2+ 0.014O - 0.001 = 0, a6=1. Ɂɚɩɢɲɟɦ ɦɚɬɪɢɰɭ Ƚɭɪɜɢɰɚ ɞɥɹ ɩɨɥɭɱɟɧɧɨɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ P6(O): 59

M P6

0 0 0 § 0.014 0.001 0 ¨ 0 ¨ 1.904 0.354 0.014 0.001 0 ¨ 3.3 3.87 1.904 0.354 0.014 0.001 ¨ 1 3.3 3.87 1.904 0.354 ¨0 ¨0 0 0 1 3.3 3.87 ¨ ¨0 0 0 0 0 1 ©

· ¸ ¸ ¸ ¸ ¸ ¸ ¸ ¸ ¹

ȼɵɱɢɫɥɢɦ ɝɥɚɜɧɵɟ ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɢɧɨɪɵ ɦɚɬɪɢɰɵ Ƚɭɪɜɢɰɚ

M P6 :

'1 = 0.014 > 0, '2 = 0.007 > 0, '3 = 0.012 > 0, '4 = 0.039 > 0, '5 = 0.106 > 0. ɋɥɟɞɨɜɚɬɟɥɶɧɨ,

ɩɪɢ

ɞɚɧɧɵɯ

ɜɟɪɨɹɬɧɨɫɬɹɯ

ɦɧɨɝɨɱɥɟɧ

P6(O)

ɹɜɥɹɟɬɫɹ

ɭɫɬɨɣɱɢɜɵɦ, ɚ ɡɚɞɚɱɚ (2.1), (2.2) ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɭɫɬɨɣɱɢɜɚ. ɋɨɫɬɚɜɥɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɞɥɹ ɞɚɧɧɨɣ ɦɚɬɪɢɰɵ W (ɬɚɤɠɟ ɤɚɤ ɢ ɞɥɹ ɫɥɭɱɚɟɜ, ɤɨɝɞɚ n > 3) ɢ ɢɫɫɥɟɞɨɜɚɧɢɟ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɜɟɫɶɦɚ ɬɪɭɞɨɟɦɤɢɣ ɩɪɨɰɟɫɫ, ɬɪɟɛɭɸɳɢɣ ɡɧɚɱɢɬɟɥɶɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɜɪɟɦɟɧɢ. ɉɨɷɬɨɦɭ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɪɚɡɥɢɱɧɵɟ ɩɚɤɟɬɵ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ, ɧɚɩɪɢɦɟɪ: ɷɥɟɤɬɪɨɧɧɵɟ ɬɚɛɥɢɰɵ

Excel,

ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ

ɫɢɫɬɟɦɭ

MathCad,

ɩɚɤɟɬɵ

MapleV,

Mathematica4, MatLab [2, 14, 30, 31, 32, 33, 73, 77]. 2.4. Ⱥɥɝɨɪɢɬɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ

ɉɨɪɹɞɨɤ

ɜɵɩɨɥɧɟɧɢɹ

ɞɟɣɫɬɜɢɣ

ɞɥɹ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (2.2) ɫ ɡɚɞɚɧɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (2.1) ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫɭɧɤɟ 2.3. ɉɪɢɜɟɞɟɦ ɚɥɝɨɪɢɬɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɜ ɩ. 2.1.

60

Ɂɚɩɢɫɚɬɶ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ

ɋɨɫɬɚɜɢɬɶ ɦɚɬɪɢɰɭ W ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ

ɋɨɫɬɚɜɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɦɚɬɪɢɰɵ W

ɋɨɫɬɚɜɢɬɶ ɦɚɬɪɢɰɭ Ƚɭɪɜɢɰɚ ɞɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɚɬɪɢɰɵ W

ȼɵɱɢɫɥɢɬɶ ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɢɧɨɪɵ ɦɚɬɪɢɰɵ Ƚɭɪɜɢɰɚ

Ɉɩɪɟɞɟɥɢɬɶ ɭɫɬɨɣɱɢɜɨɫɬɶ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ Ɋɢɫɭɧɨɤ 2.3 - ɋɯɟɦɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ

ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ Ⱦɥɹ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɧɚ

ɭɫɬɨɣɱɢɜɨɫɬɶ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ (2.2) ɫ ɡɚɞɚɧɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (2.1), ɨɩɢɫɵɜɚɸɳɟɣ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ n ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ, 61

ɧɟɨɛɯɨɞɢɦɨ: 1) ɡɚɩɢɫɚɬɶ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɨɩɢɫɵɜɚɸɳɭɸ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ; 2) ɫɨɫɬɚɜɢɬɶ ɦɚɬɪɢɰɭ W ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɜɜɟɞɹ ɤɨɧɤɪɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ

W1(i, j ) , W2(i) , i, j=1,…,n;

3) ɫɨɫɬɚɜɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ det (W–OI) = 0 ɞɥɹ ɩɨɥɭɱɟɧɧɨɣ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ W; 4) ɫɨɫɬɚɜɢɬɶ ɦɚɬɪɢɰɭ Ƚɭɪɜɢɰɚ ɞɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ W; 5) ɜɵɱɢɫɥɢɬɶ ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɢɧɨɪɵ ɞɥɹ ɩɨɥɭɱɟɧɧɨɣ ɦɚɬɪɢɰɵ Ƚɭɪɜɢɰɚ; 6) ɫɞɟɥɚɬɶ

ɜɵɜɨɞ

ɨɛ

ɭɫɬɨɣɱɢɜɨɫɬɢ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ. ɇɚ

ɨɫɧɨɜɚɧɢɢ

ɩɨɥɭɱɟɧɧɵɯ

ɫɜɟɞɟɧɢɣ

ɨɛ

ɭɫɬɨɣɱɢɜɨɫɬɢ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɦɨɠɧɨ ɫɭɞɢɬɶ ɨ ɫɨɫɬɨɹɧɢɢ ɪɵɧɤɚ ɬɪɭɞɚ. 2.4.1. ɉɨɫɬɪɨɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ

ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɜɵɱɢɫɥɟɧɢɟ ɨɩɪɟɞɟɥɢɬɟɥɹ ɦɚɬɪɢɰɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ W ɫɢɫɬɟɦɵ (2.2) ɞɥɹ ɫɤɨɥɶɤɨ-ɧɢɛɭɞɶ ɜɵɫɨɤɨɝɨ ɩɨɪɹɞɤɚ ɦɚɬɪɢɰɵ ɝɪɨɦɨɡɞɤɨ ɢ ɜɟɫɶɦɚ ɬɪɭɞɨɟɦɤɨ. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɜɵɱɢɫɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ai ɬɪɟɛɭɟɬ ɨɝɪɨɦɧɨɝɨ ɱɢɫɥɚ ɨɩɟɪɚɰɢɣ. Ɋɚɡɪɚɛɨɬɚɧɵ ɫɩɟɰɢɚɥɶɧɵɟ ɦɟɬɨɞɵ ɪɚɡɜɟɪɬɵɜɚɧɢɹ ɨɩɪɟɞɟɥɢɬɟɥɹ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɣ

ɦɚɬɪɢɰɵ,

ɧɟ

ɬɪɟɛɭɸɳɢɟ

ɟɝɨ

ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɝɨ ɜɵɱɢɫɥɟɧɢɹ (ɦɟɬɨɞɵ Ⱥ. ɇ. Ʉɪɵɥɨɜɚ, Ⱥ. Ɇ. Ⱦɚɧɢɥɟɜɫɤɨɝɨ, Ʌɟɜɟɪɶɟ, Ⱦ. Ʉ. Ɏɚɞɞɟɟɜɚ, ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɟɬɨɞ ɢ ɞɪ. [94]). ɉɪɢɦɟɪ 2.1. ɚ) Ɇɟɬɨɞ Ⱥ.ɇ. Ʉɪɵɥɨɜɚ. ɉɭɫɬɶ ~W - Oȿ~ = (-1)n(On + a1On-1 + a2On-2 + … + an-1O + an)

(2.13)

- ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ W n-ɝɨ ɩɨɪɹɞɤɚ. Ɍɚɤ ɤɚɤ n - ɜɫɟɝɞɚ 62

ɱɟɬɧɨɟ ɱɢɫɥɨ, ɬɨ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ W n-ɝɨ ɩɨɪɹɞɤɚ (2.13) ɩɪɢɦɟɬ ɜɢɞ ~W - Oȿ~ = On + a1On-1 + a2On-2 + … + an-1O + an.

(2.13ƍ)

Ɇɟɬɨɞ ɨɫɧɨɜɚɧ ɧɚ ɜɵɩɨɥɧɟɧɢɢ ɪɚɜɟɧɫɬɜ ɯ(k) = Wɯ(k - 1), k = 1, 2, …, n,

(2.14)

ɤɨɬɨɪɵɟ ɭɞɨɛɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɵɱɢɫɥɟɧɢɹ ɜɟɤɬɨɪɨɜ ɯ(1), ɯ(2), …, ɯ(n), ɝɞɟ ɯ(0) - ɩɪɨɢɡɜɨɥɶɧɵɣ ɜɟɤɬɨɪ. Ɇɟɬɨɞɨɦ Ⱥ.ɇ. Ʉɪɵɥɨɜɚ ɧɚɣɞɟɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ (2.3) ɞɥɹ ɡɧɚɱɟɧɢɣ W2( 1 )

0.1, W2( 2 )

0.2, W1( 1,1 )

W

0.3, W1( 1,2 ) 0 § -0.1 ¨ ¨ 0 - 0.2 ¨ 0.1 0.2 ¨¨ 0.2 © 0.1

0.4, W1( 2 ,1 ) 0.3 0.4 -0. 7 0

0.5, W1( 2 ,2 )

0. 5 0.6 0 -1.1

0.6

(2.15)

· ¸ ¸ ¸ ¸¸ ¹

Ɂɚɩɢɫɚɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɜ ɜɢɞɟ ~W - Oȿ~ = O4 + a1O3 + a2O2 + a3O + a4, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ a1, a2, a3, a4 ɜɵɛɟɪɟɦ ɜ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɨɝɨ ɜɟɤɬɨɪ ɯ(0) = (1, 2, 3, 0)Ɍ ɢ ɩɨ ɮɨɪɦɭɥɚɦ (2.14) ɧɚɣɞɟɦ ɜɟɤɬɨɪɵ § 0 .2 · § 0.25 · ¸ ¨ ¨ ¸ 0 . 2 0 . 5 ¨ ¸ ¨ ¸ ɯ1 = ¨ 1.6 ¸ , ɯ2 = ¨ 1.14 ¸ , ɯ3 = ¨¨ ¸¸ ¨¨ ¸¸ 0 . 7 0 . 75 © ¹ © ¹

§ 0.214 · § 0.179 · ¸ ¨ ¨ ¸ ¨ 0.478 ¸ ¨ 0.41 ¸ ¨ 0.923 ¸ , ɯ4= ¨ 0.773 ¸ . ¨¨ ¸¸ ¨¨ ¸¸ 0 . 65 0 . 535 ¹ © © ¹

Ⱦɚɥɟɟ, ɢɫɩɨɥɶɡɭɹ ɧɚɣɞɟɧɧɵɟ ɜɟɤɬɨɪɵ ɯ(i), i = 0,1,2,3,4, ɡɚɩɢɲɟɦ ɜɟɤɬɨɪɧɨɟ ɭɪɚɜɧɟɧɢɟ (2.13): § 0.214 · § 0 .2 · § 0.25 · §1· § 0.179 · ¨ ¨ ¸ ¸ ¨ ¸ ¨ ¸ ¨ ¸ 0 . 478 0 . 2 0 . 5 0 . 41 ¨ ¨ ¸ ¸ ¨ ¸ ¨ 2¸ ¨ ¸ ¨ 0.773 ¸ + a1 ¨ 0.923 ¸ + a2 ¨ 1.14 ¸ + a3 ¨ 1.6 ¸ + a4 ¨ 3 ¸ = ¨¨ ¨¨ ¸¸ ¸¸ ¨¨ ¸¸ ¨ ¸ ¨¨ ¸¸ ¨ 0¸ 0 . 65 0 . 7 0 . 75 © © © ¹ ¹ ¹ © ¹ © 0.535 ¹

§0· ¨ ¸ ¨0¸ ¨0¸ ¨ ¸ ¨0¸ © ¹

.

ɗɬɨ ɪɚɜɟɧɫɬɜɨ ɹɜɥɹɟɬɫɹ ɜɟɤɬɨɪɧɨɣ ɮɨɪɦɨɣ ɡɚɩɢɫɢ ɫɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɢɦɟɸɳɟɣ ɟɞɢɧɫɬɜɟɧɧɨɟ ɪɟɲɟɧɢɟ a1 = 2.1, a2 = 1.35, a3 = 0.261, a4=0.015. ɉɨɷɬɨɦɭ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ W ɢɦɟɟɬ ɜɢɞ: ~W - Oȿ~ = O4 + 2.1 O3 + 1.35O2 + 0.261O + 0.015. 63

ȼ ɩɚɤɟɬɟ MathCad ɫɨɫɬɚɜɢɦ ɦɚɬɪɢɰɭ W ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɢɫɬɟɦɵ (2.2) ɞɥɹ (i , j ) ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɣ W2(i ) , W1 , i,j=1,2.

Ɂɚɞɚɞɢɦ ɜɟɤɬɨɪ ɯ(0) ɢ ɨɩɪɟɞɟɥɢɦ ɜɫɟ ɜɟɤɬɨɪɵ ɯ(1), ɯ(2), ɯ(3), ɯ(4): x0fn( x y) if ( x size 1 x 1 0) x( n)

matrix( size 1 x0fn) T· § T x ( n 1 ) W © ¹ if n z 0

ra 1 x( size)

ɋɨɫɬɚɜɢɦ ɦɚɬɪɢɰɭ ɜɟɤɬɨɪɨɜ ɯ(0), ɯ(1), ɯ(2), ɯ(3), ɯ(4): lslq( ly lx) x( size lx 1) ly Mlslq matrix( size size lslq)

Ɉɩɪɟɞɟɥɢɦ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W:

a lsolve( Mlslq ra)

a

§ 2.1 ¨ ¨ 1.35 ¨ 0.261 ¨ © 0.015

· ¸ ¸ ¸ ¸ ¹

Ɏɪɚɝɦɟɧɬ ɪɚɛɨɱɟɝɨ ɞɨɤɭɦɟɧɬɚ MathCad ɫ ɜɵɱɢɫɥɟɧɢɹɦɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɨɩɪɟɞɟɥɢɬɟɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W, ɢɫɩɨɥɶɡɭɹ ɦɟɬɨɞ Ⱥ.ɇ. Ʉɪɵɥɨɜɚ, ɩɪɢɜɟɞɟɧ ɧɚ ɪɢɫ. 2.4. ɛ) ɂɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɟɬɨɞ [94]. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ (2.13ƍ) ɜɵɛɟɪɟɦ n ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɣ O1, O2, … On ɩɟɪɟɦɟɧɧɨɝɨ O ɢ ɩɨɨɱɟɪɟɞɧɨ ɩɨɞɫɬɚɜɢɦ ɜ ɨɛɟ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ (2.13). ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ

Ȝ1n ɚ1 Ȝ1n-1 + … + ɚ n-1 Ȝ1 + a n W-Ȝ1 E , ° n n-1 ° Ȝ2 ɚ1 Ȝ2 + … + ɚ n-1 Ȝ2+ a n = W-Ȝ2 E , ® °................................................................... ° Ȝ n ɚ Ȝ n-1 + … + ɚ Ȝ + a = W-Ȝ E 1 n n-1 n n n ¯ n

(2.16)

ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɢɡɜɟɫɬɧɵɯ ɚ1, ɚ2, … ɚn. ɋɢɫɬɟɦɚ (2.16) ɢɦɟɟɬ ɟɞɢɧɫɬɜɟɧɧɨɟ ɪɟɲɟɧɢɟ, ɨɩɪɟɞɟɥɹɸɳɟɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ. 64

Ɋɢɫɭɧɨɤ 2.4 - ȼɵɱɢɫɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɩɨɥɢɧɨɦɚ ɜ ɫɪɟɞɟ MathCad ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɚ Ⱥ.ɇ. Ʉɪɵɥɨɜɚ ɂɧɬɟɪɩɨɥɹɰɢɨɧɧɵɦ ɦɟɬɨɞɨɦ ɧɚɣɞɟɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ (2.3) ɞɥɹ ɡɧɚɱɟɧɢɣ (2.15). Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɚ1, ɚ2, ɚ3, ɚ4 ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ~W - Oȿ~ = O4 + a1O3 + a2O2 + a3O + a4 ɜɵɛɟɪɟɦ 4 ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹ O1=1, O2=2, O3=3, O4=4 ɢ ɞɥɹ ɤɚɠɞɨɝɨ ɢɡ ɧɢɯ ɜɵɱɢɫɥɢɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɨɩɪɟɞɟɥɢɬɟɥɶ: ~W - O1ȿ~= ~W - ȿ~= 3.726, ~W - O2ȿ~= ~W - 2ȿ~= 22.737, 65

~W - O3ȿ~= ~W - 3ȿ~= 69.648, ~W - O4ȿ~= ~W - 4ȿ~= 157.059. ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɹ O1, O2, O3, O4 ɢ ɜɵɱɢɫɥɟɧɧɵɟ ɨɩɪɟɞɟɥɢɬɟɥɢ ɜ (2.16), ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ

1 ɚ1 + a 2 + ɚ3 + a4 = 3.726 , °16 8ɚ + 4a + 2ɚ + a = 22.737 , ° 1 2 3 4 ® °81 27ɚ1 9a 2+ 3ɚ3 + a4= 69.648, °¯256 64ɚ1 +16a 2 + 4ɚ3 + a4 = 157.059 , ɢɦɟɸɳɭɸ ɟɞɢɧɫɬɜɟɧɧɨɟ ɪɟɲɟɧɢɟ ɚ1 = 2.1, ɚ2 = 1.35, ɚ3 = 0.261, ɚ4 = 0.015 . ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ W ɢɦɟɟɬ ɜɢɞ: ~W - Oȿ~ = O4 + 2.1O3 + 1.35O2 + 0.261O + 0.015. ȼ ɩɚɤɟɬɟ MathCad ɫɨɫɬɚɜɢɦ ɦɚɬɪɢɰɭ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɢ ɫɜɨɛɨɞɧɵɯ ɱɥɟɧɨɜ ɫɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ (2.16) ɞɥɹ ɡɧɚɱɟɧɢɣ (2.15): WO ( n) W E n leq_r( a b)

WO ( a 1) ( a 1)

size

Mleq_r matrix( size 1 leq_r) Mleq_r

leq_l( a b) ( a 1)

size1b

Mleq_l matrix( size size leq_l)

§ 3.726 · ¨ ¸ 22.737 ¨ ¸ ¨ 69.648 ¸ ¨ ¸ © 157.059 ¹

§1 ¨ ¨8 Mleq_l ¨ 27 ¨ © 64

1 1 1·

¸

4 2 1¸ 9 3 1¸

¸

16 4 1 ¹

Ɉɩɪɟɞɟɥɢɦ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W:

a

lsolve( Mleq_l Mleq_r )

a

§ 2.1 ¨ ¨ 1.35 ¨ 0.261 ¨ © 0.015

· ¸ ¸ ¸ ¸ ¹

ɇɚ ɪɢɫ. 2.5 ɩɨɤɚɡɚɧ ɮɪɚɝɦɟɧɬ ɪɚɛɨɱɟɝɨ ɞɨɤɭɦɟɧɬɚ MathCad ɫ 66

ɜɵɱɢɫɥɟɧɢɹɦɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɨɩɪɟɞɟɥɢɬɟɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɣ ɦɚɬɪɢɰɵ W, ɢɫɩɨɥɶɡɭɹ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɟɬɨɞ. ɜ) Ɇɟɬɨɞ Ⱦ. Ʉ. Ɏɚɞɞɟɟɜɚ [94]. Ɇɟɬɨɞ

Ⱦ.

Ʉ.

Ɏɚɞɞɟɟɜɚ

ɞɥɹ

ɜɵɱɢɫɥɟɧɢɹ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɦɧɨɝɨɱɥɟɧɚ (2.13) ɦɚɬɪɢɰɵ W ɫɨɫɬɨɢɬ ɜ ɩɪɨɜɟɞɟɧɢɢ ɫɥɟɞɭɸɳɢɯ ɜɵɱɢɫɥɟɧɢɣ: Wi = Bi-1W, ai =

SpWi , Bi = Wi – aiE, i = 1, 2, …, n, i

(2.17)

ɝɞɟ ȼ0 = ȿ (ɬ. ɟ. W1 = W), ɚ SpWi – ɫɥɟɞ ɦɚɬɪɢɰɵ Wi, ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɜɧɨɣ ɫɭɦɦɟ ɟɟ ɞɢɚɝɨɧɚɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ.

Ɋɢɫɭɧɨɤ 2.5 - ȼɵɱɢɫɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɩɨɥɢɧɨɦɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɨɝɨ ɦɟɬɨɞɚ ɜ ɩɚɤɟɬɟ MathCad

67

Ɇɟɬɨɞɨɦ Ⱦ.Ʉ. Ɏɚɞɞɟɟɜɚ ɜɵɱɢɫɥɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣ ɦɧɨɝɨɱɥɟɧ ɦɚɬɪɢɰɵ (2.3) ɞɥɹ ɡɧɚɱɟɧɢɣ (2.15).

W1

0 0.3 0. 5 · § -0.1 ¨ ¸ 0.4 0.6 ¸ ¨ 0 - 0.2 ¨ 0.1 0.2 -0. 7 0 ¸, ¨¨ ¸¸ 0.1 0.2 0 -1.1 © ¹

W

a1 =

SpW1 = -2.1, 1

0 0.3 0.5 · § 2 ¨ ¸ ¨ 0 1.9 0.4 0.6 ¸ B1 = W1– a1E = ¨ 0.1 0.2 1.4 0 ¸. ¨¨ ¸¸ 0.1 0.2 0 1 © ¹

Ⱦɚɥɟɟ ɩɨ ɚɧɚɥɨɝɢɢ ɨɩɪɟɞɟɥɹɟɦ a2 =

SpW3 SpW2 = -1.35, a3 = = -0.261. 2 3

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɧɚ ɱɟɬɜɟɪɬɨɦ ɲɚɝɟ ɜɵɱɢɫɥɟɧɢɣ ɩɨɥɭɱɢɦ: 0 0 0 · § 0.015 ¨ ¸ 0.015 0 0 ¸ ¨ 0 SpW4 , a4 = = -0.015, W4 =W B3 = ¨ ¸ 0.015 0 0 0 4 ¸ ¨¨ 0.015 ¸¹ 0 0 © 0

§0 ¨ ¨0 B4 = W4 – a4E = ¨ 0 ¨ ¨0 ©

0 0 0· ¸ 0 0 0¸ 0 0 0¸ . ¸ 0 0 0 ¸¹

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,~W - Oȿ~ = O4 + 2.1O3 + 1.35O2 + 0.261O + 0.015. ȼ ɩɚɤɟɬɟ MathCad ɜɵɱɢɫɥɢɦ SpWi – ɫɥɟɞ ɦɚɬɪɢɰɵ Wi, i=1,…,4: mW( i)

W if i 2

§ mW( i 1) tr( mW( i 1) ) E· W if i t 2 ¨ ¸ i1 © ¹ fa( i x)

tr( mW( i 1) ) i 1

Ɉɩɪɟɞɟɥɢɦ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W:

68

a

matrix ( size 1 fa)

a

§ 2.1 ¨ ¨ 1.35 ¨ 0.261 ¨ © 0.015

· ¸ ¸ ¸ ¸ ¹

ɇɚ ɪɢɫ. 2.6 ɩɨɤɚɡɚɧ ɮɪɚɝɦɟɧɬ ɪɚɛɨɱɟɝɨ ɞɨɤɭɦɟɧɬɚ MathCad ɫ ɜɵɱɢɫɥɟɧɢɹɦɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɨɩɪɟɞɟɥɢɬɟɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɣ ɦɚɬɪɢɰɵ W c ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɚ Ⱦ.Ʉ. Ɏɚɞɞɟɟɜɚ.

Ɋɢɫɭɧɨɤ 2.6 - ȼɵɱɢɫɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɩɨɥɢɧɨɦɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɚ Ⱦ. Ʉ. Ɏɚɞɞɟɟɜɚ ɜ ɩɚɤɟɬɟ MathCad Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɩɚɤɟɬɚ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ MathCad ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ ɧɟ ɬɪɟɛɭɟɬ 69

ɨɝɪɨɦɧɨɝɨ ɱɢɫɥɚ ɨɩɟɪɚɰɢɣ. Ʉɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɝɨ ɜɵɱɢɫɥɟɧɢɹ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɦ ɦɟɬɨɞɨɦ, ɦɟɬɨɞɚɦɢ Ⱥ. ɇ. Ʉɪɵɥɨɜɚ, Ⱦ. Ʉ. Ɏɚɞɞɟɟɜɚ ɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɚɤɟɬɚ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ MathCad ɢɦɟɸɬ ɧɭɥɟɜɭɸ ɩɨɝɪɟɲɧɨɫɬɶ. 2.4.2. Ɉɫɨɛɟɧɧɨɫɬɢ ɜɵɱɢɫɥɟɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ

ɉɨɫɥɟ ɜɵɱɢɫɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɜɵɱɢɫɥɹɸɬɫɹ ɡɚɬɟɦ ɩɨ ɤɚɤɨɦɭ-ɥɢɛɨ ɦɟɬɨɞɭ ɞɥɹ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɜɵɱɢɫɥɟɧɢɹ ɤɨɪɧɟɣ ɩɨɥɢɧɨɦɚ. Ɉɞɧɢɦ ɢɡ ɥɭɱɲɢɯ ɫɩɨɫɨɛɨɜ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɜɵɱɢɫɥɟɧɢɹ ɤɨɪɧɟɣ ɩɨɥɢɧɨɦɚ M(t) = a0tn+ a1tn-1 + … + an-1t + an ɹɜɥɹɟɬɫɹ ɫɩɨɫɨɛ ɇɶɸɬɨɧɚ [17, 41, 57, 97]. ɉɭɫɬɶ ɮɭɧɤɰɢɹ f(ɯ) ɞɜɚɠɞɵ ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɚ ɧɚ ɨɬɪɟɡɤɟ [a; b], ɫɨɞɟɪɠɚɳɟɦ ɤɨɪɟɧɶ [ ɭɪɚɜɧɟɧɢɹ f(x)=0,

(2.18)

ɝɞɟ f: R1 o R1 –ɚɥɝɟɛɪɚɢɱɟɫɤɚɹ ɢɥɢ ɬɪɚɧɫɰɟɧɞɟɧɬɧɚɹ ɮɭɧɤɰɢɹ. ɂɬɟɪɚɰɢɨɧɧɵɣ ɩɪɨɰɟɫɫ ɇɶɸɬɨɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɧɟɣɧɵɦ ɭɪɚɜɧɟɧɢɟɦ f(ɯk) + f´( ɯk)(ɯk+1 - ɯk) = 0

(2.19)

ɢɥɢ ɜ ɹɜɧɨɦ ɜɢɞɟ ɮɨɪɦɭɥɨɣ ɯk+1 = ɯk -

f ( xk ) , f c( xk )

(2.20)

ɝɞɟ k = 0, 1, 2, …, ɢ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɧɚ ɷɥɟɦɟɧɬɚɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɯk ɩɟɪɜɚɹ ɩɪɨɢɡɜɨɞɧɚɹ ɞɚɧɧɨɣ ɮɭɧɤɰɢɢ ɜ ɧɭɥɶ ɧɟ ɨɛɪɚɳɚɟɬɫɹ. ɉɪɢɦɟɪ 2.2. ɇɚɣɬɢ ɜɫɟ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ ɦɚɬɪɢɰɵ (2.3) ɞɥɹ ɡɧɚɱɟɧɢɣ (2.15) Pn(O) = O4 + 2.1O3 + 1.35O2 + 0.261O + 0.015 ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ 0,001. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɫɩɨɫɨɛɨɦ ɇɶɸɬɨɧɚ [97]. 70

ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ (2.20) ɩɪɨɜɟɞɟɦ ɢɬɟɪɚɰɢɨɧɧɵɣ ɩɪɨɰɟɫɫ. Ɋɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 2.1. Ⱦɥɹ ɨɤɨɧɱɚɧɢɹ ɢɬɟɪɚɰɢɨɧɧɨɝɨ ɩɪɨɰɟɫɫɚ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɢɥɢ ɭɫɥɨɜɢɟ | f(xi)| < H , ɢɥɢ ɭɫɥɨɜɢɟ ɛɥɢɡɨɫɬɢ 2ɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ | xi - xi - 1 | < H. Ɍɚɛɥɢɰɚ 2.1 - Ɋɟɡɭɥɶɬɚɬɵ ɢɬɟɪɚɰɢɨɧɧɨɝɨ ɩɪɨɰɟɫɫɚ

i

On

On+1

_On+1 - On_

0

0

-0.401

1

-0.401

-1.959

0.442

2

-1.959

-1.638

0.321

3

-1.638

-1.414

0.224

4

-1.414

-1.269

0.145

5

-1.269

-1.194

0.075

6

-1.194

-1.171

0.023

7

-1.171

-1.169

0.002

8

-1.169

0

9

0

ɉɪɨɜɟɞɹ 9 ɢɬɟɪɚɰɢɣ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ O1 | -1.169. ɉɪɨɜɨɞɹ ɚɧɚɥɨɝɢɱɧɵɟ ɜɵɱɢɫɥɟɧɢɹ ɧɚ ɨɬɪɟɡɤɚɯ

[-0.5;-0], [-0.4;0],

[-0.3;0], ɩɨɥɭɱɢɦ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ O1 | -0.6, O1 | -0.231, O1 | -0.1. ȼ

ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ

ɫɢɫɬɟɦɟ

MathCad

ɨɪɝɚɧɢɡɚɰɢɹ

ɢɬɟɪɚɰɢɨɧɧɵɯ

ɜɵɱɢɫɥɟɧɢɣ ɩɨ ɦɟɬɨɞɭ ɇɶɸɬɨɧɚ ɪɟɚɥɢɡɭɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ until(a,z) [63], ɤɨɬɨɪɚɹ ɜɨɡɜɪɚɳɚɟɬ z, ɩɨɤɚ ɜɵɪɚɠɟɧɢɟ a ɧɟ ɫɬɚɧɨɜɢɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɦ; ɚ ɞɨɥɠɧɨ ɫɨɞɟɪɠɚɬɶ ɞɢɫɤɪɟɬɧɵɣ ɚɪɝɭɦɟɧɬ. ɂɦɟɟɬ ɦɟɫɬɨ ɫɥɟɞɭɸɳɚɹ ɡɚɩɢɫɶ: § f (O ) · Oi 1 : until ¨¨ Oi Oi 1 H , Oi ' i ¸¸ . f (O i ) ¹ ©

ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ MathCad ɞɥɹ ɨɪɝɚɧɢɡɚɰɢɢ 71

ɢɬɟɪɚɰɢɨɧɧɵɯ ɜɵɱɢɫɥɟɧɢɣ ɩɨ ɦɟɬɨɞɭ ɩɨɡɜɨɥɹɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɵɫɬɪɨ ɢ ɬɨɱɧɨ ɩɨɥɭɱɢɬɶ ɪɟɡɭɥɶɬɚɬ. Ɉɛɵɱɧɨ ɫɨɛɫɬɜɟɧɧɵɟ ɜɟɤɬɨɪɵ ɦɚɬɪɢɰɵ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ, ɩɪɨɜɟɞɟɧɧɵɯ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɤɬɨɪɚ, ɩɪɢɧɚɞɥɟɠɚɳɟɝɨ ɬɨɦɭ ɢɥɢ ɞɪɭɝɨɦɭ ɫɨɛɫɬɜɟɧɧɨɦɭ ɡɧɚɱɟɧɢɸ, ɷɬɨ ɫɨɛɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɭɠɟ ɜɵɱɢɫɥɟɧɨ. Ɍɚɤɢɟ ɦɟɬɨɞɵ ɹɜɥɹɸɬɫɹ ɬɨɱɧɵɦɢ, ɬ. ɟ. ɟɫɥɢ ɢɯ ɨɫɭɳɟɫɬɜɥɹɬɶ ɞɥɹ ɦɚɬɪɢɰ, ɷɥɟɦɟɧɬɵ ɤɨɬɨɪɵɯ ɡɚɞɚɧɵ ɬɨɱɧɨ (ɪɚɰɢɨɧɚɥɶɧɵɦɢ ɱɢɫɥɚɦɢ) ɢ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɜɨɞɢɬɶ ɬɨɱɧɨ (ɩɨ ɩɪɚɜɢɥɚɦ ɞɟɣɫɬɜɢɣ ɧɚɞ ɨɛɵɤɧɨɜɟɧɧɵɦɢ ɞɪɨɛɹɦɢ), ɬɨ ɜ ɪɟɡɭɥɶɬɚɬɟ ɛɭɞɟɬ ɩɨɥɭɱɟɧɨ ɬɨɱɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ, ɢ ɤɨɦɩɨɧɟɧɬɵ ɫɨɛɫɬɜɟɧɧɵɯ ɜɟɤɬɨɪɨɜ ɨɤɚɠɭɬɫɹ ɜɵɪɚɠɟɧɧɵɦɢ ɬɨɱɧɵɦɢ ɮɨɪɦɭɥɚɦɢ ɱɟɪɟɡ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ. Ɍɚɤɠɟ ɢɦɟɸɬɫɹ ɢɬɟɪɚɰɢɨɧɧɵɟ ɦɟɬɨɞɵ, ɜ ɤɨɬɨɪɵɯ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɨɥɭɱɚɸɬɫɹ ɤɚɤ ɩɪɟɞɟɥɵ ɧɟɤɨɬɨɪɵɯ ɱɢɫɥɨɜɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ, ɬɚɤ ɠɟ ɤɚɤ ɢ ɤɨɦɩɨɧɟɧɬɵ

ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɢɦ ɫɨɛɫɬɜɟɧɧɵɯ ɜɟɤɬɨɪɨɜ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɜ

ɢɬɟɪɚɰɢɨɧɧɵɯ ɦɟɬɨɞɚɯ, ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɜɵɱɢɫɥɹɸɬɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ, ɛɟɡ

ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ

ɜɵɱɢɫɥɟɧɢɹ

ɤɨɷɮɮɢɰɢɟɧɬɨɜ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɩɨɥɢɧɨɦɚ, ɱɬɨ ɡɧɚɱɢɬɟɥɶɧɨ ɭɩɪɨɳɚɟɬ ɡɚɞɚɱɭ, ɬɚɤ ɤɚɤ ɜɵɱɢɫɥɟɧɢɟ ɤɨɪɧɟɣ ɩɨɥɢɧɨɦɚ, ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɬɨɪɨɝɨ ɢɡɜɟɫɬɧɵ, ɬɪɭɞɨɟɦɤɢɣ ɩɪɨɰɟɫɫ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ MathCad ɩɨɡɜɨɥɹɟɬ ɧɚɯɨɞɢɬɶ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɛɟɡ ɬɪɭɞɨɟɦɤɢɯ ɜɵɱɢɫɥɟɧɢɣ. ɇɚ ɪɢɫ. 2.7 ɩɨɤɚɡɚɧ ɮɪɚɝɦɟɧɬ ɪɚɛɨɱɟɝɨ ɞɨɤɭɦɟɧɬɚ ɜɵɱɢɫɥɟɧɢɣ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɦɚɬɪɢɰɵ (2.3) ɞɥɹ ɡɧɚɱɟɧɢɣ (2.15). ȼ ɫɢɫɬɟɦɟ MathCad ɮɭɧɤɰɢɹ eigenvals [61] ɩɨɡɜɨɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɜɫɟ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ, ɚ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ eigenvecs ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɫɟ ɫɨɛɫɬɜɟɧɧɵɟ ɜɟɤɬɨɪɵ.

72

2.4.3. Ⱥɧɚɥɢɡ ɭɫɬɨɣɱɢɜɨɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ MathCad

Ɂɧɚɹ ɜɫɟ ɫɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɟɝɨ ɭɫɬɨɣɱɢɜɨɫɬɶ. ȿɫɥɢ ɜɫɟ ɤɨɪɧɢ Oj ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɢɦɟɸɬ ɨɬɪɢɰɚɬɟɥɶɧɭɸ ɜɟɳɟɫɬɜɟɧɧɭɸ ɱɚɫɬɶ,

ɬ. ɟ. ReOj < 0, ɬɨ

ɨɧ ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɵɦ (ɫɦ. ɩ. 1.5).

Ɋɢɫɭɧɨɤ 2.7 - ȼɵɱɢɫɥɟɧɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɦɧɨɝɨɱɥɟɧɚ ɜ ɫɢɫɬɟɦɟ MathCad ȿɫɥɢ ɜɵɱɢɫɥɟɧɢɟ ɜɫɟɯ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ (2.5) ɜɵɡɵɜɚɟɬ ɡɚɬɪɭɞɧɟɧɢɹ ɢɥɢ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɵɦ, ɬɨ ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɩɪɢɦɟɧɢɜ ɤɪɢɬɟɪɢɣ Ɋɚɭɫɚ-Ƚɭɪɜɢɰɚ. ɋɨɝɥɚɫɧɨ ɬɟɨɪɟɦɟ 1.2 (Ⱥ. ɋɬɨɞɨɥɚ) (ɫɦ. ɩ. 1.5) ɭɫɬɨɣɱɢɜɨɫɬɶ ɦɧɨɝɨɱɥɟɧɚ (2.5), ɚ ɡɧɚɱɢɬ ɢ ɦɚɬɪɢɰɵ (2.3), ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɜɵɱɢɫɥɢɜ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ (ɫɦ. ɩ. 2.4.1). ȼɫɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɭɫɬɨɣɱɢɜɨɝɨ 73

ɦɧɨɝɨɱɥɟɧɚ ɩɨɥɨɠɢɬɟɥɶɧɵ. ɇɨ

ɩɨɥɨɠɢɬɟɥɶɧɨɫɬɶ

ɤɨɷɮɮɢɰɢɟɧɬɨɜ

ɟɫɬɶ

ɧɟɨɛɯɨɞɢɦɨɟ,

ɧɨ

ɧɟ

ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɟ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɧɟɪɚɜɟɧɫɬɜ (2.21). Ⱦɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɦɧɨɝɨɱɥɟɧɚ (2.5) ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ ɜɵɩɨɥɧɟɧɢɹ ɤɪɢɬɟɪɢɹ ɊɚɭɫɚȽɭɪɜɢɰɚ (ɫɦ. ɩ. 1.5). ɉɪɢɦɟɪ 2.3. ɂɫɫɥɟɞɨɜɚɬɶ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (2.2) ɫ ɡɚɞɚɧɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (2.1), ɨɩɢɫɵɜɚɸɳɭɸ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ 3 ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɷɤɨɧɨɦɢɤɢ, ɟɫɥɢ

W2( 1 )

0.1, W2( 2 )

0.2 , W2( 3 )

0.3,

W1( 1,1 )

0.3, W1( 1,2 )

0.2 , W1( 1,3 )

0.1,

W1( 2 ,1 )

0.4 , W1( 2 ,2 )

0.1, W1( 2 ,3 )

0.5,

W1( 3 ,1 )

0.6 , W1( 3,2 )

0.2, W1( 3 ,3 )

0.3.

Ɋɟɲɢɦ ɩɪɢɦɟɪ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ MathCad. Ⱦɥɹ ɚɧɚɥɢɡɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɨɩɢɫɵɜɚɸɳɟɣ ɞɢɧɚɦɢɤɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɛɨɱɟɣ ɫɢɥɵ ɞɥɹ ɬɪɟɯ ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɟɣ

ɷɤɨɧɨɦɢɤɢ

ɫɨɫɬɚɜɢɦ

ɦɚɬɪɢɰɭ

W

ɤɨɷɮɮɢɰɢɟɧɬɨɜ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɜɜɟɞɹ ɤɨɧɤɪɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ

W1(i, j ) ,

W2(i)

(i,

j=1,…,n);

ɡɚɬɟɦ

ɫɨɫɬɚɜɢɦ

ɦɚɬɪɢɰɭ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɚɬɪɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ W.

Ƚɭɪɜɢɰɚ

ɞɥɹ

ɇɚ ɨɫɧɨɜɚɧɢɢ

ɜɵɱɢɫɥɟɧɧɵɯ ɞɢɚɝɨɧɚɥɶɧɵɯ ɦɢɧɨɪɨɜ ɩɨɥɭɱɟɧɧɨɣ ɦɚɬɪɢɰɵ Ƚɭɪɜɢɰɚ ɫɞɟɥɚɟɦ ɜɵɜɨɞ ɨɛ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ. ɇɚ ɪɢɫ. 2.8 ɩɨɤɚɡɚɧ ɮɪɚɝɦɟɧɬ ɪɚɛɨɱɟɝɨ ɞɨɤɭɦɟɧɬɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ MathCad ɫ ɪɟɲɟɧɢɟɦ ɩɪɢɦɟɪɚ 2.3. Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɛɵɥ ɢɫɩɨɥɶɡɨɜɚɧ ɦɟɬɨɞ Ⱦ.Ʉ. Ɏɚɞɞɟɟɜɚ. ȼ ɩɪɢɥɨɠɟɧɢɹɯ 1, 2 ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɟɲɟɧɢɹ ɩɪɢɦɟɪɚ 2.3 ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ MathCad ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɨɝɨ ɦɟɬɨɞɚ ɢ ɦɟɬɨɞɚ Ⱥ. ɇ. Ʉɪɵɥɨɜɚ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɨɥɢɧɨɦɚ. 74

N_otr P

rows

P 0

size

N_otr 2

0 P

fnW_R_U

if cols P 0 (a b)

rows

P 0

N_otr rows

if b t N_otr a N_otr

ª P 0 a b N_otr º if a ¬ ¼

0 N_otr

fnW ( a b )

N_otr

0

P 0 a b N_otr i

P 1

b N_otr

0 if a t N_otr b t N_otr 0 §

¨ ©

¦

¸ ¹

i

fnW_R_U

P 1 b

( i b ) · if a

fnW_R_U (a b)

b

if ( a N_otr ) ( b t N_otr )

if a t N_otr b N_otr

if a N_otr b N_otr 0

ª¬ P 1 º¼ a if a W

matrix ( size size fnW )

mW ( i)

W

b E

identity ( size )

if i 2

§ mW ( i 1 ) tr ( mW ( i 1 ) ) E · W if i t 2 ¨ ¸ i 1 © ¹ tr ( mW ( i 1 ) ) i 1

fa ( i x ) a

matrix ( size 1 fa )

ka ( i)

1

if i

size

a size i 1 if i z size MPf ( i j )

if ( i N_otr ) r_e m i 2 1 0 ka ( r_e j )

if j d r_e

if i t N_otr l_e m ( i N_otr ) 2 1 0 ka ( l_e j size ) MP stability

if j t l_e

matrix ( size size MPf ) s m 0 for

i 0 size 1

s m s 1

submatrix ( MP 0 i 0 i)

if

! 0

stability matrix: yes -1, no - 0.

Ɋɢɫɭɧɨɤ 2.8 - Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ ɜ ɩɚɤɟɬɟ MathCad 75

ɋɨɫɬɚɜɢɦ

ɦɚɬɪɢɰɭ

ɤɨɷɮɮɢɰɢɟɧɬɨɜ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

(i ) (i , j ) ɭɪɚɜɧɟɧɢɣ (2.2) ɞɥɹ ɞɚɧɧɵɯ ɡɧɚɱɟɧɢɣ W1 , W2 , i,j =1,…,3 (ɪɢɫ. 2.9):

N_otr rows P 0 P

size N_otr 2

0 P if cols P0

fnW_R_U( a b)

rows P0

N_otr

0

P0 a bN_otr

if b t N_otr a N_otr

ª P0 a bN_otr º if a ¬ ¼

i 0 N_otr fnW( a b)

N_otr rows P 1

b N_otr

0 if a t N_otr b t N_otr 0 §

¨ ©

¦

fnW_R_U( i b) · if a

¸ ¹

i

b

fnW_R_U( a b) if ( a N_otr ) ( b t N_otr )

P1 b

if a t N_otr b N_otr

if a N_otr b N_otr 0

ª¬ P1 º¼ a if a W matrix( size size fnW)

W

§ 0.1 ¨ ¨ 0 ¨ 0 ¨ ¨ 0.1 ¨ 0.1 ¨ © 0.1

b E identity( size)

0

0

0.3

0.4

0.6 ·

0.2

0

0.2

0.1

0

0.3

0.1

0.5

0.2 ¸ 0.3 ¸

0.2

0.3

0.6

0

0.2

0.3

0

1

0.2

0.3

0

0

¸ ¸

0 ¸ 0 ¸

¸

1.1 ¹

Ɋɢɫɭɧɨɤ 2.9 - Ɇɚɬɪɢɰɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ W ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ

ɭɪɚɜɧɟɧɢɣ ɜ ɫɢɫɬɟɦɟ MathCad ȼɵɱɢɫɥɢɦ ɤɨɷɮɮɢɰɢɟɧɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W (ɪɢɫ. 2.10):

76

mW( i)

W if i 2

§ mW( i 1) tr( mW( i 1) ) E· W if i t 2 ¨ ¸ i 1 © ¹ tr( mW( i 1) ) i 1

fa( i x)

3.3 § · ¨ ¸ 3.87 ¨ ¸ ¨ ¸ 1.904 ¨ ¸ 0.353 ¨ ¸ 0.014 ¨ ¸ ¨ 3¸ © 1.008 u 10 ¹

a matrix( size 1 fa) a

Ɋɢɫɭɧɨɤ 2.10 - ȼɵɱɢɫɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ

ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W ɜ ɫɢɫɬɟɦɟ MathCad Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɦɚɬɪɢɰɵ W ɫɨɫɬɚɜɢɦ ɦɚɬɪɢɰɭ Ƚɭɪɜɢɰɚ (ɪɢɫ. 2.11): ka ( i)

1

if i

size

a size i 1 MPf ( i j )

if i z size

if ( i N_otr ) r_e m i 2 1 0 ka ( r_e j )

if

j d r_e

if i t N_otr l_e m ( i N_otr ) 2 1 0 ka ( l_e j size ) MP

MP

if j t l_e

matrix ( size size MPf )

§ 0.014 ¨ ¨ 1.904 ¨ ¨ 3.3 ¨ ¨ 0 ¨ 0 ¨ © 0

1.008

u 10

3

0

0 1.008

u 10

3

0

0

0

0

0.353

0.014

3.87

1.904

0.353

0.014

1

3.3

3.87

1.904

0.353

0

0

1

3.3

3.87

0

0

0

0

1

1.008

u 10

3

· ¸ ¸ ¸ ¸ ¸ ¸ ¸ ¸ ¹

Ɋɢɫɭɧɨɤ 2.11 - ɋɨɫɬɚɜɥɟɧɢɟ ɦɚɬɪɢɰɵ Ƚɭɪɜɢɰɚ ɞɥɹ ɦɚɬɪɢɰɵ W ɜ ɫɢɫɬɟɦɟ

MathCad 77

ɇɚ ɨɫɧɨɜɚɧɢɢ ɧɟɨɛɯɨɞɢɦɨɝɨ ɢ ɞɨɫɬɚɬɨɱɧɨɝɨ ɩɪɢɡɧɚɤɚ ɭɫɬɨɣɱɢɜɨɫɬɢ (ɤɪɢɬɟɪɢɣ

Ɋɚɭɫɚ-Ƚɭɪɜɢɰɚ)

ɫɞɟɥɚɟɦ

ɜɵɜɨɞ

ɨɛ

ɭɫɬɨɣɱɢɜɨɫɬɢ

ɫɢɫɬɟɦɵ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (2.2) ɫ ɡɚɞɚɧɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (2.1), ɝɞɟ 1 – ɨɡɧɚɱɚɟɬ ɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ (ɪɢɫ. 2.12): stability

sm 0 for i 0 size 1 s m s 1 if

submatrix ( MP 0 i 0 i) ! 0

stability matrix: yes -1, no - 0.

Ɋɢɫɭɧɨɤ 2.12 - Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ ɜ ɫɢɫɬɟɦɟ MathCad

ɂɡ ɪɢɫɭɧɤɚ 2.12 ɜɢɞɧɨ, ɱɬɨ ɩɨɥɭɱɟɧɧɚɹ ɫɢɫɬɟɦɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɪɢ ɡɚɞɚɧɧɵɯ ɜɟɪɨɹɬɧɨɫɬɹɯ ɛɭɞɟɬ ɭɫɬɨɣɱɢɜɚ, ɚ ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɢ (i , j ) ɪɵɧɨɤ ɬɪɭɞɚ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ, ɞɥɹ ɡɧɚɱɟɧɢɣ W1 ,

W2(i ) (i,j =1,…,3) ɢ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ (2.1). ɋ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɶ (2.1), (2.2) ɜ ɞɚɧɧɨɦ ɩɪɢɦɟɪɟ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɭɪɨɜɧɟɦ ɡɚɧɹɬɨɫɬɢ (2.2) ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɨɬɤɥɨɧɟɧɢɹɯ ɨɬ (2.2) ɫɢɫɬɟɦɚ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɫɧɨɜɚ ɜɨɡɜɪɚɬɢɬɫɹ ɤ ɧɚɱɚɥɶɧɨɦɭ ɫɨɫɬɨɹɧɢɸ. 2.5. ȼɵɜɨɞɵ

Ɉɛɨɛɳɚɹ ɦɚɬɟɪɢɚɥ, ɢɡɥɨɠɟɧɧɵɣ ɜɨ ɜɬɨɪɨɣ ɱɚɫɬɢ ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɫɞɟɥɚɟɦ ɤɪɚɬɤɢɟ ɜɵɜɨɞɵ: 1. ɞɥɹ

Ɋɚɡɪɚɛɨɬɚɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ

ɧɟɫɤɨɥɶɤɢɯ

ɪɚɡɥɢɱɧɵɯ

ɨɬɪɚɫɥɟɣ

ɷɤɨɧɨɦɢɤɢ,

ɩɨɡɜɨɥɹɸɳɚɹ

ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɬɟɧɞɟɧɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ. 2.

ɉɪɟɞɥɨɠɟɧɚ

ɦɟɬɨɞɢɤɚ

ɨɩɪɟɞɟɥɟɧɢɹ

ɭɫɬɨɣɱɢɜɨɝɨ

ɫɨɫɬɨɹɧɢɹ

ɢ

ɞɢɧɚɦɢɤɢ ɪɵɧɤɚ ɬɪɭɞɚ ɩɪɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɢ ɧɚ ɧɟɦ ɪɚɛɨɱɟɣ ɫɢɥɵ. 3.

ɍɤɚɡɚɧɧɚɹ ɦɟɬɨɞɢɤɚ ɪɟɚɥɢɡɨɜɚɧɚ ɜ ɜɢɞɟ ɩɪɨɝɪɚɦɦɧɨɝɨ ɩɪɨɞɭɤɬɚ (ɫ 78

ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɚɤɟɬɚ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ MathCad). ɋ ɩɨɦɨɳɶɸ ɪɚɡɪɚɛɨɬɚɧɧɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ ɦɨɠɧɨ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɬɨɥɶɤɨ ɭɫɬɨɣɱɢɜɨɫɬɶ ɪɵɧɤɚ ɬɪɭɞɚ, ɩɪɨɫɥɟɞɢɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɬɟɧɞɟɧɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ. ȼɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɩɨɫɬɪɨɟɧɢɹ ɬɚɤɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɭɱɢɬɵɜɚɬɶ ɢ ɞɪɭɝɢɟ ɩɚɪɚɦɟɬɪɵ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ. Ⱦɥɹ ɷɬɨɝɨ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɚɩɩɚɪɚɬ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ.

79

ȽɅȺȼȺ 3. ȼȿɊɈəɌɇɈɋɌɇȺə ɆɈȾȿɅɖ ȻɂɊɀɂ ɌɊɍȾȺ ɄȺɄ ɆȿɌɈȾɂɄȺ ȼɕɑɂɋɅȿɇɂə ɈɋɇɈȼɇɕɏ ɏȺɊȺɄɌȿɊɂɋɌɂɄ ɊɕɇɄȺ ɌɊɍȾȺ 3.1. Ɉɛɨɫɧɨɜɚɧɢɟ ɜɟɪɨɹɬɧɨɫɬɧɨɝɨ ɩɨɞɯɨɞɚ ɤ ɨɩɢɫɚɧɢɸ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ

ɇɚ

ɫɨɜɪɟɦɟɧɧɨɦ

ɩɟɪɦɚɧɟɧɬɧɨɣ

ɷɬɚɩɟ

ɷɤɨɧɨɦɢɱɟɫɤɨɣ

ɩɥɨɞɨɬɜɨɪɧɵɦɢ

ɩɨɞɯɨɞɵ

ɢ

ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɦɟɬɨɞɵ

ɪɚɡɜɢɬɢɹ ɢ

ɜ

ɪɢɫɤɚ

ɢɦɢɬɚɰɢɨɧɧɨɝɨ

ɭɫɥɨɜɢɹɯ ɹɜɥɹɸɬɫɹ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ.

ɉɪɟɞɥɨɠɟɧɧɚɹ ɜ ɝɥɚɜɟ 2 ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ (2.8) ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɨɫɥɟɞɢɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɬɟɧɞɟɧɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ ɢ ɢɫɫɥɟɞɨɜɚɬɶ ɪɵɧɨɤ ɧɚ ɩɪɟɞɦɟɬ ɟɝɨ ɭɫɬɨɣɱɢɜɨɫɬɢ. ɇɟɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ ɪɵɧɤɚ ɬɪɭɞɚ ɜ ɭɫɥɨɜɢɹɯ ɫɬɚɧɨɜɥɟɧɢɹ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɤ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɦ ɩɟɪɟɯɨɞɧɵɦ ɩɪɨɰɟɫɫɚɦ ɢ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɬɶ ɧɚ ɞɢɧɚɦɢɤɭ ɭɪɨɜɧɹ ɡɚɧɹɬɨɫɬɢ. ɉɨɥɭɱɟɧɧɵɟ ɫɜɟɞɟɧɢɹ ɨ ɞɢɧɚɦɢɤɟ ɭɪɨɜɧɹ ɡɚɧɹɬɨɫɬɢ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɭɥɭɱɲɟɧɢɹ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ, ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɨɞɧɨɣ ɢɡ ɫɨɫɬɚɜɧɵɯ ɱɚɫɬɟɣ ɮɭɧɤɰɢɨɧɚɥɶɧɨ - ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɪɵɧɤɚ ɬɪɭɞɚ. Ȼɢɪɠɚ

ɬɪɭɞɚ

ɹɜɥɹɟɬɫɹ

ɤɚɬɚɥɢɡɚɬɨɪɨɦ

ɫɨɫɬɨɹɧɢɹ

ɪɵɧɤɚ

ɬɪɭɞɚ.

ɍɫɬɨɣɱɢɜɨɫɬɶ ɢɥɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɪɵɧɤɚ ɬɪɭɞɚ ɩɨɜɥɟɱɟɬ ɡɚ ɫɨɛɨɣ ɢɡɦɟɧɟɧɢɹ ɜ ɪɚɛɨɬɟ ɛɢɪɠɢ ɬɪɭɞɚ, ɫɜɹɡɚɧɧɵɟ ɫ ɨɛɫɥɭɠɢɜɚɧɢɟɦ ɩɨɬɨɤɨɜ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɫ ɪɚɡɥɢɱɧɨɣ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ. ɉɪɢɦɟɧɟɧɢɟ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɨɡɜɨɥɹɟɬ ɨɩɢɫɚɬɶ ɩɪɨɰɟɫɫɵ, ɩɪɨɬɟɤɚɸɳɢɟ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɛɢɪɠɭ ɬɪɭɞɚ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɢɫɬɟɦɭ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɫɨɝɥɚɫɭɸɳɟɣ ɬɚɤɢɟ ɩɪɨɰɟɫɫɵ ɤɚɤ ɫɩɪɨɫ ɢ ɩɪɟɞɥɨɠɟɧɢɟ ɧɚ ɪɚɛɨɱɭɸ ɫɢɥɭ [80]. ɉɪɢ ɷɬɨɦ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɨɫɬɟɣɲɢɣ. ɂɧɬɟɧɫɢɜɧɨɫɬɶɸ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɫɩɪɨɫ ɧɚ ɬɪɭɞ, ɩɪɟɞɥɨɠɟɧɢɹ 80

ɬɪɭɞɚ, ɚ ɬɚɤɠɟ ɫɨɝɥɚɫɨɜɚɧɢɟ ɫɩɪɨɫɚ ɢ ɩɪɟɞɥɨɠɟɧɢɹ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɩɨɥɭɱɟɧɧɵɯ ɜ ɩɪɨɰɟɫɫɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɚɧɧɵɯ ɦɨɠɧɨ ɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɡɚɧɹɬɨɫɬɶ ɧɚɫɟɥɟɧɢɹ. ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ ɩɨɡɜɨɥɢɬ ɨɩɪɟɞɟɥɢɬɶ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɫɧɨɜɧɵɯ ɫɨɰɢɚɥɶɧɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɪɚɡɜɢɬɢɹ. ɋɨɡɞɚɧɢɟ ɦɨɞɟɥɟɣ ɛɢɪɠɢ ɬɪɭɞɚ ɨɛɟɫɩɟɱɢɬ ɜɵɛɨɪ ɫɬɪɚɬɟɝɢɢ ɜ ɫɮɟɪɟ ɡɚɧɹɬɨɫɬɢ, ɭɱɢɬɵɜɚɹ ɩɪɢ ɷɬɨɦ ɷɤɨɧɨɦɢɱɟɫɤɢɟ, ɩɨɥɢɬɢɱɟɫɤɢɟ, ɫɨɰɢɚɥɶɧɵɟ ɚɫɩɟɤɬɵ. Ɉɫɧɨɜɧɨɣ ɡɚɞɚɱɟɣ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ ɢɡɭɱɟɧɢɟ ɪɟɠɢɦɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ

ɨɛɫɥɭɠɢɜɚɸɳɟɣ

ɫɢɫɬɟɦɵ

ɢ

ɢɫɫɥɟɞɨɜɚɧɢɟ

ɹɜɥɟɧɢɣ,

ɜɨɡɧɢɤɚɸɳɢɯ ɜ ɩɪɨɰɟɫɫɟ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ʌɸɛɨɟ ɨɩɢɫɚɧɢɟ ɫɢɫɬɟɦɵ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɬɟɪɦɢɧɚɯ ɧɟɢɡɛɟɠɧɨ ɭɩɪɨɳɚɟɬ ɩɪɚɤɬɢɱɟɫɤɭɸ ɫɢɬɭɚɰɢɸ ɜɫɥɟɞɫɬɜɢɟ ɬɨɝɨ, ɱɬɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɢɞɟɚɥɢɡɢɪɨɜɚɧɧɵɟ ɩɨɧɹɬɢɹ [10]. ɉɪɢ ɷɬɨɦ ɜɨɡɧɢɤɚɸɬ ɡɚɞɚɱɢ ɨɩɬɢɦɢɡɚɰɢɢ: ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɞɨɫɬɢɱɶ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɭɪɨɜɧɹ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɫɨɤɪɚɳɟɧɢɹ ɨɱɟɪɟɞɢ ɢɥɢ ɩɨɬɟɪɶ ɬɪɟɛɨɜɚɧɢɣ) ɩɪɢ ɦɢɧɢɦɚɥɶɧɵɯ ɡɚɬɪɚɬɚɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɨɫɬɨɟɦ ɨɛɫɥɭɠɢɜɚɸɳɢɯ ɭɫɬɪɨɣɫɬɜ. Ɉɩɬɢɦɢɡɚɰɢɸ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɦɨɠɧɨ ɩɪɨɜɨɞɢɬɶ ɫ ɞɜɭɯ ɬɨɱɟɤ ɡɪɟɧɢɹ: ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɪɚɛɨɬɨɞɚɬɟɥɹ ɢɥɢ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɛɟɡɪɚɛɨɬɧɵɯ, ɩɨɥɭɱɚɸɳɢɯ ɨɛɫɥɭɠɢɜɚɧɢɟ. ɉɨɫɬɪɨɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɢɬ ɪɟɲɢɬɶ ɨɩɬɢɦɢɡɚɰɢɨɧɧɭɸ ɡɚɞɚɱɭ ɜɵɛɨɪɚ ɪɚɰɢɨɧɚɥɶɧɨɣ ɫɬɪɭɤɬɭɪɵ ɫɢɫɬɟɦɵ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫ ɭɱɟɬɨɦ ɜɫɟɯ ɨɛɫɬɨɹɬɟɥɶɫɬɜ ɢ ɨɫɨɛɟɧɧɨɫɬɟɣ ɭɫɥɨɜɢɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ. 3.2. Ɋɚɡɪɚɛɨɬɤɚ ɜɟɪɨɹɬɧɨɫɬɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ

Ȼɢɪɠɭ ɬɪɭɞɚ ɦɨɠɧɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɧɟɤɨɬɨɪɭɸ ɫɢɫɬɟɦɭ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɋɆɈ) ɫ ɨɠɢɞɚɧɢɟɦ (ɨɱɟɪɟɞɶɸ): ɨɬɞɟɥɵ ɛɢɪɠɢ – ɤɚɧɚɥɵ ɋɆɈ, ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ – ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɜ ɋɆɈ, ɨɱɟɪɟɞɶ ɧɚ ɛɢɪɠɟ – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɜ ɋɆɈ ɢ ɬ.ɞ. [16, 23, 24, 25]. ɉɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɜ ɬɚɤɨɣ ɋɆɈ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɚɦɢ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ, 81

ɨɪɞɢɧɚɪɧɨɫɬɢ, ɛɟɡ ɩɨɫɥɟɞɟɣɫɬɜɢɹ ɢɧɬɟɧɫɢɜɧɨɫɬɢ O, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɹɜɥɹɟɬɫɹ ɩɪɨɫɬɟɣɲɢɦ. ȼɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ Ɍɨɛ — ɩɨɤɚɡɚɬɟɥɶɧɨɟ, ɫ ɩɚɪɚɦɟɬɪɨɦ P=const ɨɩɪɟɞɟɥɹɟɦɵɦ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ ɜɵɪɚɠɟɧɢɟɦ (1.21), ɝɞɟ P - ɜɟɥɢɱɢɧɚ, ɨɛɪɚɬɧɚɹ ɫɪɟɞɧɟɦɭ ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ:

1 , mtɨɛ

P

mtɨɛ Ɍɪɟɛɨɜɚɧɢɟ

ɨɬ

ɛɟɡɪɚɛɨɬɧɨɝɨ

M [Tɨɛ ] . ɫɬɚɧɨɜɢɬɫɹ

ɜ

ɨɱɟɪɟɞɶ

ɢ

ɨɠɢɞɚɟɬ

ɨɛɫɥɭɠɢɜɚɧɢɹ. ȼɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɝɪɚɧɢɱɟɧɨ ɧɟɤɨɬɨɪɵɦ ɫɪɨɤɨɦ Ɍɨɠ; ɟɫɥɢ ɞɨ ɢɫɬɟɱɟɧɢɹ ɷɬɨɝɨ ɫɪɨɤɚ ɬɪɟɛɨɜɚɧɢɟ ɧɟ ɛɭɞɟɬ ɩɪɢɧɹɬɨ ɤ ɨɛɫɥɭɠɢɜɚɧɢɸ, ɬɨ ɨɧɨ ɩɨɤɢɞɚɟɬ

ɨɱɟɪɟɞɶ.

ɋɪɨɤ

ɨɠɢɞɚɧɢɹ

Ɍɨɠ ɛɭɞɟɦ

ɫɱɢɬɚɬɶ

ɫɥɭɱɚɣɧɵɦ

ɢ

ɪɚɫɩɪɟɞɟɥɟɧɧɵɦ ɬɚɤ ɠɟ ɩɨ ɩɨɤɚɡɚɬɟɥɶɧɨɦɭ ɡɚɤɨɧɭ, ɫ ɩɚɪɚɦɟɬɪɨɦ Q = const, ɨɩɪɟɞɟɥɹɟɦɵɦ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ ɜɵɪɚɠɟɧɢɟɦ (1.23), ɝɞɟ ɩɚɪɚɦɟɬɪ

Q — ɜɟɥɢɱɢɧɚ, ɨɛɪɚɬɧɚɹ ɫɪɟɞɧɟɦɭ ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ ɜ ɨɱɟɪɟɞɢ:

Q

1 mtɨɠ ,

mtɨɠ

M [Tɨɠ ] .

Ɍɚɤ ɤɚɤ ɤɨɥɢɱɟɫɬɜɨ ɛɟɡɪɚɛɨɬɧɵɯ, ɫɬɨɹɳɢɯ ɜ ɨɱɟɪɟɞɢ ɧɚ ɛɢɪɠɭ ɬɪɭɞɚ, ɡɧɚɱɢɬɟɥɶɧɨ, ɬɨ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɟɝɨ ɛɟɫɤɨɧɟɱɧɨ ɛɨɥɶɲɢɦ. ɉɪɢ ɩɨɤɚɡɚɬɟɥɶɧɨɦ ɡɚɤɨɧɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɪɨɤɚ ɨɠɢɞɚɧɢɹ ɩɪɨɩɭɫɤɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɛɢɪɠɢ ɬɪɭɞɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɜ ɤɚɤɨɦ ɩɨɪɹɞɤɟ ɨɛɫɥɭɠɢɜɚɸɬɫɹ ɬɪɟɛɨɜɚɧɢɹ. ɉɪɟɞɩɨɥɚɝɚɟɦ, ɱɬɨ ɛɢɪɠɚ ɬɪɭɞɚ ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɫɥɟɞɭɸɳɢɯ ɫɨɫɬɨɹɧɢɹɯ [78]: ɯ0 - ɧɢ ɨɞɢɧ ɨɬɞɟɥ ɧɟ ɡɚɧɹɬ (ɨɱɟɪɟɞɢ ɧɟɬ), ɯ1 - ɡɚɧɹɬ ɪɨɜɧɨ ɨɞɢɧ ɨɬɞɟɥ (ɨɱɟɪɟɞɢ ɧɟɬ), ……………………………………………………... ɯɤ - ɡɚɧɹɬɨ ɪɨɜɧɨ k ɨɬɞɟɥɨɜ (ɨɱɟɪɟɞɢ ɧɟɬ), 82

…………………………………………………….. ɯn - ɡɚɧɹɬɵ ɜɫɟ n ɨɬɞɟɥɨɜ (ɨɱɟɪɟɞɢ ɧɟɬ), ɯn+1 - ɡɚɧɹɬɵ ɜɫɟ n ɨɬɞɟɥɨɜ, ɨɞɧɨ ɬɪɟɛɨɜɚɧɢɟ ɫɬɨɢɬ ɜ ɨɱɟɪɟɞɢ, …………………………………………………….. xn+s - ɡɚɧɹɬɵ ɜɫɟ n ɨɬɞɟɥɨɜ, s ɬɪɟɛɨɜɚɧɢɣ ɫɬɨɹɬ ɜ ɨɱɟɪɟɞɢ, …………………………………………………….. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ pk(t) (k=0, 1, … n, …) ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɛɢɪɠɚ ɬɪɭɞɚ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɯɤ. ȼɟɪɨɹɬɧɨɫɬɢ

pk(t)

ɭɞɨɜɥɟɬɜɨɪɹɸɬ

ɫɢɫɬɟɦɟ

ɛɟɫɤɨɧɟɱɧɨɝɨ

ɱɢɫɥɚ

ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ Ʉɨɥɦɨɝɨɪɨɜɚ (1.14) ɢ ɪɚɜɟɧɫɬɜɚ (1.17): dp0 (t ) Op0 (t ) Pp1 (t ), dt dp1 (t ) Op0 (t ) (O P ) p1 (t ) 2Pp2 (t ), dt ................................................................................................

½ ° ° ° ° ° ° ° dpk (t ) Opk 1 (t ) (O kP ) pk (t ) (k 1) Ppk 1 (t ), (1 d k d n 1), ° dt ° ................................................................................................ ° ¾ dpn (t ) ° Opn1 (t ) (O kP ) pn (t ) (nP Q ) pn1 (t ), dt ° ° ................................................................................................ ° dpn s (t ) Opn s1 (t ) (O nP sQ ) pn s (t ) [nP ( s 1)Q ] pn s 1 (t ),°° dt ° ................................................................................................ ° f ° p 1 . ° ¦ k k 0 ¿

(3.1)

ɋɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɧɚ ɩɪɚɤɬɢɤɟ ɜɟɪɨɹɬɧɨɫɬɢ pn+s(t) ɫɬɚɧɨɜɹɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɚɥɵɦɢ ɩɪɢ ɜɨɡɪɚɫɬɚɧɢɢ s, ɚ ɡɧɚɱɢɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɨɬɛɪɨɲɟɧɵ. ȼ ɫɬɚɰɢɨɧɚɪɧɨɦ ɪɟɠɢɦɟ ɫɢɫɬɟɦɚ (3.1) ɢɦɟɟɬ ɜɢɞ:

83

Op0 Pp1

0,

½ ° Op0 (O P ) p1 2 Pp2 0, ° ..........................................................................................° ° Opk 1 (O kP ) pk (k 1) Ppk 1 0, (1 d k d n 1), ° ..........................................................................................° ° Opn1 (O nP ) pn (nP Q ) pn1 0, ¾ ..........................................................................................°° Opn s1 (O nP sQ ) pn s [nP ( s 1)Q ) pn s1 0, ° ° ..........................................................................................° f ° p 1 ° ¦ k k 0 ¿

(3.2)

ɂɡ ɫɨɨɬɧɨɲɟɧɢɣ (3.2) ɦɨɠɧɨ ɧɚɣɬɢ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɮɭɧɤɰɢɨɧɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ [16]: 1) pk - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ ɯɤ (ɡɚɧɹɬɨ ɪɨɜɧɨ k ɨɬɞɟɥɨɜ, ɨɱɟɪɟɞɢ ɧɟɬ): ɞɥɹ ɥɸɛɨɝɨ k < n p k

Ok p0 , k! P k

(3.3)

2) pn - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ ɯn (ɡɚɧɹɬɨ ɪɨɜɧɨ n ɨɬɞɟɥɨɜ, ɨɱɟɪɟɞɢ ɧɟɬ): ɞɥɹ ɥɸɛɨɝɨ k = n pn

On p0 , k! P n

(3.4)

3) pn+s - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ xn+s (ɡɚɧɹɬɵ ɜɫɟ n ɨɬɞɟɥɨɜ, s ɬɪɟɛɨɜɚɧɢɣ ɫɬɨɹɬ ɜ ɨɱɟɪɟɞɢ): ɞɥɹ k>n (k=n+s) ɩɪɢ ɥɸɛɨɦ s t 1 pn s

On s p 0 s

n!P n (nP mQ )

,

(3.5)

m 1

4) p0 - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ ɯ0 (ɧɢ ɨɞɢɧ ɨɬɞɟɥ ɧɢ ɡɚɧɹɬ, ɨɱɟɪɟɞɢ ɧɟɬ)

84

p0

1 f Ok ¦ ¦ k k 0 k! P s 1

.

On s

n

(3.6)

s

n! P n (nP mQ ) m 1

Ɉɛɨɡɧɚɱɢɜ

O P Q P

½ ° ¾, E° °¿

D°

ɝɞɟ ɩɚɪɚɦɟɬɪ D - ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ,

ɩɪɢɯɨɞɹɳɟɟɫɹ ɧɚ ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ, ɩɚɪɚɦɟɬɪ E ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɭɯɨɞɨɜ ɬɪɟɛɨɜɚɧɢɹ, ɫɬɨɹɳɟɝɨ ɜ ɨɱɟɪɟɞɢ, ɩɪɢɯɨɞɹɳɟɟɫɹ ɧɚ ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ, ɬɨɝɞɚ ɮɨɪɦɭɥɵ (3.3), (3.4), (3.5) ɢ (3.6) ɩɪɢɦɭɬ ɜɢɞ: 1) pk - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ ɯɤ (ɡɚɧɹɬɨ ɪɨɜɧɨ k ɨɬɞɟɥɨɜ, ɨɱɟɪɟɞɢ ɧɟɬ):

Dk k!

pk

ɞɥɹ ɥɸɛɨɝɨ 0 d k d n

n

D

k

¦ k!

k 0

D

n

n!

Ds

f

¦ s 1

,

(3.7)

s

(n mE ) m 1

2) pn+s - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ xn+s (ɡɚɧɹɬɵ ɜɫɟ n ɨɬɞɟɥɨɜ, s ɬɪɟɛɨɜɚɧɢɣ ɫɬɨɹɬ ɜ ɨɱɟɪɟɞɢ): ɞɥɹ k>n (k=n+s) ɩɪɢ ɥɸɛɨɦ s t 1

Dn n! pn s

Ds s

(n mE ) m 1

n

Dk

¦ k! k 0

Dn n!

Ds

f

¦ s 1

;

(3.8)

s

(n mE ) m 1

3) p0 - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ ɯ0 (ɧɢ ɨɞɢɧ ɨɬɞɟɥ ɧɢ ɡɚɧɹɬ, ɨɱɟɪɟɞɢ ɧɟɬ)

85

1

p0

n

¦ k 0

Dk k!

Dn

.

Ds

f

¦ n!

(3.9)

s

(n mE )

s 1

m 1

Ʉ ɜɟɪɨɹɬɧɨɫɬɧɵɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɮɭɧɤɰɢɨɧɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɦɨɠɧɨ ɬɚɤɠɟ ɨɬɧɟɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɱɢɫɥɚ ɬɪɟɛɨɜɚɧɢɣ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɱɟɪɟɞɢ, ms ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɬɪɟɛɨɜɚɧɢɟ ɩɨɤɢɧɟɬ ɛɢɪɠɭ ɧɟɨɛɫɥɭɠɟɧɧɵɦ PH [91]. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɱɢɫɥɚ ɬɪɟɛɨɜɚɧɢɣ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɱɟɪɟɞɢ, ms, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ:

Dn n!

¦

M [s]

¦ sp

n s

n

(n mE )

D

n

D

k

¦ k!

s 1

s

s 1

f

ms

sD s

f

m 1 f

n!

k 0

¦ s 1

.

Ds

(3.10)

s

(n mE ) m 1

ȼɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɬɪɟɛɨɜɚɧɢɟ ɩɨɤɢɧɟɬ ɛɢɪɠɭ ɧɟɨɛɫɥɭɠɟɧɧɵɦ, PH, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ:

Dn n! PH

E D

n

D

k 0

¦ s 1

k

¦ k!

sD s

f

D

s

(n mE )

m 1 n f

n!

¦ s 1

Ds

.

(3.11)

s

(n mE ) m 1

Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɩɭɫɤɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɛɢɪɠɢ ɬɪɭɞɚ, q, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ: q = 1 - PH.

(3.12)

ȼ ɫɥɭɱɚɟ ɧɟɭɫɬɨɣɱɢɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ ɛɢɪɠɭ ɬɪɭɞɚ ɦɨɠɧɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɱɢɫɬɭɸ ɫɢɫɬɟɦɭ ɫ ɨɠɢɞɚɧɢɟɦ (Eo0), ɬɚɤ ɤɚɤ ɭɜɟɥɢɱɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɩɨɜɥɟɱɟɬ ɡɚ ɫɨɛɨɣ ɭɜɟɥɢɱɟɧɢɟ ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ.

ȼɟɪɨɹɬɧɨɫɬɶ

ɬɨɝɨ,

ɱɬɨ

ɬɪɟɛɨɜɚɧɢɟ

ɩɨɤɢɧɟɬ

ɛɢɪɠɭ

ɬɪɭɞɚ

ɧɟɨɛɫɥɭɠɟɧɧɵɦ PH = 0, ɬ. ɟ. ɛɟɡɪɚɛɨɬɧɵɣ ɨɛɹɡɚɬɟɥɶɧɨ ɞɨɠɞɟɬɫɹ ɨɛɫɥɭɠɢɜɚɧɢɹ 86

ɫɜɨɟɝɨ ɬɪɟɛɨɜɚɧɢɹ. ɉɪɢ tof ɫɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ ɫɢɫɬɟɦɵ ɧɚɫɬɭɩɢɬ, ɤɨɝɞɚ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɡɚ ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ, ɧɟ ɩɪɟɜɵɫɢɬ ɤɨɥɢɱɟɫɬɜɨ ɨɛɫɥɭɠɢɜɚɸɳɢɯ ɤɚɧɚɥɨɜ, ɬ. ɟ. D
Dk pk

k! n

¦

(0 d k d n);

D n 1 k! n!(n D )

D

k 0

k

(3.13)

2)pn+s - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ ɫɨɫɬɨɹɧɢɢ xn+s (ɡɚɧɹɬɵ ɜɫɟ n ɨɬɞɟɥɨɜ, s ɬɪɟɛɨɜɚɧɢɣ ɫɬɨɹɬ ɜ ɨɱɟɪɟɞɢ):

D n s pn s

n! n s n

¦ k 0

3)

(S t 0);

D n 1 k! n!(n D )

Dk

(3.14)

p0 - ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɜ

ɫɨɫɬɨɹɧɢɢ ɯ0 (ɧɢ ɨɞɢɧ ɨɬɞɟɥ ɧɢ ɡɚɧɹɬ, ɨɱɟɪɟɞɢ ɧɟɬ)

1

p0

n

¦

D n 1 ; k! n!(n D ) k

D

k 0

(3.15)

4)ms - ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɱɢɫɥɚ ɬɪɟɛɨɜɚɧɢɣ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɨɱɟɪɟɞɢ:

D n 1 n n!(1 ms

n

¦ k 0

D

k

k!

D n

)2

D n 1 n!(n D )

87

.

(3.16)

3.2.1. ɉɪɢɦɟɪɵ ɜɵɱɢɫɥɟɧɢɹ ɨɫɧɨɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɛɢɪɠɢ ɬɪɭɞɚ ɉɪɢɦɟɪ 3.1. Ɉɩɪɟɞɟɥɢɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɧɚɯɨɞɢɬɫɹ

ɨɞɢɧ ɢɥɢ ɯɨɬɹ ɛɵ ɨɞɢɧ ɛɟɡɪɚɛɨɬɧɵɣ, ɟɫɥɢ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɛɟɡɪɚɛɨɬɧɵɯ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɞɚɧɧɨɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ, ɪɚɜɧɨ 5. Ɋɟɲɟɧɢɟ 1. ɇɚ ɨɫɧɨɜɚɧɢɢ (1.19) ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɨɞɧɨɝɨ ɛɟɡɪɚɛɨɬɧɨɝɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɫɥɟɞɭɸɳɚɹ:

P( X

1)

( Ot ) 1 5 e 1!

5e 5

0.034,

2. ȼɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɯɨɬɹ ɛɵ ɨɞɢɧ ɛɟɡɪɚɛɨɬɧɵɣ, ɪɚɜɧɚ ɜɟɪɨɹɬɧɨɫɬɢ ɬɨɝɨ, ɱɬɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɧɟ ɦɟɧɟɟ ɨɞɧɨɝɨ ɛɟɡɪɚɛɨɬɧɨɝɨ:

P ( X t 1) 1 P ( X

( Ot ) 0 5 0) 1 e 0!

1 e 5

0.993 .

ɉɪɢɦɟɪ 3.2. Ɉɩɪɟɞɟɥɢɬɶ ɧɟɨɛɯɨɞɢɦɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɧɚɥɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ

ɞɥɹ ɛɢɪɠɢ ɬɪɭɞɚ, ɨɛɥɚɞɚɸɳɟɣ ɩɪɨɩɭɫɤɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ, ɩɪɢ ɤɨɬɨɪɨɣ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɥɭɱɟɧɢɹ ɛɟɡɪɚɛɨɬɧɵɦ ɨɬɤɚɡɚ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɧɟ ɩɪɟɜɨɫɯɨɞɢɥɨ ɛɵ 0.01. ɉɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɩɥɨɬɧɨɫɬɶɸ Ȝ = 0.5 ɬɪɟɛɨɜɚɧɢɣ ɜ ɱɚɫ, ɚ ɫɪɟɞɧɹɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ – 0.25 ɱɚɫɚ. Ɋɟɲɟɧɢɟ 1. ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ: Ȝ = 0.5; ȝ = 1/mt ɨɛ = 4; Ɋɨɬɤ ɞɨɥɠɧɨ ɛɵɬɶ ɧɟ ɛɨɥɟɟ 0.01. 2. Ⱥɧɚɥɢɬɢɱɟɫɤɢɟ ɜɵɪɚɠɟɧɢɹ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɞɥɹ ɪɚɫɱɟɬɚ (3.3), (3.6). 3. Ɉɩɪɟɞɟɥɹɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɞɥɹ ɤɨɥɢɱɟɫɬɜɚ ɥɢɧɢɣ k = 1, 2, 3, …, ɩɨɤɚ Ɋɨɬɤ ɧɟ ɫɬɚɧɟɬ ɦɟɧɶɲɟɣ ɢɥɢ ɪɚɜɧɨɣ 0.01. Ɍɚɛɥɢɰɚ 3.1 - Ɋɟɡɭɥɶɬɚɬɵ ɷɤɫɩɟɪɢɦɟɧɬɨɜ

ɑɢɫɥɨ ɤɚɧɚɥɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ ȼɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ

1

2

0.37727 0.051095

3

4

0.01028

0.00273

Ⱥɧɚɥɢɡ ɬɚɛɥɢɰɵ 3.1 ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɞɥɹ ɭɞɨɜɥɟɬɜɨɪɟɧɢɹ ɩɪɟɞɴɹɜɥɹɟɦɵɦ 88

ɬɪɟɛɨɜɚɧɢɹɦ ɛɢɪɠɚ ɞɨɥɠɧɚ ɢɦɟɬɶ 4 ɤɚɧɚɥɚ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɬɨɝɞɚ Pɨɛɫɥɭɠ = 1 Ɋɨɬɤ = 0.99727, ɬ.ɟ. 99% ɬɪɟɛɨɜɚɧɢɣ ɛɭɞɟɬ ɨɛɫɥɭɠɟɧɨ. ɉɪɢɦɟɪ 3.3. Ⱦɥɹ ɩɪɢɦɟɪɚ 3.2 ɞɨɛɚɜɢɦ ɭɫɥɨɜɢɟ ɧɟɨɝɪɚɧɢɱɟɧɧɨɝɨ ɜɪɟɦɟɧɢ

ɨɠɢɞɚɧɢɹ. ɇɚɣɬɢ ɜɟɪɨɹɬɧɨɫɬɢ p0, p1, p2, p3, p4, ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɥɢɱɢɹ ɨɱɟɪɟɞɢ Pk ɢ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɨɱɟɪɟɞɢ ms. Ɋɟɲɟɧɢɟ. 1. Ɍɚɤ ɤɚɤ D
k

P

0.6 0.4 0.2 0 -0.2

0.000009 0.00029 0.00689 0.11031

0.8825

-0.4 pk

Ɋɢɫɭɧɨɤ 3.1 - Ɂɚɜɢɫɢɦɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɧɚɥɢɱɢɹ ɨɱɟɪɟɞɢ Pk ɨɬ

ɜɟɪɨɹɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɹ pk ɇɚ ɪɢɫɭɧɤɟ 3.1 ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɧɚɥɢɱɢɹ ɨɱɟɪɟɞɢ Pk ɨɬ 89

ɜɟɪɨɹɬɧɨɫɬɢ

ɫɨɫɬɨɹɧɢɹ

pk.

ɉɨɫɬɪɨɟɧɧɚɹ

ɥɢɧɢɹ

ɬɪɟɧɞɚ

ɞɟɦɨɧɫɬɪɢɪɭɟɬ

ɬɟɧɞɟɧɰɢɸ ɭɦɟɧɶɲɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɢ ɧɚɥɢɱɢɹ ɨɱɟɪɟɞɢ Pk ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɜɟɪɨɹɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɹ pk.. Ɋɟɡɭɥɶɬɚɬɵ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɩɪɢɦɟɪɚɯ 3.2 ɢ 3.3, ɫɜɢɞɟɬɟɥɶɫɬɜɭɸɬ ɨ ɬɨɦ, ɱɬɨ ɩɪɢ ɡɚɞɚɧɧɵɯ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɢ ɫɪɟɞɧɟɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɫɪɟɞɧɟɟ ɜɪɟɦɹ, ɩɪɨɜɟɞɟɧɧɨɟ ɜ ɨɱɟɪɟɞɹɯ ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɡɚɧɹɬɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɵ. ɇɨ ɷɬɨ ɧɟ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨɛ ɷɮɮɟɤɬɢɜɧɨɣ ɪɚɛɨɬɟ ɛɢɪɠɢ ɬɪɭɞɚ. Ɉɞɧɨɣ ɢɡ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɛɢɪɠɢ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɱɟɪɟɞɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɨ ɜɪɟɦɹ ɭɦɟɧɶɲɚɟɬɫɹ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ ɤɨɥɢɱɟɫɬɜɚ ɨɛɫɥɭɠɢɜɚɸɳɢɯ ɭɫɬɪɨɣɫɬɜ. Ɉɞɧɚɤɨ ɤɚɠɞɨɟ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɭɫɬɪɨɣɫɬɜɨ ɬɪɟɛɭɟɬ ɨɩɪɟɞɟɥɟɧɧɵɯ ɦɚɬɟɪɢɚɥɶɧɵɯ

ɡɚɬɪɚɬ,

ɩɪɢ

ɷɬɨɦ

ɭɜɟɥɢɱɢɜɚɟɬɫɹ

ɜɪɟɦɹ

ɛɟɡɞɟɣɫɬɜɢɹ

ɨɛɫɥɭɠɢɜɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɢɡ-ɡɚ ɨɬɫɭɬɫɬɜɢɹ ɬɪɟɛɨɜɚɧɢɣ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɱɬɨ ɬɚɤɠɟ ɹɜɥɹɟɬɫɹ ɧɟɝɚɬɢɜɧɵɦ ɹɜɥɟɧɢɟɦ. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɜɵɱɢɫɥɟɧɢɟ ɮɨɪɦɭɥ, ɜ ɱɚɫɬɧɨɫɬɢ (3.7) - (3.11) ɢ (3.13) – (3.16), ɜɟɫɶɦɚ ɡɚɬɪɭɞɧɢɬɟɥɶɧɨ, ɬɚɤ ɤɚɤ ɜɨɡɧɢɤɚɸɬ ɜɵɱɢɫɥɢɬɟɥɶɧɵɟ ɬɪɭɞɧɨɫɬɢ ɫɭɦɦɢɪɨɜɚɧɢɹ ɞɪɨɛɟɣ, ɭ ɤɨɬɨɪɵɯ ɜ ɡɧɚɦɟɧɚɬɟɥɟ – ɮɚɤɬɨɪɢɚɥɵ ɧɚɬɭɪɚɥɶɧɨɝɨ ɪɹɞɚ ɱɢɫɟɥ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɠɟ ɷɦɩɢɪɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ «ɫɪɟɞɧɟɣ ɡɚɝɪɭɡɤɢ» 0,79 ɩɪɢɜɨɞɢɬ ɤ ɫɭɳɟɫɬɜɟɧɧɵɦ ɩɨɝɪɟɲɧɨɫɬɹɦ [72]. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ

p0, pɤ, pn+s, ms, ɊH ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ ɦɟɬɨɞɵ ɢɦɢɬɚɰɢɨɧɧɨɝɨ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ. 3.3. Ɋɚɡɪɚɛɨɬɤɚ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ 3.3.1. Ɉɫɨɛɟɧɧɨɫɬɢ ɪɟɚɥɢɡɚɰɢɢ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ

ɂɫɩɨɥɶɡɭɹ ɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ, ɛɚɡɢɪɭɸɳɢɣɫɹ ɧɚ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɧɟɜɨɡɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜ ɹɜɧɨɦ ɜɢɞɟ ɢɫɤɨɦɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɛɟɡ ɭɩɪɨɳɟɧɢɹ ɦɨɞɟɥɢ. ɉɨɷɬɨɦɭ ɛɭɞɟɦ ɨɪɢɟɧɬɢɪɨɜɚɬɶɫɹ ɧɚ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɩɨɞɯɨɞɚ [35, 36, 37]. 90

ɉɨɫɬɪɨɟɧɢɟ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɡɧɚɱɢɬɟɥɶɧɨ ɫɨɤɪɚɬɢɬɶ ɦɚɬɟɪɢɚɥɶɧɵɟ ɢ ɜɪɟɦɟɧɧɵɟ ɪɟɫɭɪɫɵ. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɩɨɡɜɨɥɹɟɬ ɨɛɟɫɩɟɱɢɬɶ ɭɧɢɮɢɤɚɰɢɸ ɮɨɪɦ ɞɨɤɭɦɟɧɬɚɰɢɢ ɢ ɜɧɟɞɪɟɧɢɟ ɞɪɭɝɢɯ ɛɨɥɟɟ ɪɚɰɢɨɧɚɥɶɧɵɯ

ɧɨɫɢɬɟɥɟɣ

ɢɧɮɨɪɦɚɰɢɢ;

ɪɚɰɢɨɧɚɥɢɡɚɰɢɸ

ɫɯɟɦɵ

ɞɨɤɭɦɟɧɬɨɨɛɨɪɨɬɚ; ɜɵɫɜɨɛɨɠɞɟɧɢɟ ɤɜɚɥɢɮɢɰɢɪɨɜɚɧɧɵɯ ɫɩɟɰɢɚɥɢɫɬɨɜ ɨɬ ɜɵɩɨɥɧɟɧɢɹ ɪɭɬɢɧɧɨɣ ɪɚɛɨɬɵ ɩɨ ɨɛɪɚɛɨɬɤɟ ɞɚɧɧɵɯ, ɩɟɪɟɱɟɧɶ ɢ ɫɨɞɟɪɠɚɧɢɟ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɦɚɫɫɢɜɨɜ, ɢɫɯɨɞɹ ɢɡ ɤɨɦɩɥɟɤɫɧɨɝɨ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɤɨɦɩɥɟɤɫɧɨɣ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ. Ȼɢɪɠɚ ɬɪɭɞɚ ɤɚɤ ɫɨɫɬɚɜɧɚɹ ɱɚɫɬɶ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ

ɩɟɪɫɩɟɤɬɢɜɧɭɸ,

ɞɢɧɚɦɢɱɧɨ

ɪɚɡɜɢɜɚɸɳɭɸɫɹ

ɫɢɫɬɟɦɭ

ɷɤɨɧɨɦɢɤɢ.

Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɪɚɡɪɚɛɨɬɤɚ ɛɢɪɠɢ ɬɪɭɞɚ ɧɚ ɫɨɜɪɟɦɟɧɧɨɦ ɷɬɚɩɟ ɧɟ ɞɚɟɬ ɞɨɫɬɚɬɨɱɧɨ ɭɛɟɞɢɬɟɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɣ ɠɟ ɩɨɞɯɨɞ ɧɟ ɜɫɟɝɞɚ ɹɜɥɹɟɬɫɹ ɩɪɢɟɦɥɟɦɵɦ. ɗɤɫɩɟɪɢɦɟɧɬ ɬɪɟɛɭɟɬ ɡɧɚɱɢɬɟɥɶɧɵɯ, ɧɟ ɜɫɟɝɞɚ ɨɩɪɚɜɞɚɧɧɵɯ, ɡɚɬɪɚɬ ɜɪɟɦɟɧɢ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɞɟɹɬɟɥɶɧɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ, ɩɨɥɭɱɟɧɧɵɯ ɜ ɩɪɨɰɟɫɫɟ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɩɨɫɬɪɨɟɧɧɵɯ ɧɚ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɛɚɡɟ,

ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɯɨɞ

ɦɨɞɟɥɢɪɭɟɦɵɯ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɬɟɤɚɸɳɢɯ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. ɉɪɟɢɦɭɳɟɫɬɜɚ ɩɨɞɨɛɧɨɝɨ ɩɨɞɯɨɞɚ ɫɜɹɡɚɧɵ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɫ ɜɨɡɦɨɠɧɨɫɬɶɸ ɫɜɨɛɨɞɧɨ ɜɚɪɶɢɪɨɜɚɬɶ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɦɟɯɚɧɢɡɦɵ ɛɟɡ ɡɧɚɱɢɬɟɥɶɧɵɯ ɡɚɬɪɚɬ ɜɪɟɦɟɧɢ ɢ ɮɢɧɚɧɫɨɜɵɯ ɪɟɫɭɪɫɨɜ. ȼ ɫɥɭɱɚɟ ɭɫɩɟɯɚ ɚɧɚɥɢɡ ɪɟɡɭɥɶɬɚɬɨɜ ɩɪɨɜɟɞɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɡɜɨɥɢɬ ɧɟ ɬɨɥɶɤɨ ɪɟɤɨɦɟɧɞɨɜɚɬɶ ɪɚɡɭɦɧɵɟ ɩɪɢɧɰɢɩɵ ɨɪɝɚɧɢɡɚɰɢɢ ɦɟɯɚɧɢɡɦɨɜ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ, ɧɨ ɢ ɛɭɞɟɬ ɫɩɨɫɨɛɫɬɜɨɜɚɬɶ ɪɚɡɜɢɬɢɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɛɚɡɵ [42]. ɉɨɞɨɛɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɜɨɡɦɨɠɧɵ ɥɢɲɶ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɷɤɨɧɨɦɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɨɬɜɟɱɚɟɬ ɨɩɪɟɞɟɥɟɧɧɵɦ ɬɪɟɛɨɜɚɧɢɹɦ [28, 44, 96] . ɉɨɫɬɪɨɟɧɧɚɹ ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ, ɜ ɪɚɦɤɚɯ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɚɞɟɤɜɚɬɧɨ ɨɬɨɛɪɚɡɢɬɶ ɨɫɧɨɜɧɵɟ ɮɚɤɬɨɪɵ ɢ ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɧɟɣ, ɩɨɡɜɨɥɢɬ ɨɬɨɛɪɚɡɢɬɶ ɯɨɞ ɫɢɫɬɟɦɧɵɯ ɫɨɛɵɬɢɣ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɮɨɪɦɚɥɢɡɚɰɢɢ ɩɨɜɟɞɟɧɢɹ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɢɫɬɟɦɧɵɯ 91

ɨɛɴɟɤɬɨɜ, ɚ ɬɚɤɠɟ ɩɨɥɭɱɢɬɶ ɨɛɨɛɳɟɧɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɦɨɞɟɥɢɪɭɟɦɨɝɨ ɩɪɨɰɟɫɫɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɛɨɬɵ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɯɨɞɟ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɩɪɨɬɟɤɚɸɳɢɦɢ ɫɨɛɵɬɢɹɦɢ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɞɚɧɧɵɟ ɨ ɧɚɢɛɨɥɟɟ ɜɚɠɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɛɢɪɠɢ ɬɪɭɞɚ. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɜ ɤɚɱɟɫɬɜɟ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɝɨ ɫɪɟɞɫɬɜɚ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɜɵɛɪɚɧɚ ɫɢɫɬɟɦɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World [9, 90]. 3.3.2. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ

ɐɟɥɶɸ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɹɜɥɹɟɬɫɹ ɫɛɨɪ ɢ ɚɧɚɥɢɡ ɨɫɧɨɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɬɟɤɚɸɳɢɯ ɜ ɧɟɣ, ɚ ɢɦɟɧɧɨ: x

ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ;

x

ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ;

x

ɩɪɨɩɭɫɤɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ;

x

ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ.

ɂɫɯɨɞɹ ɢɡ ɷɬɨɝɨ, ɡɧɚɱɟɧɢɹ ɩɨɤɚɡɚɬɟɥɟɣ ɦɨɝɭɬ ɛɵɬɶ ɩɨɥɭɱɟɧɵ: x

ɜ ɨɬɞɟɥɶɧɵɯ ɨɬɞɟɥɚɯ ɛɢɪɠɢ ɬɪɭɞɚ;

x

ɜ ɤɨɦɩɥɟɤɫɧɨɣ ɦɨɞɟɥɢ.

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɰɟɥɶɸ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɪɚɫɫɦɨɬɪɢɦ ɫɥɟɞɭɸɳɢɟ ɜɚɪɢɚɧɬɵ: x

ɪɚɫɲɢɪɟɧɢɟ ɢɥɢ ɫɨɤɪɚɳɟɧɢɟ ɪɟɫɭɪɫɨɜ ɤɨɧɤɪɟɬɧɵɯ ɨɬɞɟɥɨɜ ɛɢɪɠɢ

ɬɪɭɞɚ; x

ɫɨɡɞɚɧɢɟ ɧɨɜɵɯ ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ;

x

ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɮɭɧɤɰɢɣ ɦɟɠɞɭ ɨɬɞɟɥɚɦɢ ɛɢɪɠɢ ɬɪɭɞɚ;

x

ɢɫɩɨɥɶɡɨɜɚɧɢɟ

ɜ

ɩɪɨɰɟɫɫɟ

ɪɚɛɨɬɵ

ɛɢɪɠɢ

ɬɪɭɞɚ

ɬɟɥɟɤɨɦɦɭɧɢɤɚɰɢɨɧɧɵɯ ɫɟɬɟɣ. ɇɚ ɨɫɧɨɜɟ ɚɧɚɥɢɡɚ ɞɥɹ ɨɩɬɢɦɢɡɚɰɢɢ ɦɨɞɟɥɢɪɭɟɦɵɯ ɪɟɲɟɧɢɣ ɪɚɫɫɦɨɬɪɢɦ ɩɚɪɚɦɟɬɪɵ: a) ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɨɛɪɚɳɟɧɢɹ ɛɟɡɪɚɛɨɬɧɵɯ ɧɚ ɛɢɪɠɭ ɬɪɭɞɚ; 92

b) ɤɨɥɢɱɟɫɬɜɚ ɢ ɬɢɩɨɜ ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. ɂɫɫɥɟɞɭɟɦɵɟ ɩɚɪɚɦɟɬɪɵ ɛɭɞɟɦ ɜɚɪɶɢɪɨɜɚɬɶ, ɢɫɩɨɥɶɡɭɹ ɪɟɚɥɶɧɵɟ ɞɚɧɧɵɟ ɢɡ ɪɚɛɨɬɵ ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɪɨɞɫɤɨɝɨ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ, ɤɚɞɪɨɜɨɝɨ ɚɝɟɧɬɫɬɜɚ ɇɈɍ «Ȼɚɤɚɥɚɜɪ» (ɝ. ɋɬɚɜɪɨɩɨɥɶ) ɢ ɞɚɧɧɵɟ ɚɧɚɥɢɡɚ [3, 66]. ɉɨɫɬɪɨɟɧɧɚɹ ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ ɫɩɨɫɨɛɫɬɜɭɟɬ ɩɨɥɭɱɟɧɢɸ ɢ ɚɧɚɥɢɡɭ ɫɬɚɬɢɫɬɢɤɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɪɟɫɭɪɫɨɜ, ɧɚ ɤɨɬɨɪɵɟ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɨɤɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɬɨɤɨɜ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. ȼ ɢɫɫɥɟɞɭɟɦɨɣ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɜɜɟɞɟɦ ɫɥɟɞɭɸɳɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: x

ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɪɚɡɥɢɱɧɵɟ

ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ; x

ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɚɯ ɛɢɪɠɢ ɬɪɭɞɚ;

x

ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ;

x

ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɪɟɫɭɪɫɨɜ ɦɟɠɞɭ ɨɬɞɟɥɚɦɢ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ

ɜɵɩɨɥɧɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɭɧɤɰɢɣ; x

ɜɡɜɟɲɟɧɧɨɟ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟ

ɫɬɟɩɟɧɶ ɪɚɫɫɟɹɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɜɨɟɝɨ ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ; x

ɤɨɷɮɮɢɰɢɟɧɬ

ɢɫɩɨɥɶɡɨɜɚɧɢɹ

ɜɪɟɦɟɧɢ

(ɞɨɥɹ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ)

ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. ɉɨɥɭɱɟɧɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ

ɜ

ɪɟɡɭɥɶɬɚɬɟ ɞɚɧɧɵɟ

ɢɦɢɬɚɰɢɨɧɧɨɝɨ

ɩɪɟɞɫɬɚɜɢɦ

ɜ

ɨɬɱɟɬɚɯ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ

ɝɪɚɮɢɤɚɯ,

ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ. 3.3.3. Ⱥɧɚɥɢɡ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɫɬɪɭɤɬɭɪɵ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ

ɇɚ ɛɢɪɠɭ ɬɪɭɞɚ ɫ ɧɟɫɤɨɥɶɤɢɦɢ ɤɚɧɚɥɚɦɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɨɫɬɭɩɚɸɬ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. ɉɨɫɬɭɩɚɸɳɢɟ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɨɛɪɚɡɭɸɬ ɩɪɨɫɬɟɣɲɢɣ ɩɨɬɨɤ (ɫɦ. ɩ. 1.6.2). ɂɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ ɩɨɫɬɭɩɥɟɧɢɹ 93

ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɪɚɫɩɪɟɞɟɥɟɧɵ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ. ȼɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɫɩɟɰɢɚɥɢɫɬɚɦɢ ɨɬɞɟɥɨɜ ɩɟɪɜɢɱɧɨɝɨ ɢ ɩɨɜɬɨɪɧɨɝɨ ɩɪɢɟɦɚ ɛɢɪɠɢ ɬɪɭɞɚ ɬɚɤɠɟ ɪɚɫɩɪɟɞɟɥɟɧɨ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ, ɨɛɫɥɭɠɢɜɚɧɢɟ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɫɩɟɰɢɚɥɢɫɬɚɦɢ ɞɪɭɝɢɯ ɨɬɞɟɥɨɜ ɪɚɫɩɪɟɞɟɥɟɧɨ ɪɚɜɧɨɦɟɪɧɨ, ɬ. ɤ. ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɪɟɝɥɚɦɟɧɬɢɪɭɟɬɫɹ ɩɨɪɹɞɤɨɦ ɪɚɛɨɬɵ, ɭɫɬɚɧɨɜɥɟɧɧɵɦ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. Ɉɛɫɥɭɠɢɜɚɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɦɟɪɟ ɩɨɫɬɭɩɥɟɧɢɹ: ɩɟɪɜɵɦ ɩɪɢɲɟɥ - ɩɟɪɜɵɦ ɨɛɫɥɭɠɢɥɫɹ. ɉɨɞ ɨɛɫɥɭɠɢɜɚɧɢɟɦ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɩɨɧɢɦɚɟɬɫɹ ɩɪɢɟɦ ɛɟɡɪɚɛɨɬɧɨɝɨ ɫɩɟɰɢɚɥɢɫɬɨɦ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɨɬɞɟɥɚ ɛɢɪɠɢ ɬɪɭɞɚ. ɋɨɝɥɚɫɧɨ [1] ɛɟɡɪɚɛɨɬɧɵɟ ɪɟɝɢɫɬɪɢɪɭɸɬɫɹ ɜ ɫɥɭɠɛɟ ɡɚɧɹɬɨɫɬɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɨɪɹɞɤɨɦ, ɭɫɬɚɧɨɜɥɟɧɧɵɦ ɡɚɤɨɧɨɦ, ɜ ɫɥɟɞɭɸɳɟɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ: 1. ɉɟɪɜɢɱɧɚɹ ɪɟɝɢɫɬɪɚɰɢɹ ɧɟɡɚɧɹɬɵɯ ɝɪɚɠɞɚɧ. 2. Ɋɟɝɢɫɬɪɚɰɢɹ ɧɟɡɚɧɹɬɵɯ ɝɪɚɠɞɚɧ ɜ ɰɟɥɹɯ ɩɨɢɫɤɚ ɩɨɞɯɨɞɹɳɟɣ ɪɚɛɨɬɵ. 3. Ɋɟɝɢɫɬɪɚɰɢɹ ɝɪɚɠɞɚɧ ɜ ɤɚɱɟɫɬɜɟ ɛɟɡɪɚɛɨɬɧɵɯ. 4. ɉɟɪɟɪɟɝɢɫɬɪɚɰɢɹ ɛɟɡɪɚɛɨɬɧɵɯ ɝɪɚɠɞɚɧ. ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɜ ɮɭɧɤɰɢɨɧɚɥɶɧɭɸ ɫɬɪɭɤɬɭɪɭ ɪɚɛɨɬɵ ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɪɨɞɫɤɨɝɨ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ ɡɚ 2003 ɝɨɞ (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 2), ɜɵɞɟɥɢɦ ɫɥɟɞɭɸɳɢɟ ɨɫɧɨɜɧɵɟ ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ: ɨɬɞɟɥ ɩɟɪɜɢɱɧɨɝɨ ɩɪɢɟɦɚ; ɨɬɞɟɥ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɚ; ɤɨɧɫɭɥɶɬɚɰɢɨɧɧɵɣ ɨɬɞɟɥ; ɨɬɞɟɥ ɩɟɪɟɨɛɭɱɟɧɢɹ; ɨɬɞɟɥ ɩɪɟɞɨɫɬɚɜɥɟɧɢɹ ɪɚɛɨɬɵ. ɉɪɢ ɫɨɫɬɚɜɥɟɧɢɢ ɦɨɞɟɥɢ ɫɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɬɪɟɛɨɜɚɧɢɟ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨɫɬɭɩɚɟɬ ɜ ɨɬɞɟɥ ɩɟɪɜɢɱɧɨɝɨ ɩɪɢɟɦɚ, ɡɚɬɟɦ ɜ ɨɬɞɟɥ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɚ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɜ ɤɨɧɫɭɥɶɬɚɰɢɨɧɧɨɦ ɨɬɞɟɥɟ, ɨɬɞɟɥɟ ɩɟɪɟɨɛɭɱɟɧɢɹ ɢ ɨɬɞɟɥɟ ɩɪɟɞɨɫɬɚɜɥɟɧɢɹ ɪɚɛɨɬɵ ɩɪɨɢɫɯɨɞɢɬ ɩɚɪɚɥɥɟɥɶɧɨ. ɉɨɞ ɨɛɫɥɭɠɢɜɚɧɢɟɦ ɜ ɤɨɧɫɭɥɶɬɚɰɢɨɧɧɨɦ ɨɬɞɟɥɟ ɩɨɧɢɦɚɟɬɫɹ ɤɨɧɫɭɥɶɬɢɪɨɜɚɧɢɟ ɪɚɡɥɢɱɧɵɦɢ

ɫɩɟɰɢɚɥɢɫɬɚɦɢ, ɧɚɩɪɢɦɟɪ,

ɩɫɢɯɨɥɨɝɨɦ, ɸɪɢɫɬɨɦ ɢ ɬ.

ɞ.

Ɏɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɦɨɞɟɥɢ ɢɦɟɟɬ ɰɢɤɥɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ 94

ɪɟɚɥɶɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɷɬɚɩɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ ɛɟɡɪɚɛɨɬɧɨɝɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɦɨɞɟɥɶɧɵɟ ɫɨɛɵɬɢɹ ɩɪɨɬɟɤɚɸɬ ɜ ɞɢɫɤɪɟɬɧɨɦ ɜɪɟɦɟɧɢ. ȿɞɢɧɢɰɟɣ ɜɪɟɦɟɧɢ ɹɜɥɹɟɬɫɹ ɦɨɞɟɥɶɧɵɣ ɬɚɤɬ. ȼ ɩɪɨɰɟɫɫɟ ɫɨɫɬɚɜɥɟɧɢɹ ɦɨɞɟɥɢ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɬɪɢ ɷɬɚɩɚ ɨɛɫɥɭɠɢɜɚɧɢɹ ɛɟɡɪɚɛɨɬɧɨɝɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ (ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɦ) ɛɟɡɪɚɛɨɬɧɵɣ ɨɛɪɚɳɚɟɬɫɹ ɧɚ ɛɢɪɠɭ ɬɪɭɞɚ ɡɚ ɫɨɞɟɣɫɬɜɢɟɦ ɜ ɬɪɭɞɨɭɫɬɪɨɣɫɬɜɟ ɢ ɜ ɞɟɫɹɬɢɞɧɟɜɧɵɣ ɫɪɨɤ ɞɨɥɠɟɧ ɛɵɬɶ ɩɨɫɬɚɜɥɟɧ ɧɚ ɭɱɟɬ ɤɚɤ ɢɳɭɳɢɣ ɪɚɛɨɬɭ [1]. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɨɛɫɥɭɠɢɜɚɧɢɟ ɛɟɡɪɚɛɨɬɧɨɝɨ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɩɪɟɤɪɚɳɚɟɬɫɹ. ɇɚ ɜɬɨɪɨɦ ɷɬɚɩɟ (ɨɛɫɥɭɠɢɜɚɧɢɹ) ɢɡ ɩɨɫɬɚɜɥɟɧɧɵɯ ɧɚ ɭɱɟɬ ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɟ, ɤɨɬɨɪɵɟ ɩɪɢɡɧɚɸɬɫɹ ɛɟɡɪɚɛɨɬɧɵɦɢ ɫ ɩɪɟɞɨɫɬɚɜɥɟɧɢɟɦ ɩɨɥɧɨɝɨ ɫɨɰɢɚɥɶɧɨɝɨ ɩɚɤɟɬɚ. ɉɨɫɬɭɩɚɸɳɢɟ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɧɚ ɪɚɡɥɢɱɧɵɯ ɭɪɨɜɧɹɯ, ɞɨ ɟɺ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɤ ɭɬɜɟɪɠɞɟɧɢɸ. Ɂɚɦɟɱɚɧɢɹ ɢ ɤɨɦɦɟɧɬɚɪɢɢ ɫɩɟɰɢɚɥɢɫɬɨɜ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ ɜɤɥɸɱɚɸɬɫɹ ɜ ɦɨɞɟɥɶ ɢ ɩɪɨɰɟɫɫ ɜɚɥɢɞɚɰɢɢ ɩɨɜɬɨɪɹɟɬɫɹ, ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɛɭɞɟɬ ɩɨɥɭɱɟɧ ɧɭɠɧɵɣ ɪɟɡɭɥɶɬɚɬ, ɬ. ɟ.

ɛɟɡɪɚɛɨɬɧɨɦɭ ɩɪɟɞɨɫɬɚɜɥɹɟɬɫɹ ɪɚɛɨɬɚ, ɨɬɜɟɱɚɸɳɚɹ ɜɫɟɦ

ɧɨɪɦɚɬɢɜɧɵɦ ɬɪɟɛɨɜɚɧɢɹɦ ɢ ɡɚɩɪɨɫɚɦ ɛɟɡɪɚɛɨɬɧɨɝɨ. ɇɚ

ɬɪɟɬɶɟɦ

ɷɬɚɩɟ

(ɢɫɩɨɥɧɟɧɢɹ)

ɜɵɩɨɥɧɹɸɬɫɹ

ɦɟɪɨɩɪɢɹɬɢɹ

ɩɨ

ɭɞɨɜɥɟɬɜɨɪɟɧɢɸ ɩɨɫɬɭɩɢɜɲɢɯ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. Ȼɟɡɪɚɛɨɬɧɵɟ ɫɧɢɦɚɸɬɫɹ ɫ ɭɱɟɬɚ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɩɨ ɢɫɬɟɱɟɧɢɸ ɫɪɨɤɚ, ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ ɡɚɤɨɧɨɞɚɬɟɥɶɫɬɜɨɦ Ɋɨɫɫɢɣɫɤɨɣ Ɏɟɞɟɪɚɰɢɢ. ɂɦɢɬɚɰɢɹ

ɨɛɫɥɭɠɢɜɚɧɢɹ

ɧɚ

ɭɤɚɡɚɧɧɵɯ

ɷɬɚɩɚɯ

ɪɟɝɭɥɢɪɭɟɬɫɹ

ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɦɢ ɚɤɬɚɦɢ. ɋɭɳɟɫɬɜɭɟɬ ɬɪɢ ɜɢɞɚ ɰɢɤɥɨɜ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɨɛɦɟɧɚ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɦɨɞɟɥɢ [40]: 1) ɰɢɤɥ ɫɛɨɪɚ ɞɚɧɧɵɯ; 2) ɩɪɨɜɟɪɤɢ

ɫɨɨɬɜɟɬɫɬɜɢɹ

ɞɚɧɧɵɯ

ɩɪɚɜɢɥɚɦ

ɢ

ɤɨɧɰɟɩɰɢɢ

ɫɮɨɪɦɢɪɨɜɚɧɧɨɣ ɦɨɞɟɥɢ; 3) ɰɢɤɥ ɭɬɜɟɪɠɞɟɧɢɹ ɨɬɨɛɪɚɧɧɵɯ ɞɚɧɧɵɯ. Ʉɚɠɞɵɣ ɢɡ ɬɪɟɯ ɰɢɤɥɨɜ ɦɨɠɟɬ ɦɧɨɝɨɤɪɚɬɧɨ ɩɨɜɬɨɪɹɬɶɫɹ ɜɨ ɜɪɟɦɹ 95

ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɤɚɠɞɨɦ ɢɡ ɨɩɪɟɞɟɥɟɧɧɵɯ ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. ɐɢɤɥ ɫɛɨɪɚ ɞɚɧɧɵɯ ɧɚɱɢɧɚɟɬɫɹ ɧɚ ɩɟɪɜɨɦ ɷɬɚɩɟ. ȿɝɨ ɰɟɥɶ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɭɫɬɚɧɨɜɥɟɧɢɢ

ɨɫɧɨɜɵ

ɞɨɤɭɦɟɧɬɢɪɨɜɚɧɢɹ,

ɢɡ

ɤɨɬɨɪɨɣ

ɢɡɜɥɟɤɚɸɬɫɹ

ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɢɧɮɨɪɦɚɰɢɢ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɜ ɦɨɞɟɥɢ. ȼɚɠɧɨɫɬɶ ɷɬɨɝɨ ɰɢɤɥɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɧɚ ɩɨɫɥɟɞɭɸɳɢɯ ɷɬɚɩɚɯ ɩɪɢɯɨɞɢɬɫɹ ɡɚɧɨɜɨ ɜɨɡɜɪɚɳɚɬɶɫɹ ɤ ɢɫɬɨɱɧɢɤɚɦ ɷɬɨɣ ɞɨɤɭɦɟɧɬɚɰɢɢ ɞɥɹ ɟɺ ɤɨɪɪɟɤɰɢɢ ɢ ɭɬɨɱɧɟɧɢɹ. ɉɨɷɬɨɦɭ ɰɢɤɥ ɫɛɨɪɚ ɞɚɧɧɵɯ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɩɨɜɬɨɪɹɸɳɚɹɫɹ, ɚ ɧɟ ɨɞɧɨɤɪɚɬɧɚɹ ɮɭɧɤɰɢɹ. ɉɨɥɭɱɟɧɢɟ ɤɚɱɟɫɬɜɟɧɧɨɣ ɩɟɪɜɢɱɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨɞɧɨ ɢɡ ɜɚɠɧɵɯ ɭɫɥɨɜɢɣ ɩɥɨɞɨɬɜɨɪɧɨɣ ɪɚɛɨɬɵ ɧɚ ɜɫɟɯ ɷɬɚɩɚɯ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɇɚ ɞɨɥɸ ɩɟɪɜɢɱɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨɛɵɱɧɨ ɩɪɢɯɨɞɢɬɫɹ ɞɨ 60 - 70% ɨɛɳɟɝɨ ɨɛɴɟɦɚ ɭɱɟɬɧɨɣ ɢɧɮɨɪɦɚɰɢɢ. Ʉɚɱɟɫɬɜɨ ɩɟɪɜɢɱɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ ɧɚ ɤɚɱɟɫɬɜɨ

ɜɫɟɝɨ

ɩɪɨɰɟɫɫɚ

ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ

ɛɢɪɠɢ

ɬɪɭɞɚ,

ɚ

ɬɚɤɠɟ

ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ, ɛɭɯɝɚɥɬɟɪɫɤɨɝɨ ɢ ɨɩɟɪɚɬɢɜɧɨɝɨ ɭɱɟɬɚ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɞɨ 80% ɨɲɢɛɨɤ ɱɟɥɨɜɟɤ ɞɨɩɭɫɤɚɟɬ ɧɚ ɧɚɱɚɥɶɧɨɣ ɫɬɚɞɢɢ ɭɱɟɬɧɨɝɨ ɩɪɨɰɟɫɫɚ, ɫɥɟɞɭɟɬ ɦɚɤɫɢɦɚɥɶɧɨ ɫɧɢɡɢɬɶ ɡɚɬɪɚɬɵ ɪɭɱɧɨɝɨ ɬɪɭɞɚ ɜ ɩɪɨɰɟɫɫɟ ɩɨɞɝɨɬɨɜɤɢ ɩɟɪɜɢɱɧɨɣ ɢɧɮɨɪɦɚɰɢɢ, ɚ ɬɚɤɠɟ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɬɶ ɦɟɬɨɞɨɥɨɝɢɸ ɩɟɪɜɢɱɧɨɝɨ ɭɱɟɬɚ. ɋɭɳɧɨɫɬɶ

ɰɢɤɥɚ ɜɚɥɢɞɚɰɢɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɷɬɨɬ ɩɪɨɰɟɫɫ

ɩɨɜɬɨɪɹɟɬɫɹ, ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɛɭɞɟɬ ɩɨɥɭɱɟɧ ɩɪɢɟɦɥɟɦɵɣ ɪɟɡɭɥɶɬɚɬ [8]. ɐɢɤɥ ɭɬɜɟɪɠɞɟɧɢɹ ɨɬɨɛɪɚɧɧɵɯ ɞɚɧɧɵɯ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɰɟɧɤɟ ɪɚɡɜɟɪɧɭɬɨɣ ɦɨɞɟɥɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɟɺ ɫɨɨɬɜɟɬɫɬɜɢɹ ɰɟɥɹɦ ɪɚɡɪɚɛɨɬɤɢ. Ɂɞɟɫɶ ɜɨɡɦɨɠɧɨ, ɱɬɨɛɵ ɨɬɞɟɥɶɧɵɟ ɩɨɞɫɢɫɬɟɦɵ ɦɨɞɟɥɢ ɛɵɥɢ ɩɪɨɜɟɪɟɧɵ ɧɚ ɫɨɨɬɜɟɬɫɬɜɢɟ ɜɚɥɢɞɧɨɫɬɢ ɩɨɫɬɪɨɟɧɧɨɣ ɦɨɞɟɥɢ ɡɚɧɨɜɨ. Ɍɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɜɵɹɜɥɟɧɨ, ɱɬɨ ɦɨɞɟɥɶ ɧɟɞɨɫɬɚɬɨɱɧɨ ɩɨɥɧɨ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɭɪɨɜɟɧɶ (ɷɬɚɩ) ɪɚɡɪɚɛɨɬɤɢ, ɢ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɞɨɥɠɢɬɶ ɢɫɫɥɟɞɨɜɚɧɢɹ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɟ. ɐɢɤɥ ɭɬɜɟɪɠɞɟɧɢɹ ɨɬɨɛɪɚɧɧɵɯ ɞɚɧɧɵɯ ɨɛɵɱɧɨ ɩɨɜɬɨɪɹɟɬɫɹ ɛɨɥɟɟ ɨɞɧɨɝɨ ɪɚɡɚ ɜ ɩɪɨɰɟɫɫɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ɉɧ ɨɛɵɱɧɨ ɜɫɬɪɟɱɚɟɬɫɹ ɜ ɤɨɧɰɟ ɷɬɚɩɚ, ɯɨɬɹ ɪɟɞɤɨ ɩɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɤɚɠɞɨɝɨ ɷɬɚɩɚ. Ɉɤɨɧɱɚɬɟɥɶɧɵɣ ɰɢɤɥ ɭɬɜɟɪɠɞɟɧɢɹ ɨɬɨɛɪɚɧɧɵɯ ɞɚɧɧɵɯ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɜ ɤɨɧɰɟ ɬɪɟɬɶɟɝɨ ɷɬɚɩɚ. 96

ɂɫɬɨɱɧɢɤɨɦ ɞɚɧɧɵɯ ɞɥɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɩɪɨɰɟɫɫɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɬɚɥɚ ɢɧɮɨɪɦɚɰɢɹ ɢɡ ɤɚɪɬɨɱɟɤ ɩɟɪɫɨɧɚɥɶɧɨɝɨ ɭɱɟɬɚ ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɪɨɞɫɤɨɝɨ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ, ɚ ɬɚɤɠɟ ɫɬɚɬɢɫɬɢɤɚ ɨɛɪɚɳɟɧɢɣ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɤɚɞɪɨɜɨɟ ɚɝɟɧɬɫɬɜɨ ɇɈɍ «Ȼɚɤɚɥɚɜɪ» (ɝ. ɋɬɚɜɪɨɩɨɥɶ). Ɍɚɛɥɢɰɚ 3.2. - Ɂɚɬɪɚɬɵ ɧɚ ɫɨɞɟɪɠɚɧɢɟ Ƚɍ ɋɬɚɜɪɨɩɨɥɶɫɤɢɣ ɝɨɪɨɞɫɤɨɣ

ɰɟɧɬɪ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ ɜ 2003 ɝɨɞɭ (ɬɵɫ. ɪɭɛ.) 2002 ɝɨɞ

2003 ɝɨɞ

2003ɝ ɜ % ɤ 2002ɝ

Ɂɚɬɪɚɬɵ ɜɫɟɝɨ

6042,2

5373,5

88,9

ɜ ɬ.ɱ. ɧɚ ɨɩɥɚɬɭ ɬɪɭɞɚ

3048,0

3012,8

98,8

Ɂɚɬɪɚɬɵ ɧɚ 1-ɝɨ ɪɚɛɨɬɧɢɤɚ

91,6

81,4

88,9

ɜ ɬ.ɱ. ɩɨ ɮɨɧɞɭ ɨɩɥɚɬɵ ɬɪɭɞɚ

46,2

45,7

98,9

Ɉɰɟɧɢɬɶ ɷɤɨɧɨɦɢɱɟɫɤɭɸ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɦɨɠɧɨ

ɧɚ

ɨɫɧɨɜɚɧɢɢ

ɞɚɧɧɵɯ

ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ

ɨɬɱɟɬɚ

ɨ

ɞɟɹɬɟɥɶɧɨɫɬɢ

ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɪɨɞɫɤɨɝɨ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ ɡɚ 2003 ɝɨɞ, ɭɱɢɬɵɜɚɹ ɱɢɫɥɟɧɧɨɫɬɶ ɪɚɛɨɬɧɢɤɨɜ ɰɟɧɬɪɚ ɢ ɡɚɬɪɚɬɵ ɧɚ ɢɯ ɫɨɞɟɪɠɚɧɢɟ (ɫɦ. ɬɚɛɥ. 3.2). ɑɢɫɥɟɧɧɨɫɬɶ ɪɚɛɨɬɧɢɤɨɜ, ɫɨɝɥɚɫɧɨ ɲɬɚɬɧɨɦɭ ɪɚɫɩɢɫɚɧɢɸ, ɜ 2003 ɝɨɞɭ ɫɨɫɬɚɜɢɥɚ 68 ɱɟɥɨɜɟɤ. Ɏɚɤɬɢɱɟɫɤɚɹ ɱɢɫɥɟɧɧɨɫɬɶ ɪɚɛɨɬɧɢɤɨɜ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ ɩɨ ɫɨɫɬɨɹɧɢɸ ɧɚ 01.01.2004 ɫɨɫɬɚɜɢɥɚ 66 ɱɟɥɨɜɟɤ. ɉɨ ɢɬɨɝɚɦ 2003 ɝɨɞɚ ɫɪɟɞɧɹɹ ɫɬɨɢɦɨɫɬɶ ɨɛɭɱɟɧɢɹ ɨɞɧɨɝɨ ɛɟɡɪɚɛɨɬɧɨɝɨ ɫɨɫɬɚɜɥɹɟɬ 3500 ɪɭɛ. ɉɪɨɦɨɞɟɥɢɪɭɟɦ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɬɟɱɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɢɧɬɟɪɜɚɥɨɜ

ɜɪɟɦɟɧɢ.

ɉɨ

ɪɟɡɭɥɶɬɚɬɚɦ

ɤɨɦɩɶɸɬɟɪɧɨɝɨ

ɷɤɫɩɟɪɢɦɟɧɬɚ

ɫ

ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɢɫɬɟɦɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World ɩɨɥɭɱɢɦ ɫɬɚɬɢɫɬɢɤɭ ɜɜɟɞɟɧɧɵɯ ɨɫɧɨɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɨɰɟɫɫɨɜ ɩɪɨɬɟɤɚɸɳɢɯ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. Ɉɰɟɧɢɦ ɜɨɡɦɨɠɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɤɚɱɟɫɬɜɚ ɛɢɪɠɢ ɬɪɭɞɚ ɢ ɞɚɞɢɦ ɪɟɤɨɦɟɧɞɚɰɢɢ ɩɨ ɟɟ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɸ ɢ ɦɨɞɟɪɧɢɡɚɰɢɢ, ɚ ɬɚɤɠɟ ɨɰɟɧɢɦ ɭɛɵɬɤɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɩɨɜɬɨɪɧɨɣ ɨɛɪɚɛɨɬɤɢ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɭɱɢɬɵɜɚɹ ɩɪɢ ɷɬɨɦ ɡɚɬɪɚɬɵ ɧɚ ɞɨɪɚɛɨɬɤɭ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ.

97

3.3.4. Ɋɚɡɪɚɛɨɬɤɚ ɫɬɪɭɤɬɭɪɵ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ

Ⱦɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɨ ɢ ɧɚɝɥɹɞɧɨ ɩɪɟɞɫɬɚɜɢɦ ɩɪɨɰɟɫɫ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɫɢɫɬɟɦɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World ɫ ɩɨɦɨɳɶɸ Q-ɫɯɟɦɵ (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 4) [50, 68, 88, 89, 93, 98]. Ȼɢɪɠɢ ɬɪɭɞɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɧɨɝɨɤɚɧɚɥɶɧɨɟ ɭɫɬɪɨɣɫɬɜɨ. Q-ɫɯɟɦɚ ɛɢɪɠɢ ɬɪɭɞɚ ɫɨɫɬɨɢɬ ɢɡ ɢɫɬɨɱɧɢɤɚ ɂ1, ɤɚɧɚɥɚ ɋ1 ɢ ɧɚɤɨɩɢɬɟɥɹ ɞɥɹ ɯɪɚɧɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɩɟɪɜɨɣ ɮɚɡɵ ɇ1, ɢɫɬɨɱɧɢɤɚ ɂ2, ɤɚɧɚɥɚ ɋ2 ɢ ɧɚɤɨɩɢɬɟɥɹ ɞɥɹ ɯɪɚɧɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜɬɨɪɨɣ ɮɚɡɵ ɇ2. ɂɫɬɨɱɧɢɤ ɂ1 ɢɦɢɬɢɪɭɟɬ ɩɟɪɜɢɱɧɨɟ ɩɨɫɬɭɩɥɟɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɚ ɢɫɬɨɱɧɢɤ ɂ2 – ɩɨɜɬɨɪɧɨɟ ɩɨɫɬɭɩɥɟɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. Ɍɚɤɠɟ ɢɦɟɸɬɫɹ ɧɚɤɨɩɢɬɟɥɢ ɞɥɹ ɯɪɚɧɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɇ3, ɇ4, ɇ5, ɤɨɬɨɪɵɟ

ɫɬɨɹɬ ɜ ɦɟɫɬɚɯ ɜɨɡɧɢɤɧɨɜɟɧɢɹ

ɨɱɟɪɟɞɢ. Ʉɚɧɚɥ ɋ1 ɫɥɭɠɢɬ ɞɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɨɛɪɚɛɨɬɤɢ ɬɪɟɛɨɜɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɢɯ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɤɚɧɚɥɵ ɋ2, Ɋ, K, Oɛ, ɨɛɫɥɭɠɢɜɚɸɬ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɦɨɞɟɥɢ. Ʉɚɧɚɥɵ Ɋ, K, Oɛ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɩɚɪɚɥɥɟɥɶɧɨ ɪɚɛɨɬɚɸɳɢɟ ɨɞɧɨɤɚɧɚɥɶɧɵɟ ɭɫɬɪɨɣɫɬɜɚ. ɂɧɬɟɧɫɢɜɧɨɫɬɶ ɜɯɨɞɧɨɝɨ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɪɚɜɧɚ O1, ɩɨɜɬɨɪɧɨɝɨ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɪɚɜɧɚ O2, ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɤɚɠɞɨɦ ɢɡ ɨɬɞɟɥɨɜ ɋ1, ɋ2, Ɋ, Ʉ, Oɛ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɚ ȝ1, ȝ2, ȝ3, ȝ4, ȝ5. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɞɟɥɶ ɛɵɥɚ ɫɬɚɰɢɨɧɚɪɧɚ, ɤɚɠɞɚɹ ɫɢɫɬɟɦɚ ɦɨɞɟɥɢ ɞɨɥɠɧɚ ɛɵɬɶ ɫɬɚɰɢɨɧɚɪɧɚ, ɬ.ɟ. ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɫɥɟɞɭɸɳɟɟ ɭɫɥɨɜɢɟ [15]:

Oi / (kiPi) d 1, i =1…N, ɝɞɟ N- ɤɨɥɢɱɟɫɬɜɨ ɫɢɫɬɟɦ,

Oi - ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɜɯɨɞɧɨɝɨ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɜ i-ɸ ɫɢɫɬɟɦɭ; ki - ɱɢɫɥɨ ɤɚɧɚɥɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ i-ɣ ɫɢɫɬɟɦɟ;

Pi - ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ɤɚɧɚɥɚ ɜ i-ɣ ɫɢɫɬɟɦɟ. ȿɫɥɢ ɯɨɬɹ ɛɵ ɞɥɹ ɨɞɧɨɣ ɫɢɫɬɟɦɵ ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɦɨɞɟɥɶ ɧɟ ɫɩɪɚɜɢɬɫɹ ɫ ɩɨɬɨɤɨɦ ɬɪɟɛɨɜɚɧɢɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨ ɭɜɟɥɢɱɢɜɚɬɶ ɱɢɫɥɨ ɤɚɧɚɥɨɜ ɨɛɫɥɭɠɢɜɚɧɢɹ ɞɥɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɢɫɬɟɦɵ, ɥɢɛɨ ɩɟɪɟɪɚɫɩɪɟɞɟɥɢɬɶ ɩɨɬɨɤ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ. ɇɚɩɪɢɦɟɪ, ɟɫɥɢ ɫɨɡɞɚɟɬɫɹ ɨɱɟɪɟɞɶ ɜ ɬɨɬ ɢɥɢ 98

ɢɧɨɣ ɨɬɞɟɥ, ɬɨ ɜ ɰɟɥɹɯ ɪɚɡɝɪɭɡɤɢ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɦɨɠɧɨ ɩɨɞɤɥɸɱɢɬɶ ɤ ɪɚɛɨɬɟ ɞɪɭɝɨɣ ɨɬɞɟɥ. ȼɜɟɞɟɦ ɢɞɟɧɬɢɮɢɤɚɬɨɪɵ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɦɨɞɟɥɢ: 1)

Sp1 – ɨɬɞɟɥ ɩɟɪɜɢɱɧɨɝɨ ɩɪɢɟɦɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɫ ɨɞɧɢɦ

ɤɚɧɚɥɨɦ ɨɛɫɥɭɠɢɜɚɧɢɹ; 2)

Sp2 – ɨɬɞɟɥ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɫ ɨɞɧɢɦ

ɤɚɧɚɥɨɦ ɨɛɫɥɭɠɢɜɚɧɢɹ; 3)

SpQ1 – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɬɞɟɥ ɩɟɪɜɢɱɧɨɝɨ

ɩɪɢɟɦɚ; 4)

SpQ2 – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɬɞɟɥ ɜɬɨɪɢɱɧɨɝɨ

ɩɪɢɟɦɚ; 5)

Rab

–

ɨɬɞɟɥ

ɩɪɟɞɨɫɬɚɜɥɟɧɢɹ

ɪɚɛɨɬɵ

ɫ

ɨɞɧɢɦ

ɤɚɧɚɥɨɦ

ɨɛɫɥɭɠɢɜɚɧɢɹ; 6)

RabQ – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɬɞɟɥ ɩɪɟɞɨɫɬɚɜɥɟɧɢɹ

ɪɚɛɨɬɵ; 7)

Kon – ɤɨɧɫɭɥɶɬɚɰɢɨɧɧɵɣ ɨɬɞɟɥ ɩɪɢɟɦɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ

ɫ ɨɞɧɢɦ ɤɚɧɚɥɨɦ ɨɛɫɥɭɠɢɜɚɧɢɹ; 8)

KonQ – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɤɨɧɫɭɥɶɬɚɰɢɨɧɧɵɣ

ɨɬɞɟɥ; 9)

Ob – ɨɬɞɟɥ ɩɟɪɟɨɛɭɱɟɧɢɹ ɫ ɨɞɧɢɦ ɤɚɧɚɥɨɦ ɨɛɫɥɭɠɢɜɚɧɢɹ;

10)

ObQ – ɨɱɟɪɟɞɶ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥ ɩɟɪɟɨɛɭɱɟɧɢɹ;

11)

VrSp1 – ɢɦɹ ɬɚɛɥɢɰɵ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɬɚɛɭɥɢɪɨɜɚɬɶɫɹ ɜɪɟɦɹ

ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɜ ɨɬɞɟɥɟ ɩɟɪɜɢɱɧɨɝɨ ɩɪɢɟɦɚ; 12)

VrSp2 – ɢɦɹ ɬɚɛɥɢɰɵ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɬɚɛɭɥɢɪɨɜɚɬɶɫɹ ɜɪɟɦɹ

ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɜ ɨɬɞɟɥɟ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɚ; 13)

VrKon – ɢɦɹ ɬɚɛɥɢɰɵ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɬɚɛɭɥɢɪɨɜɚɬɶɫɹ ɜɪɟɦɹ

ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɜ ɤɨɧɫɭɥɶɬɚɰɢɨɧɧɨɦ ɨɬɞɟɥɟ; 14)

VrOb – ɢɦɹ ɬɚɛɥɢɰɵ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɬɚɛɭɥɢɪɨɜɚɬɶɫɹ ɜɪɟɦɹ

ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɜ ɨɬɞɟɥɟ ɩɟɪɟɨɛɭɱɟɧɢɹ; 15)

VrRab – ɢɦɹ ɬɚɛɥɢɰɵ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɬɚɛɭɥɢɪɨɜɚɬɶɫɹ ɜɪɟɦɹ 99

ɩɪɟɛɵɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɜ ɨɬɞɟɥɟ ɩɪɟɞɨɫɬɚɜɥɟɧɢɹ ɪɚɛɨɬɵ; 16)

VerObrSp1 - ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Sp1;

17)

VerObrSp2 - ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Sp2;

18)

VerObrRab - ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Rab;

19)

VerObrKon - ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Kon;

20)

VerObrOb - ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Ob;

21)

VerBirga - ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ;

22)

VOtk - ɜɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɬɪɟɛɨɜɚɧɢɹ ɧɚ ɛɢɪɠɟ

ɬɪɭɞɚ. ɉɨ ɞɚɧɧɵɦ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ ɝ. ɋɬɚɜɪɨɩɨɥɹ ɜ 2003 ɝɨɞɭ ɡɚ ɫɨɞɟɣɫɬɜɢɟɦ ɜ ɬɪɭɞɨɭɫɬɪɨɣɫɬɜɟ ɨɛɪɚɬɢɥɨɫɶ 49,2 ɬɵɫ. ɱɟɥ., ɩɨɫɬɚɜɥɟɧɵ ɧɚ ɭɱɟɬ ɤɚɤ ɢɳɭɳɢɟ ɪɚɛɨɬɭ - 13,24 ɬɵɫ. ɱɟɥ., ɢɡ ɩɨɫɬɚɜɥɟɧɧɵɯ ɧɚ ɭɱɟɬ ɩɪɢɡɧɚɧɵ ɛɟɡɪɚɛɨɬɧɵɦɢ 4,9 ɬɵɫ. ɱɟɥ.. ɋɥɭɠɛɨɣ ɡɚɧɹɬɨɫɬɢ ɬɪɭɞɨɭɫɬɪɨɟɧɨ ɫ ɭɱɟɬɨɦ ɩɟɪɟɨɛɭɱɟɧɢɹ 8,1 ɬɵɫ. ɱɟɥ. Ɂɚ 2003 ɝɨɞ ɧɚ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɟ ɨɛɭɱɟɧɢɟ ɧɚɩɪɚɜɥɟɧɨ 1,3 ɬɵɫ. ɱɟɥ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɷɬɢɯ ɞɚɧɧɵɯ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɨɫɜɨɛɨɠɞɟɧɢɣ

P

ɞɥɹ

ɨɬɞɟɥɨɜ C2, Ɋ, K, Oɛ ɛɢɪɠɢ ɬɪɭɞɚ ɛɭɞɟɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɚ 26.9 %, 37.0 %, 9.8 %, 61.2 %. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ Q-ɫɯɟɦɨɣ ɢ ɜɜɟɞɟɧɧɵɦɢ ɢɞɟɧɬɢɮɢɤɚɬɨɪɚɦɢ ɩɨɫɬɪɨɢɦ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɜɢɞɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɛɥɨɤɨɜ, ɜɤɥɸɱɚɹ ɷɥɟɦɟɧɬɵ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɟ ɞɥɹ ɭɩɪɚɜɥɟɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɟɦ ɧɚ ɹɡɵɤɟ GPSS World (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 4) [9]. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɛɥɨɤɨɜ ɜ ɦɨɞɟɥɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɫɢɬɭɚɰɢɣ, ɜ ɤɨɬɨɪɵɯ ɨɤɚɡɵɜɚɟɬɫɹ ɛɟɡɪɚɛɨɬɧɵɣ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ. Ɍɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɩɨɫɬɭɩɚɸɬ ɜ ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ, ɟɫɥɢ ɧɟɨɛɯɨɞɢɦɨ, ɬɨ ɠɞɭɬ ɨɱɟɪɟɞɢ, ɡɚɬɟɦ ɨɛɫɥɭɠɢɜɚɸɬɫɹ ɫɩɟɰɢɚɥɢɫɬɚɦɢ ɩɟɪɜɢɱɧɨɝɨ ɢ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɨɜ. Ɂɚɬɟɦ ɬɪɟɛɨɜɚɧɢɟ ɩɪɨɯɨɞɢɬ ɩɚɪɚɥɥɟɥɶɧɨɟ ɨɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɚɯ Ɋ, Ʉ, Ɉɛ. ɉɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɪɟɲɟɧɢɢ ɜɨɩɪɨɫɚ, ɬ. ɟ. ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɛɟɡɪɚɛɨɬɧɵɣ ɩɪɢɧɢɦɚɟɬ ɩɪɟɞɥɨɠɟɧɧɵɣ ɜɚɪɢɚɧɬ ɪɚɛɨɬɵ, ɬɪɟɛɨɜɚɧɢɟ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɩɨɤɢɞɚɟɬ ɫɢɫɬɟɦɭ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɨɬɞɟɥ ɜɬɨɪɢɱɧɨɝɨ ɩɪɢɟɦɚ 100

ɧɚ ɞɨɨɛɫɥɭɠɢɜɚɧɢɟ. 3.3.5. Ɋɟɡɭɥɶɬɚɬɵ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ

ɉɪɨɦɨɞɟɥɢɪɭɟɦ ɜ ɫɢɫɬɟɦɟ GPSS World ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɬɟɱɟɧɢɟ ɨɞɧɨɝɨ ɪɚɛɨɱɟɝɨ ɞɧɹ (8 ɱɚɫɨɜ = 480 ɦɢɧɭɬ), ɞɟɫɹɬɢ ɪɚɛɨɱɢɯ ɞɧɟɣ (8 ɱɚɫɨɜ ɯ 10 ɞɧɟɣ = 4800 ɦɢɧɭɬ). Ɋɚɫɫɦɨɬɪɢɦ ɪɚɡɥɢɱɧɵɟ ɜɚɪɢɚɧɬɵ ɦɨɞɟɥɢ, ɢɡɦɟɧɹɹ ɤɨɥɢɱɟɫɬɜɨ ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ ɢɥɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɹɹ ɢɯ ɮɭɧɤɰɢɢ. ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ

ɜɵɯɨɞɧɭɸ

ɫɬɚɬɢɫɬɢɤɭ

ɩɨɫɬɪɨɟɧɧɨɣ

ɦɨɞɟɥɢ,

ɩɪɢ

ɡɚɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ ɦɨɞɟɥɢɪɨɜɚɧɢɹ [9]. Ɋɚɡɛɪɨɫ

ɪɟɡɭɥɶɬɚɬɨɜ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɩɪɢ

ɜɚɪɶɢɪɨɜɚɧɢɢ

ɱɢɫɥɚ

ɦɨɞɟɥɢɪɭɟɦɵɯ ɬɚɤɬɨɜ ɨɬ 50 ɞɨ 10000 ɧɟ ɩɪɟɜɵɲɚɟɬ 1%. 3.3.5.1. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɨɛɡɨɪ ɪɟɡɭɥɶɬɚɬɨɜ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ

ɉɨɞɪɨɛɧɨɟ ɢɡɥɨɠɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɪɢɜɨɞɢɬɫɹ ɞɥɹ ɨɞɧɨɝɨ ɧɚɛɨɪɚ ɛɚɡɨɜɵɯ ɩɨɤɚɡɚɬɟɥɟɣ ɭɱɚɫɬɧɢɤɨɜ ɛɢɪɠɢ ɬɪɭɞɚ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜ ɬɚɛɥ. 3.3. Ⱥɧɚɥɢɡ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɡɜɨɥɢɥ ɜɵɹɜɢɬɶ ɪɹɞ ɭɫɬɨɣɱɢɜɵɯ ɬɟɧɞɟɧɰɢɣ

ɜ

ɩɨɜɟɞɟɧɢɢ

ɬɪɟɛɨɜɚɧɢɣ

ɨɬ

ɛɟɡɪɚɛɨɬɧɵɯ

(ɧɚ

ɩɪɢɦɟɪɟ

ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɪɨɞɫɤɨɝɨ ɰɟɧɬɪɚ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ). 1. Ɋɚɫɫɦɚɬɪɢɜɚɟɦɚɹ

ɨɪɝɚɧɢɡɚɰɢɹ

ɛɢɪɠɢ

ɬɪɭɞɚ

ɞɚɟɬ

ɡɚɦɟɬɧɵɣ

ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ, ɤɨɝɞɚ ɤɨɥɢɱɟɫɬɜɨ ɩɨɫɬɭɩɚɸɳɢɯ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɩɪɟɜɵɲɚɟɬ ɨɩɪɟɞɟɥɟɧɧɵɣ ɩɨɪɨɝ (ɞɥɹ ɞɚɧɧɨɣ ɫɟɪɢɢ 3 ɦɢɧ). ɉɪɢ ɤɨɥɢɱɟɫɬɜɟ ɩɨɫɬɭɩɚɸɳɢɯ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɧɢɠɟ ɷɬɨɝɨ ɩɨɪɨɝɚ ɜɡɚɢɦɨɡɚɜɢɫɢɦɨɫɬɶ ɨɪɝɚɧɢɡɨɜɚɧɧɨɫɬɢ

ɨɬɞɟɥɨɜ

ɛɢɪɠɢ

ɫɭɳɟɫɬɜɟɧɧɨ

ɬɪɭɞɚ

ɫɧɢɠɚɟɬɫɹ

ɨɫɥɚɛɟɜɚɟɬ, ɥɢɛɨ

ɚ

ɷɮɮɟɤɬ

ɫɬɚɧɨɜɢɬɫɹ

ɢɯ

ɜɨɨɛɳɟ

ɧɟɡɚɦɟɬɧɵɦ. 2. ȼɟɪɨɹɬɧɨɫɬɶ ɡɚɧɹɬɨɫɬɢ ɦɨɞɟɥɢɪɭɟɦɨɣ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɜɫɟɯ ɨɬɞɟɥɨɜ ɧɚɢɛɨɥɶɲɟɝɨ ɡɧɚɱɟɧɢɹ ɞɨɫɬɢɝɚɟɬ ɩɪɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɪɚɜɧɨɣ 6 ɦɢɧ. 101

3. ɇɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ ɦɢɧɢɦɚɥɶɧɵɦɢ ɡɚɬɪɚɬɵ ɛɭɞɭɬ ɩɪɢ ɜɪɟɦɟɧɢ ɩɨɫɬɭɩɥɟɧɢɢ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɪɚɜɧɨɦ 8 ɦɢɧ., ɷɬɨ ɪɟɲɟɧɢɟ ɧɟ ɛɭɞɟɬ ɨɩɬɢɦɚɥɶɧɵɦ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɛɭɞɭɬ ɦɚɥɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɡɚɧɹɬɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ, ɬ.ɟ. ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ ɛɭɞɭɬ ɩɪɨɫɬɚɢɜɚɬɶ ɨɫɧɨɜɧɭɸ ɱɚɫɬɶ ɩɟɪɢɨɞɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɩɨɫɬɭɩɥɟɧɢɹɦɢ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɢɯ ɤɨɥɢɱɟɫɬɜɨ ɭɦɟɧɶɲɚɟɬɫɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɢ ɭɦɟɧɶɲɚɟɬɫɹ ɜɪɟɦɹ, ɩɪɨɜɟɞɟɧɧɨɟ ɜ ɨɱɟɪɟɞɹɯ. ɉɪɨɦɨɞɟɥɢɪɭɟɦ ɜ ɫɢɫɬɟɦɟ GPSS World ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɬɟɱɟɧɢɟ ɨɞɧɨɝɨ ɪɚɛɨɱɟɝɨ ɞɧɹ (8 ɱɚɫɨɜ = 480 ɦɢɧɭɬ) (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 4). Ʉɨɧɤɪɟɬɧɵɟ

ɪɟɡɭɥɶɬɚɬɵ

ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ

ɫɟɪɢɢ

ɩɪɟɞɫɬɚɜɥɟɧɵ

ɪɢɫɭɧɤɚɯ 3.2 - 3.6, ɜ ɬɚɛɥɢɰɚɯ 3.3 - 3.4, ɩɪɢɥɨɠɟɧɢɹɯ 8 - 12.

100 80 60 40 20 0 Sp1

Sp2

Rab

Kon

Ob

Ɋɢɫɭɧɨɤ 3.2 - Ʉɨɥɢɱɟɫɬɜɨ ɨɛɫɥɭɠɟɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɩɨ ɨɬɞɟɥɚɦ

12 10

Sp1

8

Sp2

6

Rab

4

Kon

2

Ob

0

Ɋɢɫɭɧɨɤ 3.3 - ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɡɚɧɹɬɢɹ ɨɬɞɟɥɚ ɨɞɧɢɦ ɛɟɡɪɚɛɨɬɧɵɦ

Ɋɟɡɭɥɶɬɚɬɵ ɢɦɢɬɚɰɢɨɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 3.3.

102

ɧɚ

Ɍɚɛɥɢɰɚ 3. 3 - Ɋɟɡɭɥɶɬɚɬɵ ɢɦɢɬɚɰɢɨɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɨɬɞɟɥɚɦ

ʋ

ɬɪɟɛɨɜɚɧɢɣ ɨɬɞɟɥɚ ɨɞɧɢɦ ɛɟɡɪɚɛɨɬɧɵɦ

Sp1

Sp2

Rab

Kon

Ob

1

5

7±3

5±3

5±3

5±3

2

6

6±3

5±3

5±3

5±3

3

7

6±3

5±3

5±3

5±3

4

8

7±3

6±3

5±3

5±3

5

9

7±3

6±3

6±3

5±3

1

77

71

42

25

3

2

68

81

49

26

4

3

63

81

48

30

2

4

56

69

45

22

1

5

49

65

43

19

2

1

0.977

0.986

0.416

0.249

0.036

2

0.982

0.984

0.501

0.280

0.041

3

0.998

0.982

0.528

0.273

0.020

4

0.998

0.972

0.511

0.229

0.014

5

0.998

0.968

0.554

0.244

0.021

1

6.091

6.667

4.751

4.787

5.804

2

6.929

5.830

4.903

5.176

4.925

3

7.603

5.822

5.279

4.362

4.885

4

8.554

6.763

5.450

4.988

6.948

5

9.776

7.145

6.189

6.153

5.143

ɷɤɫɩɟɪɢɦɟɧɬɚ

ɬɪɟɛɨɜɚɧɢɣ

ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɛɫɥɭɠɟɧɧɵɯ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɡɚɧɹɬɢɹ ɨɬɞɟɥɚ

ɋɪɟɞɧɟɟ ɜɪɟɦɹ

Ʉɨɷɮɮɢɰɢɟɧɬ

Ʉɨɥɢɱɟɫɬɜɨ

ɂɧɬɟɧɫɢɜɧɨɫɬɶ

ɋɨɞɟɪɠɚɧɢɟ

ɂɡ ɬɚɛɥɢɰɵ 3.3 ɜɢɞɧɨ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥɚɯ ɛɢɪɠɢ ɬɪɭɞɚ ɭɦɟɧɶɲɚɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨ ɨɛɫɥɭɠɟɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɬɚɤ ɤɚɤ ɞɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɹɜɥɹɸɬɫɹ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɦɢ (ɪɢɫ. 3.2). Ɍɚɤɠɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜɪɟɦɹ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ ɛɟɡɪɚɛɨɬɧɨɝɨ (ɪɢɫ. 3.3). ȼɵɫɨɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɨɬɞɟɥɨɜ Sp1 ɢ Sp2 ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ

ɛɨɥɶɲɨɣ

ɢɯ

ɡɚɝɪɭɠɟɧɧɨɫɬɢ

(ɪɢɫ. 103

3.4).

Ɉɩɬɢɦɚɥɶɧɵɦ

ɤɨɷɮɮɢɰɢɟɧɬ

ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɜ ɨɬɞɟɥɟ Rab. ȼɟɪɨɹɬɧɨɫɬɶ ɡɚɧɹɬɨɫɬɢ ɦɨɞɟɥɢɪɭɟɦɨɣ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɜɫɟɯ ɨɬɞɟɥɨɜ ɧɚɢɛɨɥɶɲɟɝɨ ɡɧɚɱɟɧɢɹ ɞɨɫɬɢɝɚɟɬ ɩɪɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɪɚɜɧɨɣ 6 ɦɢɧ. Ob Kon Rab Sp2 Sp1 0

0.2

0.4

0.6

0.8

1

1.2

Ɋɢɫɭɧɨɤ 3.4 - ȼɟɪɨɹɬɧɨɫɬɶ ɡɚɧɹɬɨɫɬɢ ɨɬɞɟɥɨɜ

ȼɪɟɦɹ, ɩɪɨɜɟɞɟɧɧɨɟ ɛɟɡɪɚɛɨɬɧɵɦɢ ɜ ɨɱɟɪɟɞɢ ɜ ɬɨɬ ɢɥɢ ɢɧɨɣ ɨɬɞɟɥ, ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɬɚɛɥɢɰɟ 3.4. Ɍɚɛɥɢɰɚ 3. 4 - ɋɜɟɞɟɧɢɹ ɨɛ ɨɱɟɪɟɞɹɯ ɩɨ ɨɬɞɟɥɚɦ

Kon

Ob

1

2

3

4

5

6

7

1

5

7±3

5±3

5±3

5±3

6

6±3

5±3

5±3

5±3

3

7

6±3

5±3

5±3

5±3

4

8

7±3

6±3

5±3

5±3

5

9

7±3

6±3

6±3

5±3

132

123

42

25

3

2

146

126

49

27

4

3

154

120

48

30

2

4

162

116

45

22

1

5

152

99

43

19

2

1

106.13

114.87

0.17

0.14

0

2

124.76

87.35

0.38

0.42

0

3

144.44

87.36

1.05

0.04

0

4

166.95

96.89

0.48

0.03

0

5

166.82

95.49

0.65

0.21

0

ɨɱɟɪɟɞɶ

1

ɨɱɟɪɟɞɢ

2

ɩɪɟɛɵɜɚɧɢɹ ɜ

Ʉɨɥɢɱɟɫɬɜɨ ɋɪɟɞɧɟɟ ɜɪɟɦɹ

ɬɪɟɛɨɜɚɧɢɣ

Rab

ɩɪɨɲɟɞɲɢɯ ɱɟɪɟɡ

Sp2

ɨɛɫɥɭɠɢɜɚɧɢɹ

Sp1

ɛɟɡɪɚɛɨɬɧɵɯ,

ʋ ɷɤɫɩɟɪɢɦɟɧɬɚ

ɂɧɬɟɧɫɢɜɧɨɫɬɶ

ɋɨɞɟɪɠɚɧɢɟ

104

ɋɪɟɞɧɟɟ ɜɪɟɦɹ, ɩɪɨɜɟɞɟɧɧɨɟ ɜ ɨɱɟɪɟɞɹɯ ɫ ɭɱɟɬɨɦ ɜɫɟɯ ɜɯɨɞɨɜ, ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɜ ɨɬɞɟɥɟ Sp1 ɩɪɢ ɜɪɟɦɟɧɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɪɚɜɧɨɦ 9 ɦɢɧ. ɢ ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ 7 ɦɢɧ. 200 150 100 50 0 Sp1

Sp2

Rab

Kon

Ob

Ɋɢɫɭɧɨɤ 3.5 - Ʉɨɥɢɱɟɫɬɜɨ ɛɟɡɪɚɛɨɬɧɵɯ ɩɨ ɨɬɞɟɥɚɦ, ɩɪɨɲɟɞɲɢɯ ɱɟɪɟɡ ɨɱɟɪɟɞɶ

ɋɪɟɞɧɟɟ ɜɪɟɦɹ, ɩɪɨɜɟɞɟɧɧɨɟ ɜ ɨɱɟɪɟɞɢ, ɞɥɹ ɛɢɪɠɢ ɬɪɭɞɚ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɩɪɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɪɚɜɧɨɣ 5 ɦɢɧ. (ɪɢɫ. 3.5, 3.6). 200 Sp1

150

Sp2

100

Rab Kon

50

Ob

0

Ɋɢɫɭɧɨɤ 3.6 - ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɱɟɪɟɞɢ

ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɬɞɟɥɚɯ Sp1 ɢ Sp2 ɧɚɛɥɸɞɚɟɬɫɹ ɭɫɬɨɣɱɢɜɚɹ ɬɟɧɞɟɧɰɢɹ ɭɦɟɧɶɲɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɢ ɢɯ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɚ ɞɥɹ ɨɬɞɟɥɨɜ Rab, Kon ɢ Ob ɯɚɪɚɤɬɟɪɧɚ ɫɬɚɛɢɥɶɧɨɫɬɶ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ (ɫɦ. ɬɚɛɥ. 3.5, ɪɢɫ. 3.7). 1.2 1

Sp1

0.8

Sp2

0.6

Rab

0.4

Kon Ob

0.2 0

Ɋɢɫɭɧɨɤ 3.7 - ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɛɟɡɪɚɛɨɬɧɵɯ 105

ȼ ɫɜɹɡɢ ɫ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɩɨɜɬɨɪɧɨɣ ɨɛɪɚɛɨɬɤɢ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɡɚɬɪɚɬɵ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ ɦɨɝɭɬ ɛɵɬɶ ɭɜɟɥɢɱɟɧɵ. ȼ ɬɚɛɥɢɰɟ 3.6 ɩɪɢɜɟɞɟɧɵ ɦɚɤɫɢɦɚɥɶɧɵɟ ɭɛɵɬɤɢ ɛɢɪɠɢ ɬɪɭɞɚ ɡɚ ɨɞɢɧ ɞɟɧɶ ɪɚɛɨɬɵ, ɢɫɯɨɞɹ ɢɡ ɬɨɝɨ, ɱɬɨ ɡɚɬɪɚɬɵ ɧɚ ɞɨɪɚɛɨɬɤɭ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɫɨɫɬɚɜɥɹɸɬ 135.67 ɪɭɛ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɪɚɫɯɨɞɵ ɦɨɝɭɬ ɫɨɫɬɚɜɢɬɶ ɛɨɥɟɟ 10 000 ɪɭɛɥɟɣ ɜ ɞɟɧɶ (ɪɢɫ. 3.8.). Ɍɚɛɥɢɰɚ 3. 5 - ɋɜɟɞɟɧɢɹ ɩɨ ɬɚɛɥɢɰɚɦ

ɚɪɝɭɦɟɧɬɚ

ɬɪɟɛɨɜɚɧɢɣ ɬɚɛɭɥɢɪɭɟɦɨɝɨ ɨɬɤɥɨɧɟɧɢɟ

ɨɛɫɥɭɠɢɜɚɧɢɹ ɡɧɚɱɟɧɢɟ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɟ ɨɛɫɥɭɠɢɜɚɧɢɹ

ɋɪɟɞɧɟɜɡɜɟɲɟɧɧɨɟ ȼɟɪɨɹɬɧɨɫɬɶ

ȼɡɜɟɲɟɧɧɨɟ

ɂɧɬɟɧɫɢɜɧɨɫɬɶ

ɋɨɞɟɪɠɚɧɢɟ

ʋ

Sp1

Sp2

Rab

Kon

Ob

1

5

7±3

5±3

5±3

5±3

2

6

6±3

5±3

5±3

5±3

3

7

6±3

5±3

5±3

5±3

4

8

7±3

6±3

5±3

5±3

5

9

7±3

6±3

6±3

5±3

1

94.14

168.50

173.70

180.64

110.18

2

119.16

145.89

147.79

147.15

141.77

3

139.88

153.75

171.30

141.95

132.05

4

168.48

164.71

167.59

179.13

71.40

5

159.84

148.67

153.46

146.67

241.96

1

68.38

107.42

112.77

103.71

47.94

2

81.89

102.30

104.62

89.84

86.78

3

94.12

95.78

104.69

81.27

96.65

4

113.67

108.77

116.35

96.27

0

5

116.55

92.29

98.96

92.28

111.99

1

0.576

0.569

1.0

1.0

1.0

2

0.459

0.635

1.0

0.926

1.0

3

0.403

0.667

1.0

1.0

1.0

4

0.340

0.586

0.978

1.0

1.0

5

0.316

0.646

0.977

1.0

1.0

ɷɤɫɩɟɪɢɦɟɧɬɚ

106

ɪɭɛ.

12000 10000 8000 6000 4000 2000 0

Sp1 Sp2 Rab Kon 30

25

20

Ob

ɦɢɧ.

Ɋɢɫɭɧɨɤ 3.8 - Ɂɚɜɢɫɢɦɨɫɬɶ ɡɚɬɪɚɬ ɧɚ ɞɨɪɚɛɨɬɤɭ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɨɬ

ɛɟɡɪɚɛɨɬɧɨɝɨ ɨɬ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɉɪɨɦɨɞɟɥɢɪɭɟɦ ɜ ɫɢɫɬɟɦɟ GPSS World ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɬɟɱɟɧɢɟ ɞɟɫɹɬɢ ɪɚɛɨɱɢɯ ɞɧɟɣ (8 ɱɚɫɨɜ ɯ 10 ɞɧɟɣ = 4800 ɦɢɧɭɬ) (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 4). Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɧɨ ɦɨɞɟɥɢɪɨɜɚɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɛɢɪɠɢ ɬɪɭɞɚ ɧɚ ɪɚɡɥɢɱɧɵɯ ɜɪɟɦɟɧɧɵɯ ɢɧɬɟɪɜɚɥɚɯ ɫ ɰɟɥɶɸ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɫɢɬɭɚɰɢɢ. Ɍɚɛɥɢɰɚ 3. 6 - Ɋɚɫɯɨɞɵ ɛɢɪɠɢ ɬɪɭɞɚ ɩɪɢ ɩɨɜɬɨɪɧɨɣ ɨɛɪɚɛɨɬɤɢ ɬɪɟɛɨɜɚɧɢɣ

ɂɧɬɟɧɫɢɜɧɨɫɬɶ Ɇɚɤɫɢɦɚɥɶɧɵɟ ɭɛɵɬɤɢ, ɪɭɛ. ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɦɢɧ. Sp1 Sp2 Rab Kon Ob 9 2849.1 6376.5 3527.4 1628 542.68 8 2577.7 6512.2 3391.8 2170.7 407.01 7 3120.4 10582 5426.8 2984.7 542.68 ɇɚ ɪɢɫɭɧɤɟ 2 ɩɨɤɚɡɚɧɚ ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ.

ɋɬɚɬɢɫɬɢɤɚ ɩɪɨɜɟɞɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɬɨɦ, ɱɬɨ ɪɚɛɨɬɚ ɛɢɪɠɢ ɬɪɭɞɚ ɬɪɟɛɭɟɬ ɤɨɪɪɟɤɬɢɪɨɜɤɢ ɪɚɡɥɢɱɧɵɯ ɜɪɟɦɟɧɧɵɯ ɷɬɚɩɚɯ. Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɛɭɞɟɬ ɧɚɤɚɩɥɢɜɚɬɶɫɹ ɨɱɟɪɟɞɶ. ɉɨɷɬɨɦɭ ɧɟɨɛɯɨɞɢɦɨ ɫɥɟɞɢɬɶ ɡɚ ɫɢɬɭɚɰɢɟɣ ɩɨ ɨɬɞɟɥɚɦ ɢ ɜɨɜɪɟɦɹ ɪɟɝɭɥɢɪɨɜɚɬɶ ɩɪɨɰɟɫɫ ɨɛɫɥɭɠɢɜɚɧɢɹ ɛɟɡɪɚɛɨɬɧɵɯ.

107

ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ

0.84 0.83 0.82 0.81 0.8 0.79 0.78 0.77 0.76 0.75 1

2

3

4

5

ɇɨɦɟɪ ɷɤɫɩɟɪɢɦɟɧɬɚ

Ɋɢɫɭɧɨɤ 3.9 - ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɫɥɟ ɩɪɨɜɟɞɟɧɢɹ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɫɬɪɨɟɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɫɥɟɞɭɸɳɢɟ ɭɫɬɨɣɱɢɜɵɟ ɬɟɧɞɟɧɰɢɢ: 1. ɉɪɟɞɥɨɠɟɧɧɚɹ

ɨɪɝɚɧɢɡɚɰɢɹ

ɛɢɪɠɢ

ɬɪɭɞɚ

ɞɚɟɬ

ɡɚɦɟɬɧɵɣ

ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ ɜ ɩɪɨɰɟɫɫɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. 2. ȼɚɪɶɢɪɨɜɚɧɢɟ ɩɨɤɚɡɚɬɟɥɟɣ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ,

ɢɧɬɟɧɫɢɜɧɨɫɬɢ

ɢɯ

ɨɛɫɥɭɠɢɜɚɧɢɹ

ɩɨɡɜɨɥɹɟɬ

ɨɩɪɟɞɟɥɢɬɶ

ɨɩɬɢɦɚɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. 3. Ɉɞɧɚ ɢɡ ɭɫɬɨɣɱɢɜɨ ɧɚɛɥɸɞɚɟɦɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɧɚɢɛɨɥɶɲɚɹ ɧɚɝɪɭɡɤɚ ɜ ɩɪɨɰɟɫɫɟ ɨɛɫɥɭɠɢɜɚɧɢɹ ɥɨɠɢɬɫɹ ɧɚ ɨɬɞɟɥɵ ɩɟɪɜɢɱɧɨɝɨ ɢ ɩɨɜɬɨɪɧɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ⱥɧɚɥɢɡɢɪɭɹ

ɞɚɧɧɵɟ

ɬɚɛɥɢɰ

3.3

–

3.5,

ɫɬɚɬɢɫɬɢɤɭ

ɩɪɨɜɟɞɟɧɧɵɯ

ɷɤɫɩɟɪɢɦɟɧɬɨɜ (ɫɦ. ɩɪɢɥɨɠɟɧɢɹ 4) ɫɞɟɥɚɟɦ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ ɨɛ ɨɱɟɪɟɞɹɯ: -

ɱɟɦ

ɛɟɡɪɚɛɨɬɧɵɯ,

ɛɨɥɶɲɟ

ɢɧɬɟɧɫɢɜɧɨɫɬɶ

ɨɛɫɥɭɠɢɜɚɟɦɵɯ

ɜɧɟ

ɩɨɫɬɭɩɥɟɧɢɹ

ɨɱɟɪɟɞɢ,

ɬɟɦ

ɬɪɟɛɨɜɚɧɢɣ

ɜɵɲɟ

ɨɬ

ɦɚɤɫɢɦɚɥɶɧɨɟ

ɫɨɞɟɪɠɢɦɨɟ ɨɱɟɪɟɞɢ, ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɱɟɪɟɞɢ, ɚ ɬɚɤɠɟ ɜɟɪɨɹɬɧɨɫɬɶ ɡɚɧɹɬɨɫɬɢ ɭɫɬɪɨɣɫɬɜɚ; -

ɱɟɦ

ɦɟɧɶɲɟ

ɢɧɬɟɧɫɢɜɧɨɫɬɶ

ɩɨɫɬɭɩɥɟɧɢɹ

ɬɪɟɛɨɜɚɧɢɣ

ɨɬ

ɛɟɡɪɚɛɨɬɧɵɯ ɢɡ ɩɟɪɜɨɝɨ ɢɫɬɨɱɧɢɤɚ, ɬɟɦ ɛɨɥɶɲɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɫɨɞɟɪɠɢɦɨɟ ɨɱɟɪɟɞɢ ɢ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɜ ɨɱɟɪɟɞɢ. 108

ɉɨɷɬɨɦɭ ɞɥɹ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɨɣ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɨɩɬɢɦɚɥɶɧɨɟ ɜɪɟɦɹ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɩɪɟɞɟɥɚɯ 6 ɦɢɧ. ɢɥɢ 7 ɦɢɧ. ɉɪɢ ɷɬɨɦ ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɬɞɟɥɚɯ Sp1, Sp2, Rab, Kon ɞɨɥɠɧɨ ɛɵɬɶ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ 6 ɦɢɧ., 5 ɦɢɧ., 5 ɦɢɧ., 5 ɦɢɧ. Ɍɚɤ ɤɚɤ ɤɨɥɢɱɟɫɬɜɨ ɨɛɫɥɭɠɟɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɨɬɞɟɥɟ Ob ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɨ, ɧɟɨɛɯɨɞɢɦɨ ɨɪɝɚɧɢɡɨɜɚɬɶ ɪɚɛɨɬɭ ɜ ɧɟɦ ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ, ɧɚɩɪɢɦɟɪ, ɨɞɢɧ ɢɥɢ ɞɜɚ ɪɚɡɚ ɜ ɧɟɞɟɥɸ. ȼ ɫɜɹɡɢ ɫ ɬɟɦ, ɱɬɨ ɨɫɧɨɜɧɚɹ ɧɚɝɪɭɡɤɚ ɩɨɫɬɭɩɚɸɳɟɝɨ ɩɨɬɨɤɚ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɥɨɠɢɬɫɹ ɧɚ ɨɬɞɟɥɵ Sp1 ɢ Sp2, ɬɨ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɪɝɚɧɢɡɨɜɚɬɶ ɜ ɧɢɯ ɩɚɪɚɥɥɟɥɶɧɭɸ ɪɚɛɨɬɭ ɧɟɫɤɨɥɶɤɢɯ ɫɩɟɰɢɚɥɢɫɬɨɜ. ɉɪɢ ɛɨɥɶɲɨɦ ɩɨɬɨɤɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɜɨɡɦɨɠɧɨ ɜɤɥɸɱɟɧɢɟ ɜ ɪɚɛɨɬɭ ɨɬɞɟɥɨɜ Rab, Kon. ɇɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ ɦɢɧɢɦɚɥɶɧɵɦɢ ɡɚɬɪɚɬɵ ɛɭɞɭɬ ɢ ɩɪɢ ɜɪɟɦɟɧɢ ɩɨɫɬɭɩɥɟɧɢɢ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɪɚɜɧɨɦ 8 ɦɢɧ., ɷɬɨ ɪɟɲɟɧɢɟ ɧɟ ɛɭɞɟɬ ɨɩɬɢɦɚɥɶɧɵɦ, ɬɚɤ ɤɚɤ ɬɨɝɞɚ ɛɭɞɭɬ ɦɚɥɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɡɚɧɹɬɨɫɬɢ ɛɢɪɠɢ ɬɪɭɞɚ, ɬ.ɟ. ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ ɛɭɞɭɬ ɩɪɨɫɬɚɢɜɚɬɶ ɨɫɧɨɜɧɭɸ ɱɚɫɬɶ ɩɟɪɢɨɞɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɩɨɫɬɭɩɥɟɧɢɹɦɢ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ ɢɯ ɤɨɥɢɱɟɫɬɜɨ ɭɦɟɧɶɲɚɟɬɫɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɢ ɭɦɟɧɶɲɚɟɬɫɹ ɜɪɟɦɹ, ɩɪɨɜɟɞɟɧɧɨɟ ɜ ɨɱɟɪɟɞɹɯ. ɍɤɚɡɚɧɧɵɟ ɭɡɤɢɟ ɦɟɫɬɚ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ ɦɨɠɧɨ ɥɢɤɜɢɞɢɪɨɜɚɬɶ ɫ ɩɨɦɨɳɶɸ ɫɨɡɞɚɧɢɹ ɬɟɥɟɤɨɦɦɭɧɢɤɚɰɢɨɧɧɵɯ ɫɟɬɟɣ. ɋɨɡɞɚɧɢɟ ɷɥɟɤɬɪɨɧɧɨɣ ɛɚɡɵ ɞɚɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ, ɫ ɩɪɢɫɜɨɟɧɢɟɦ ɤɚɠɞɨɦɭ ɢɡ ɧɢɯ ɢɞɟɧɬɢɮɢɤɚɰɢɨɧɧɨɝɨ ɧɨɦɟɪɚ, ɩɨɡɜɨɥɢɬ ɫɭɳɟɫɬɜɟɧɧɨ ɭɥɭɱɲɢɬɶ ɪɚɛɨɬɭ ɛɢɪɠɢ ɬɪɭɞɚ. 3.4. ȼɵɜɨɞɵ

ɉɨɥɭɱɟɧɧɵɟ ɞɚɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɨɜɟɞɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɡɜɨɥɹɸɬ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ. 1.

ȼɟɪɨɹɬɧɨɫɬɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɨɫɧɨɜɧɵɟ

ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɮɭɧɤɰɢɨɧɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɭɫɬɨɣɱɢɜɨɝɨ ɢ 109

ɧɟɭɫɬɨɣɱɢɜɨɝɨ ɫɨɫɬɨɹɧɢɣ ɪɵɧɤɚ ɬɪɭɞɚ. 2.

ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ, ɪɟɚɥɢɡɨɜɚɧɧɚɹ ɧɚ ɹɡɵɤɟ GPSS

ɩɨɡɜɨɥɹɟɬ ɷɮɮɟɤɬɢɜɧɨ ɢ ɷɤɨɧɨɦɢɱɧɨ ɩɪɨɜɨɞɢɬɶ ɫɛɨɪ ɞɚɧɧɵɯ ɢ ɚɧɚɥɢɡ ɫɨɫɬɨɹɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ, ɧɟ ɩɪɢɛɟɝɚɹ ɤ ɧɚɬɭɪɧɵɦ ɷɤɫɩɟɪɢɦɟɧɬɚɦ. 3.

ȼɵɩɨɥɧɟɧɢɟ ɭɤɚɡɚɧɧɵɯ ɜ ɪɚɛɨɬɟ ɭɫɥɨɜɢɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ

ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɩɨɜɵɫɢɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɟɟ ɪɚɛɨɬɵ ɫ ɛɟɡɪɚɛɨɬɧɵɦɢ ɩɨ ɫɜɨɟɜɪɟɦɟɧɧɨɦɭ ɨɛɟɫɩɟɱɟɧɢɸ ɢɯ ɪɚɛɨɬɨɣ. 4.

Ɇɨɞɟɥɶɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɵ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɧɚɢɛɨɥɶɲɢɣ ɜɵɢɝɪɵɲ

ɪɵɧɨɤ ɬɪɭɞɚ ɩɨɥɭɱɚɟɬ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɩɪɟɞɥɨɠɟɧɧɚɹ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɜɚɤɚɧɫɢɹ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ ɭɞɨɜɥɟɬɜɨɪɢɬ ɬɪɟɛɨɜɚɧɢɟ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ. 5.

ɋ ɩɨɦɨɳɶɸ ɫɨɡɞɚɧɧɨɝɨ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɶɧɨɝɨ ɤɨɦɩɥɟɤɫɚ

ɭɞɚɥɨɫɶ ɩɪɨɜɟɫɬɢ ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ ɚɧɚɥɢɡ ɪɟɡɭɥɶɬɚɬɨɜ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ: ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɫɬɭɩɥɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɛɟɡɪɚɛɨɬɧɵɯ ɜ ɪɚɡɥɢɱɧɵɟ ɨɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ; ɜɪɟɦɟɧɢ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɚɯ ɛɢɪɠɢ ɬɪɭɞɚ; ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɨɬ ɛɟɡɪɚɛɨɬɧɨɝɨ; ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɟɫɭɪɫɨɜ ɦɟɠɞɭ ɨɬɞɟɥɚɦɢ ɛɢɪɠɢ ɬɪɭɞɚ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɮɭɧɤɰɢɣ; ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɫɩɨɥɶɡɨɜɚɧɢɹ (ɞɨɥɹ ɜɪɟɦɟɧɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ) ɨɬɞɟɥɨɜ ɛɢɪɠɢ ɬɪɭɞɚ. 6.

ɍɡɤɢɟ ɦɟɫɬɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ, ɜɵɹɜɥɟɧɧɵɟ ɜ

ɩɪɨɰɟɫɫɟ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɦɨɠɧɨ ɥɢɤɜɢɞɢɪɨɜɚɬɶ, ɢɫɩɨɥɶɡɭɹ ɬɟɥɟɤɨɦɦɭɧɢɤɚɰɢɨɧɧɵɟ ɫɟɬɢ.

110

ɁȺɄɅɘɑȿɇɂȿ

ɉɪɨɜɟɞɟɧɧɵɟ

ɜ

ɞɢɫɫɟɪɬɚɰɢɨɧɧɨɣ

ɪɚɛɨɬɟ

ɢɫɫɥɟɞɨɜɚɧɢɹ

ɩɨɡɜɨɥɢɥɢ

ɪɚɡɪɚɛɨɬɚɬɶ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ, ɢɫɫɥɟɞɨɜɚɬɶ ɪɵɧɨɤ ɬɪɭɞɚ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɢ ɨɩɪɟɞɟɥɢɬɶ ɨɫɧɨɜɧɵɟ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (ɩɚɪɚɦɟɬɪɵ), ɪɚɡɪɚɛɨɬɚɬɶ ɜɟɪɨɹɬɧɨɫɬɧɭɸ ɦɨɞɟɥɶ ɛɢɪɠɢ ɬɪɭɞɚ. ɉɨɥɭɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɧɚɭɱɧɵɟ ɢ ɩɪɚɤɬɢɱɟɫɤɢɟ ɪɟɡɭɥɶɬɚɬɵ. 1.

Ɋɚɡɪɚɛɨɬɚɧɚ ɚɧɚɥɢɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ

ɦɧɨɝɨɨɬɪɚɫɥɟɜɨɣ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɩɨɡɜɨɥɹɸɳɚɹ ɢɫɫɥɟɞɨɜɚɬɶ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɤɨɧɪɟɬɧɵɣ ɟɟ ɫɟɤɬɨɪ ɩɪɢ ɜɨɡɦɭɳɟɧɢɢ ɧɚɱɚɥɶɧɨɝɨ ɟɝɨ ɫɨɫɬɨɹɧɢɹ. Ⱦɚɧɧɚɹ

ɦɨɞɟɥɶ

ɹɜɥɹɟɬɫɹ

ɨɛɨɛɳɟɧɢɟɦ

ɧɚɱɚɬɨɝɨ

ɜ

ɷɬɨɦ

ɧɚɩɪɚɜɥɟɧɢɢ

ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɥɹ ɨɞɧɨɣ ɨɬɪɚɫɥɢ ɷɤɨɧɨɦɢɤɢ, ɩɪɟɞɩɪɢɧɹɬɨɝɨ Ⱥ.ɇ. ȼɚɫɢɥɶɟɜɵɦ [12]. ɉɪɢɜɟɞɟɧɵ ɩɪɢɦɟɪɵ, ɢɥɥɸɫɬɪɢɪɭɸɳɢɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɩɪɟɞɥɨɠɟɧɧɨɣ ɦɨɞɟɥɢ. 2.

Ɋɚɡɪɚɛɨɬɚɧɚ ɩɪɨɝɪɚɦɧɚɹ ɪɟɚɥɢɡɚɰɢɹ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ

ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ. 3.

ɉɪɟɞɥɨɠɟɧɚ ɦɟɬɨɞɢɤɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɪɨɰɟɫɫɚ

ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ.

Ⱦɚɧɧɚɹ ɦɟɬɨɞɢɤɚ ɪɟɚɥɢɡɨɜɚɧɚ ɧɚ ɗȼɆ ɫ

ɩɨɦɨɳɶɸ ɩɚɤɟɬɚ ɩɪɢɤɥɚɞɧɵɯ ɩɪɨɝɪɚɦɦ MathCad. 4.

Ɋɚɡɪɚɛɨɬɚɧɚ ɜɟɪɨɹɬɧɨɫɬɧɚɹ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ,

ɢɫɩɨɥɶɡɭɸɳɚɹ ɦɟɬɨɞɵ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɢ ɩɨɡɜɨɥɹɸɳɚɹ ɨɩɪɟɞɟɥɢɬɶ ɨɫɧɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɛɢɪɠɢ. 5.

ɋ ɩɨɦɨɳɶɸ ɫɢɫɬɟɦɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World ɪɚɡɪɚɛɨɬɚɧɚ

ɢɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ

ɛɢɪɠɢ ɬɪɭɞɚ, ɩɨɡɜɨɥɹɸɳɚɹ

ɜɨɫɩɪɨɢɡɜɨɞɢɬɶ ɩɪɨɰɟɫɫ ɟɟ ɪɚɛɨɬɵ. 6.

ɉɪɨɜɟɞɟɧ ɚɧɚɥɢɡ ɞɚɧɧɵɯ, ɩɨɥɭɱɟɧɧɵɯ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ,

ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɜɵɩɨɥɧɟɧɢɟ ɭɤɚɡɚɧɧɵɯ ɜ ɪɚɛɨɬɟ ɭɫɥɨɜɢɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ ɩɨɡɜɨɥɹɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɩɨɜɵɫɢɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɟɟ ɪɚɛɨɬɵ ɫ ɛɟɡɪɚɛɨɬɧɵɦɢ ɩɨ ɫɜɨɟɜɪɟɦɟɧɧɨɦɭ ɨɛɟɫɩɟɱɟɧɢɸ ɢɯ ɪɚɛɨɬɨɣ.

111

ɋɉɂɋɈɄ ɂɋɉɈɅɖɁɈȼȺɇɇɕɏ ɂɋɌɈɑɇɂɄɈȼ

1.

Ɂɚɤɨɧ «Ɉ ɡɚɧɹɬɨɫɬɢ ɧɚɫɟɥɟɧɢɹ ɜ Ɋɨɫɫɢɣɫɤɨɣ Ɏɟɞɟɪɚɰɢɢ». – Ɇ. –

1991. - ʋ 1032-1. 2.

MATHCAD 6.0 PLUS. Ɏɢɧɚɧɫɨɜɵɟ, ɢɧɠɟɧɟɪɧɵɟ ɢ ɧɚɭɱɧɵɟ ɪɚɫɱɟɬɵ

ɜ ɫɪɟɞɟ Windows 95. /ɉɟɪɟɜɨɞ ɫ ɚɧɝɥ. – Ɇ.: ɂɧɮɨɪɦɚɰɢɨɧɧɨ-ɢɡɞɚɬɟɥɶɫɤɢɣ ɞɨɦ «Ɏɢɥɢɧɴ», 1996. – 712 ɫ. 3.

Ⱥɤɢɧɢɧ

ɉ.ȼ.,

Ƚɚɟɜɫɤɢɣ

ȼ.ȼ.,

Ɋɹɡɚɧɰɟɜ

ɋ.ȼ.

ɗɤɨɧɨɦɢɤɚ

ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɤɪɚɹ. – ɋɬɚɜɪɨɩɨɥɶ: Ʉɧɢɠɧɨɟ ɢɡɞɚɬɟɥɶɫɬɜɨ, 2000. – 317 ɫ. 4.

Ⱥɦɨɫɨɜ Ⱥ.Ⱥ., Ⱦɭɛɢɧɫɤɢɣ ɘ.Ⱥ., Ʉɨɩɱɟɧɨɜɚ ɇ.ȼ. ȼɵɱɢɫɥɢɬɟɥɶɧɵɟ

ɦɟɬɨɞɵ ɞɥɹ ɢɧɠɟɧɟɪɨɜ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ. – Ɇ.: ȼɵɫɲ. ɲɤ., 1994. – 65 ɫ. 5.

Ⱥɫɟɟɜ Ⱥ. Ⱥ., Ȼɨɟɜ ȼ. Ⱦ., Ʉɭɥɟɲɨɜ ɂ. Ⱥ., ɋɟɱɟɧɟɜ Ⱦ. Ɇ. Ɉɫɧɨɜɵ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɢɫɬɟɦ ɫɜɹɡɢ ɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɧɚ GPSS/PC: ɍɱɟɛ. ɩɨɫɨɛɢɟ. ɋɉɛ.: ȼɍɋ, 2000. - 230 ɫ. 6.

Ⱥɮɚɧɚɫɶɟɜ ȼ. ɇ. ɢ ɞɪ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɬɟɨɪɢɹ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɹ

ɫɢɫɬɟɦ ɭɩɪɚɜɥɟɧɢɹ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ / ȼ.ɇ. Ⱥɮɚɧɚɫɶɟɜ, ȼ.Ȼ. Ʉɨɥɦɚɧɨɜɫɤɢɣ, ȼ.Ɋ. ɇɨɫɨɜ. - 2-ɟ ɢɡɞ., ɞɨɩ. - Ɇ.: ȼɵɫɲɚɹ ɲɤɨɥɚ, 1998 – 574 ɫ. 7.

Ȼɟɪɟɠɧɚɹ

ȿ.ȼ.,

Ȼɟɪɟɠɧɨɣ

ȼ.ɂ.

Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ

ɦɟɬɨɞɵ

ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɫɢɫɬɟɦ: ɍɱɟɛ. ɩɨɫɨɛɢɟ. – Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ, 2001. – 368 ɫ. 8.

Ȼɟɫɫɥɟɪ Ɋ., Ⱦɨɣɱ Ⱥ. ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɫɟɬɟɣ ɫɜɹɡɢ: ɋɩɪɚɜɨɱɧɢɤ: ɉɟɪ.

ɫ ɧɟɦ. – Ɇ.: Ɋɚɞɢɨ ɢ ɫɜɹɡɶ, 1988. -272 ɫ. 9.

Ȼɨɟɜ ȼ. Ⱦ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦ. ɂɧɫɬɪɭɦɟɧɬɚɥɶɧɵɟ ɫɪɟɞɫɬɜɚ

GPSS World. - ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝ:BHV-ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝ, 2004 ɝ. - 368 ɫ. 10.Ȼɭɫɥɟɧɤɨ ɇ.ɉ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. – Ɇ.: ɇɚɭɤɚ, 1978. – 400 ɫ. 11.ȼɚɪɠɚɩɟɬɹɧ Ⱥ. Ƚ., Ƚɥɭɲɟɧɤɨ ȼ. ȼ. ɋɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ: ɢɫɫɥɟɞɨɜɚɧɢɟ ɢ ɤɨɦɩɶɸɬɟɪɧɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ: ɍɱɟɛ. ɩɨɫɨɛɢɟ. - Ɇ.: ȼɭɡɨɜɫɤɚɹ ɤɧɢɝɚ, 2000. 328 ɫ. 12.

ȼɚɫɢɥɶɟɜ Ⱥ.ɇ. Ɇɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ // ɗɤɨɧɨɦɢɤɚ 112

ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ. - 2001. Ɍɨɦ 37. ʋ 2. - ɋ. 123-127. 13.

ȼɚɫɢɥɶɟɜ

ə.Ɍ.

ɋɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɟ

ɪɟɝɢɨɧɚɥɶɧɨɣ

ɡɚɧɹɬɨɫɬɢ

ɧɚɫɟɥɟɧɢɹ ɜ ɭɫɥɨɜɢɹɯ ɫɬɚɧɨɜɥɟɧɢɹ ɪɵɧɤɚ ɬɪɭɞɚ: Ⱥɜɬɨɪɟɮ. ɞɢɫɫ. ... ɞɨɤɬ. ɷɤɨɧ. ɧɚɭɤ. Ɇ. 1997. 14.

ȼɚɫɢɥɶɤɨɜ ɘ.ȼ., ȼɚɫɢɥɶɤɨɜɚ ɇ.ɇ. Ʉɨɦɩɶɸɬɟɪɧɵɟ ɬɟɯɧɨɥɨɝɢɢ

ɜɵɱɢɫɥɟɧɢɣ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɦɨɞɟɥɢɪɨɜɚɧɢɢ: ɍɱɟɛ. ɩɨɫɨɛɢɟ. – Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ, 2002. - 256 ɫ.: ɢɥ. 15.

ȼɟɧɬɰɟɥɶ

ȿ.ɋ.,

Ɉɜɱɚɪɨɜ

Ʌ.Ⱥ.

ɉɪɢɤɥɚɞɧɵɟ

ɡɚɞɚɱɢ

ɬɟɨɪɢɢ

ɜɟɪɨɹɬɧɨɫɬɟɣ. – Ɇ.: Ɋɚɞɢɨ ɢ ɫɜɹɡɶ, 1983. – 415 ɫ. 16.

ȼɟɧɬɰɟɥɶ ȿ.ɋ. Ɍɟɨɪɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ: ɍɱɟɛ. ɞɥɹ ɜɭɡɨɜ. - 7-ɟ ɢɡɞ. ɫɬɟɪ.

– Ɇ.: ȼɵɫɲ. ɲɤ., 2001. – 575 ɫ.: ɢɥ. 17.

ȼɟɪɠɛɢɰɤɢɣ ȼ.Ɇ. ɑɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ (ɥɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ ɢ

ɧɟɥɢɧɟɣɧɵɟ ɭɪɚɜɧɟɧɢɹ): ɍɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ȼɵɫɲ. ɲɤ., 2000. – 266 ɫ.: ɢɥ. 18.

ȼɟɪɠɛɢɰɤɢɣ ȼ.Ɇ. ɑɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ (Ɇɚɬɟɦɚɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɢ

ɨɛɵɤɧɨɜɟɧɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ): ɍɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ȼɵɫɲ. ɲɤ., 2001. – 382 ɫ.: ɢɥ. 19.

ȼɨɥɤɨɜ ɂ.Ʉ., Ɂɭɟɜ ɋ.Ɇ., ɐɜɟɬɤɨɜɚ Ƚ.Ɇ. ɋɥɭɱɚɣɧɵɟ ɩɪɨɰɟɫɫɵ:

ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ / ɉɨɞ ɪɟɞɚɤɰɢɟɣ ȼ.ɋ. Ɂɚɪɭɛɢɧɚ, Ⱥ.ɉ. Ʉɪɢɳɟɧɤɨ. – 2-ɟ ɢɡɞ., ɫɬɟɪɟɨɬɢɩ. – Ɇ.: ɂɡɞ-ɜɨ ɆȽɌɍ ɢɦ. Ȼɚɭɦɚɧɚ, 2003. – 448 ɫ. 20.

Ƚɚɧɬɦɚɯɟɪ Ɏ.Ɋ. Ɍɟɨɪɢɹ ɦɚɬɪɢɰ. - Ɇ.: ɇɚɭɤɚ, 1966. – 576 ɫ.

21.

Ƚɥɭɯɨɜ ȼ.ȼ., Ɇɟɞɧɢɤɨɜ Ɇ.Ⱦ., Ʉɨɪɨɛɤɨ ɋ.Ȼ. Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ

ɢ ɦɨɞɟɥɢ ɞɥɹ ɦɟɧɟɞɠɦɟɧɬɚ. – ɋɉɛ.: Ʌɚɧɶ, 2000. – 480 ɫ. 22.

Ƚɦɭɪɦɚɧ

ȼ.ȿ.

Ɋɭɤɨɜɨɞɫɬɜɨ

ɤ

ɪɟɲɟɧɢɸ

ɡɚɞɚɱ

ɩɨ

ɬɟɨɪɢɢ

ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɬɚɬɢɫɬɢɤɟ: ɍɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɜɬɭɡɨɜ. - 3-ɟ ɢɡɞ., ɩɟɪɟɪɚɛ. ɢ ɞɨɩ. – Ɇ.: ȼɵɫɲ. ɲɤ., 1979. – 400 ɫ.: ɢɥ. 23.

Ƚɦɭɪɦɚɧ ȼ.ȿ. Ɍɟɨɪɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɫɬɚɬɢɫɬɢɤɚ:

ɍɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. - ɂɡɞ. 6-ɟ, ɫɬɟɪ. – Ɇ.: ȼɵɫɲ. ɲɤ., 1998. – 479 ɫ.: ɢɥ. 24.

Ƚɧɟɞɟɧɤɨ Ȼ.ȼ., Ʉɨɜɚɥɟɧɤɨ ɂ.ɇ. ȼɜɟɞɟɧɢɟ ɜ ɬɟɨɪɢɸ ɦɚɫɫɨɜɨɝɨ

ɨɛɫɥɭɠɢɜɚɧɢɹ. – Ɇ.: ɇɚɭɤɚ. Ƚɥ. ɪɟɞ. ɮɢɡ.-ɦɚɬ. ɥɢɬ., 1987. – 336 ɫ. 113

25.

Ƚɧɟɞɟɧɤɨ Ȼ.ȼ. Ʉɭɪɫ ɬɟɨɪɢɢ ɜɟɪɨɹɬɧɨɫɬɟɣ: ɍɱɟɛɧɢɤ – Ɇ.: ɇɚɭɤɚ. Ƚɥ.

ɪɟɞ. ɮɢɡ.-ɦɚɬ. ɥɢɬ., 1988. – 448 ɫ. 26.

Ƚɧɟɞɟɧɤɨ Ȼ.ȼ., ɏɢɧɱɢɧ Ⱥ.ə. ɗɥɟɦɟɧɬɚɪɧɨɟ ɜɜɟɞɟɧɢɟ ɜ ɬɟɨɪɢɸ

ɜɟɪɨɹɬɧɨɫɬɟɣ: ɍɱɟɛɧɢɤ – Ɇ.: ɇɚɭɤɚ. Ƚɥ. ɪɟɞ. ɮɢɡ.-ɦɚɬ. ɥɢɬ., 1976. – 168 ɫ. 27.

Ƚɨɥɟɧɤɨ

Ⱦ.ɂ.

Ɇɨɞɟɥɢɪɨɜɚɧɢɟ

ɢ

ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ

ɚɧɚɥɢɡ

ɩɫɟɜɞɨɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɧɚ ɷɥɟɤɬɪɨɧɧɵɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɦɚɲɢɧɚɯ. – Ɇ.: ɇɚɭɤɚ, 1965. – 228 ɫ. 28.

Ƚɨɪɱɚɤɨɜ

Ⱥ.Ⱥ.,

Ɉɪɥɨɜ

ɂ.ȼ.

Ʉɨɦɩɶɸɬɟɪɧɵɟ

ɷɤɨɧɨɦɢɤɨ-

ɫɬɚɧɨɜɥɟɧɢɟ

ɧɟɥɢɧɟɣɧɨɝɨ

ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ. – ɘɇɂɌɂ, 1995. – 134 ɫ. 29.

Ⱦɨɛɪɨɧɪɚɜɨɜɚ

ɂ.ɋ.

ɋɢɧɟɪɝɟɬɢɤɚ:

ɦɵɲɥɟɧɢɹ. – Ʉ.: Ʌɵɛɢɞɶ, 1990. – 152 ɫ. 30.

Ⱦɶɹɤɨɧɨɜ ȼ.ɉ., Ⱥɛɪɚɦɟɧɤɨɜɚ ɂ.ȼ. MathCad 7 ɜ ɦɚɬɟɦɚɬɢɤɟ, ɮɢɡɢɤɟ

ɢ ɜ Internet. – Ɇ.: ɇɨɥɢɞɠ, 1998. – 352 ɫ. 31.

Ⱦɶɹɤɨɧɨɜ ȼ.ɉ. Ʉɨɦɩɶɸɬɟɪɧɚɹ ɦɚɬɟɦɚɬɢɤɚ. Ɍɟɨɪɢɹ ɢ ɩɪɚɤɬɢɤɚ. – Ɇ.:

ɇɨɥɢɞɠ, 2001. – 1296 ɫ. 32.

Ⱦɶɹɤɨɧɨɜ ȼ.ɉ. ɋɩɪɚɜɨɱɧɢɤ ɩɨ MathCad PLUS 6.0 – Ɇ.: ɋɄ ɉɪɟɫɫ,

1997. – 336 ɫ. 33.

Ⱦɶɹɤɨɧɨɜ ȼ.ɉ. ɋɩɪɚɜɨɱɧɢɤ ɩɨ MathCad 7.0 PRO – Ɇ.: ɋɄ ɉɪɟɫɫ,

1998. – 352 ɫ. 34.

ȿɦɟɥɶɹɧɨɜ Ⱥ.Ⱥ. ɢ ɞɪ. ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɷɤɨɧɨɦɢɱɟɫɤɢɯ

ɩɪɨɰɟɫɫɨɜ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ / Ⱥ.Ⱥ. ȿɦɟɥɶɹɧɨɜ, ȿ.Ⱥ. ȼɥɚɫɨɜɚ, Ɋ.ȼ. Ⱦɭɦɚ; ɉɨɞ ɪɟɞ. Ⱥ.Ⱥ. ȿɦɟɥɶɹɧɨɜɚ. – Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ, 2004. – 368 ɫ.: ɢɥ. 35.

Ɂɚɣɰɟɜɚ ɂ.ȼ. ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ:

ɦɚɬɟɪɢɚɥɵ

49-ɣ

ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɣ

ɤɨɧɮɟɪɟɧɰɢɢ

ɩɪɟɩɨɞɚɜɚɬɟɥɟɣ

ɢ

ɫɬɭɞɟɧɬɨɜ «ɍɧɢɜɟɪɫɢɬɟɬɫɤɚɹ ɧɚɭɤɚ – ɪɟɝɢɨɧɭ». – ɋɬɚɜɪɨɩɨɥɶ: ɂɡɞ-ɜɨ ɋȽɍ, 2004. – 201 ɫ. 36.

Ɂɚɣɰɟɜɚ ɂ.ȼ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɥɹ

ɚɧɚɥɢɡɚ ɩɪɨɰɟɫɫɨɜ ɛɢɪɠɢ ɬɪɭɞɚ // Ⱥɤɬɭɚɥɶɧɵɟ ɜɨɩɪɨɫɵ ɫɨɰɢɚɥɶɧɨɣ ɬɟɨɪɢɢ ɢ ɩɪɚɤɬɢɤɢ: ɋɛɨɪɧɢɤ ɧɚɭɱɧɵɯ ɫɬɚɬɟɣ – ȼɵɩ. III. – ɋɬɚɜɪɨɩɨɥɶ: ɋɄɋɂ, 2004.– 404ɫ. 114

37.

Ɂɚɣɰɟɜɚ ɂ.ȼ. ɉɪɢɦɟɧɟɧɢɟ

ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɥɹ

ɢɫɫɥɟɞɨɜɚɧɢɹ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ // Ɋɵɧɨɤ ɩɪɨɛɥɟɦɵ

ɢ

ɬɟɧɞɟɧɰɢɢ

ɪɚɡɜɢɬɢɹ.

ɬɪɭɞɚ, ɡɚɧɹɬɨɫɬɶ, ɞɨɯɨɞɵ:

Ɇɚɬɟɪɢɚɥɵ

ɜɫɟɪɨɫɫɢɣɫɤɨɣ

ɧɚɭɱɧɨ-

ɩɪɚɤɬɢɱɟɫɤɨɣ ɤɨɧɮɟɪɟɧɰɢɢ. – Ɉɪɟɥ: ɈȽɍ, 2005. - ɋ. 74-77. 38. ɪɵɧɤɚ

Ɂɚɣɰɟɜɚ ɂ.ȼ. ɍɬɨɱɧɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ

ɬɪɭɞɚ

ɞɥɹ

ɧɟɫɤɨɥɶɤɢɯ

ɨɬɪɚɫɥɟɣ

//

Ɉɛɨɡɪɟɧɢɟ

ɩɪɢɤɥɚɞɧɨɣ

ɢ

ɩɪɨɦɵɲɥɟɧɧɨɣ ɦɚɬɟɦɚɬɢɤɢ. – 2004. - Ɍ.11. ɜ.4. - ɋ. 809-810. 39.

Ɂɚɦɤɨɜ Ɉ.Ɉ., Ɍɨɥɫɬɨɩɹɬɟɧɤɨ Ⱥ.ȼ., ɑɟɪɟɧɧɵɯ ɘ.ɇ. Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ

ɦɟɬɨɞɵ ɜ ɷɤɨɧɨɦɢɤɟ. - 3-ɟ ɢɡɞ. – Ɇ.: Ⱦɂɋ, 2001. – 368 ɫ. 40.

ɂɜɚɳɟɧɤɨ Ⱥ.ȼ., ɋɵɩɱɟɧɤɨ Ɋ.ɉ. Ɉɫɧɨɜɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɥɨɠɧɵɯ

ɫɢɫɬɟɦ ɧɚ ɗȼɆ: ɍɱɟɛɧɢɤ. – Ʌ.: Ʌȼȼɂɍɋ, 1988. – 272 ɫ. 41.

Ʉɚɪɩɟɥɟɜɢɱ Ɏ.ɂ., ɋɚɞɨɜɫɤɢɣ Ʌ.ȿ. ɗɥɟɦɟɧɬɵ ɥɢɧɟɣɧɨɣ ɚɥɝɟɛɪɵ ɢ

ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. – Ɇ.: Ɏɢɡɦɚɬɝɢɡ, 1963. – 276 ɫ. 42.

Ʉɜɟɣɞ ɗ. Ⱥɧɚɥɢɡ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. ɉɟɪ. ɫ ɚɧɝɥ. ɉɨɞ ɪɟɞ. ɂ.ɂ.

Ⱥɧɭɪɟɟɜɚ, ɂ.Ɇ. ȼɟɪɟɳɚɝɢɧɚ. – Ɇ.: ɂɡɞ-ɜɨ «ɋɨɜɟɬɫɤɨɟ ɪɚɞɢɨ», 1969. – 520 ɫ. 43.

Ʉɨɛɟɥɟɜ ɇ.Ȼ. Ɉɫɧɨɜɵ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɥɨɠɧɵɯ

ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɫɢɫɬɟɦ: ɍɱɟɛ. ɉɨɫɨɛɢɟ. – Ɇ.: Ⱦɟɥɨ, 2003. – 336 ɫ. 44.

Ʉɨɛɟɥɟɜ ɇ.Ȼ. ɉɪɚɤɬɢɤɚ ɩɪɢɦɟɧɟɧɢɹ ɷɤɨɧɨɦɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ

ɦɨɞɟɥɟɣ. – Ɇ.: Ɏɢɧɫɬɚɬɢɧɮɨɪɦ, 2000. – 246 ɫ. 45.

Ʉɨɤɫ Ⱦ.Ɋ., ɋɦɢɬ ɍ.Ʌ. Ɍɟɨɪɢɹ ɨɱɟɪɟɞɟɣ. – Ɇ.: Ɇɢɪ, 1966. – 218 ɫ.

46.

Ʉɨɪɚɛɥɢɧ Ɇ.Ⱥ. ɂɧɮɨɪɦɚɬɢɤɚ ɩɢɫɤɚ ɭɩɪɚɜɥɟɧɱɟɫɤɢɯ ɪɟɲɟɧɢɣ. – Ɇ.:

ɋɈɅɈɇ-ɉɪɟɫɫ, 2003. – 192 ɫ.: ɢɥ. 47. Ʉɨɪɨɬɟɰ ɂ.Ⱦ. ɉɪɨɛɥɟɦɚ ɫɨɡɞɚɧɢɹ ɪɵɧɤɚ ɪɚɛɨɱɟɣ ɫɢɥɵ ɜ ɯɨɞɟ ɪɟɮɨɪɦɢɪɨɜɚɧɢɹ Ɋɨɫɫɢɢ: ɋɨɰɢɚɥɶɧɨ-ɮɢɥɨɫɨɮɫɤɢɣ ɚɫɩɟɤɬ: Ⱥɜɬɨɪɟɮ. ɞɢɫɫ. … ɞɨɤɬ. ɮɢɥɨɫ. ɧɚɭɤ. Ɋɨɫɬɨɜ-ɧɚ-Ⱦɨɧɭ. 1995. 48.

Ʉɪɚɫɧɨɜ Ɇ.Ʌ. Ɉɛɵɤɧɨɜɟɧɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ. – Ɇ.:

ȼɵɫɲ. ɲɤ., 1983. – 128 ɫ. 49.

Ʉɪɚɫɫ Ɇ.ɋ., ɑɭɩɪɵɧɨɜ Ȼ.ɉ. Ɉɫɧɨɜɵ ɦɚɬɟɦɚɬɢɤɢ ɢ ɟɟ ɩɪɢɥɨɠɟɧɢɹ ɜ

ɷɤɨɧɨɦɢɱɟɫɤɨɦ ɨɛɪɚɡɨɜɚɧɢɢ. – Ɇ.: Ⱦɟɥɨ, 2003. – 688 ɫ. 50.

Ʉɪɭɝɥɢɧɫɤɢ Ⱦ., ɍɢɧɝɨɭ ɋ., ɒɟɮɟɪɞ Ⱦɠ. ɉɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɧɚ 115

Microsoft Visual C++ 6.0 ɞɥɹ ɩɪɨɮɟɫɫɢɨɧɚɥɨɜ. ɋɉɛ.: ɉɢɬɟɪ, Ɋɭɫɫɤɚɹ ɪɟɞɚɤɰɢɹ, 2001. – 864 ɫ. 51.Ʉɭɞɪɹɜɰɟɜ ȿ.Ɇ. GPSS World. Ɉɫɧɨɜɵ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɚɡɥɢɱɧɵɯ ɫɢɫɬɟɦ. – Ɇ.: ȾɆɄ ɉɪɟɫɫ, 2003. – 320 ɫ. 52.Ʌɚɛɫɤɟɪ Ʌ.Ƚ., Ȼɚɛɟɲɤɨ Ʌ.Ɉ. Ɍɟɨɪɢɹ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɫɮɟɪɟ. - Ɇ.: Ȼɚɧɤɢ ɢ ɛɢɪɠɢ. ɂɡɞ. Ɉɛɴɟɞɢɧɟɧɢɟ «ɘɇɂɌɂ, 1998. – 320 ɫ. 53.

Ʌɨɫɤɭɬɨɜ Ⱥ.ɘ., Ɇɢɯɚɣɥɨɜ Ⱥ.ɋ. ȼɜɟɞɟɧɢɟ ɜ ɫɢɧɟɪɝɟɬɢɤɭ. - Ɇ.:

ɇɚɭɤɚ, 1990. – 272 ɫ. 54.

Ɇɚɤɫɢɦɟɣ ɂ.ȼ. ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɧɚ ɗȼɆ. – Ɇ.: Ɋɚɞɢɨ

ɢ ɫɜɹɡɶ, 1988. – 323 ɫ. 55.

Ɇɚɪɤɨɜ Ⱥ.Ⱥ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ

ɩɪɨɰɟɫɫɨɜ: ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɂɡɞ-ɜɨ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ, 1999. 56.

Ɇɚɪɬɢɧ Ɏ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɧɚ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɦɚɲɢɧɚɯ. /ɉɟɪ. ɫ

ɚɧɝɥ. – Ɇ.: ɋɨɜ. ɪɚɞɢɨ, 1972. – 288 ɫ. 57.

Ɇɵɲɤɢɧɫ Ⱥ.Ⱦ. Ʌɟɤɰɢɢ ɩɨ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɟ: ɍɱɟɛ. ɩɨɫɨɛɢɟ. – 2-ɟ

ɢɡɞ., ɩɟɪɟɪɚɛ. – Ɇ.: ɇɚɭɤɚ, 1967. – 640 ɫ. 58.

ɇɟɣɥɨɪ Ɍ. Ɇɚɲɢɧɧɵɟ ɢɦɢɬɚɰɢɨɧɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɵ ɫ ɦɨɞɟɥɹɦɢ

ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɫɢɫɬɟɦ. – Ɇ.: Ɇɢɪ, 1975. – 500 ɫ. 59.

ɇɟɣɦɚɧ ɘ. ȼɜɨɞɧɵɣ ɤɭɪɫ ɬɟɨɪɢɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ

ɫɬɚɬɢɫɬɢɤɢ. – Ɇ.: ɇɚɭɤɚ, 1968. – 448 ɫ.: ɢɥ. 60.

ɇɢɜɨɪɨɠɤɢɧɚ

Ʌ.ɂ.,

ɇɢɜɨɪɨɠɤɢɧ

ȿ.Ɇ.,

ɒɭɯɦɢɧ

Ⱥ.Ƚ.

Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɜɟɞɟɧɢɹ ɧɚɫɟɥɟɧɢɹ ɧɚ ɪɵɧɤɟ ɬɪɭɞɚ ɤɪɭɩɧɨɝɨ ɝɨɪɨɞɚ: ɉɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɪɟɝɢɫɬɪɢɪɭɟɦɨɣ ɛɟɡɪɚɛɨɬɢɰɵ. – Ɇ.: Ɋɉɗɂ, 2001. – 55 ɫ. 61.

Ɉɱɤɨɜ ȼ.Ɏ. MATHCAD 7.0 Pro ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɢ ɢɧɠɟɧɟɪɨɜ. – Ɇ.:

Ʉɨɦɩɶɸɬɟɪ ɉɪɟɫɫ, 1998. – 384 ɫ. 62.

ɉɢɫɤɭɧɨɜ ɇ.ɋ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɢ ɢɧɬɟɝɪɚɥɶɧɨɟ ɢɫɱɢɫɥɟɧɢɟ ɞɥɹ

ɜɬɭɡɨɜ. Ɍ. 2. – Ɇ.: ɇɚɭɤɚ; Ɏɢɡɦɚɬɥɢɬ, 1985. – 560 ɫ. 63.

ɉɥɢɫ Ⱥ.ɂ., ɋɥɢɜɢɧɚ ɇ.Ⱥ. MathCad. Ɇɚɬɟɦɚɬɢɱɟɫɤɢɣ ɩɪɚɤɬɢɤɭɦ ɞɥɹ 116

ɢɧɠɟɧɟɪɨɜ ɢ ɷɤɨɧɨɦɢɫɬɨɜ: ɍɱɟɛ. ɩɨɫɨɛɢɟ. – 2-ɟ ɢɡɞ., ɩɟɪɟɪɚɛ. ɢ ɞɨɩ. – Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ, 2003. – 656 ɫ.: ɢɥ. 64.

ɉɥɢɫ Ⱥ.ɂ., ɋɥɢɜɢɧɚ ɇ.Ⱥ. MathCad. Ɇɚɬɟɦɚɬɢɱɟɫɤɢɣ ɩɪɚɤɬɢɤɭɦ. –

Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ, 1999. – 655 ɫ. 65.ɉɪɨɤɨɩɨɜ Ɏ.Ɍ. Ȼɟɡɪɚɛɨɬɢɰɚ ɢ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɣ ɩɨɥɢɬɢɤɢ ɬɪɭɞɚ ɜ ɩɟɪɟɯɨɞɧɨɣ ɷɤɨɧɨɦɢɤɟ Ɋɨɫɫɢɢ: Ⱥɜɬɨɪɟɮ. ɞɢɫɫ. … ɞɨɤɬ. ɷɤɨɧ. ɧɚɭɤ. Ɇ. 1999. 66.

Ɋɟɝɢɨɧɚɥɶɧɵɣ ɪɵɧɨɤ ɬɪɭɞɚ ɜ ɭɫɥɨɜɢɹɯ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɪɨɫɫɢɣɫɤɨɣ

ɷɤɨɧɨɦɢɤɢ (ɧɚ ɦɚɬɟɪɢɚɥɚɯ ɘɠɧɨɝɨ Ɏɟɞɟɪɚɥɶɧɨɝɨ ɨɤɪɭɝɚ) / ɉɨɞ ɪɟɞ. ɉ.ȼ. Ⱥɤɢɧɢɧɚ, ɋ.ȼ. ɋɬɟɩɚɧɨɜɨɣ. – ɋɬɚɜɪɨɩɨɥɶ: ɋɟɪɜɢɫɲɤɨɥɚ, 2002. – 368 ɫ. 67.

Ɋɨɛɟɪɬ ɂ.ȼ., ɋɚɦɨɣɥɟɧɤɨ ɉ.ɂ. ɂɧɮɨɪɦɚɰɢɨɧɧɵɟ ɬɟɯɧɨɥɨɝɢɢ ɜ

ɧɚɭɤɟ ɢ ɨɛɪɚɡɨɜɚɧɢɢ. - Ɇ.: ɇɚɭɤɚ, 1998. – 178 ɫ. 68.

Ɋɨɡɟɧɛɟɪɝ ɂ. Ƚ. Ȼɢɪɠɚ ɬɪɭɞɚ // ɂɬɨɝɢ. -14 ɫɟɧɬɹɛɪɹ 1999. – ɋ. 14.

69.

Ɋɭɤɨɜɨɞɫɬɜɨ ɩɨɥɶɡɨɜɚɬɟɥɹ ɩɨ GPSS World. /ɉɟɪɟɜɨɞ ɫ ɚɧɝɥɢɣɫɤɨɝɨ/.

– Ʉɚɡɚɧɶ: ɂɡɞ-ɜɨ «Ɇɚɫɬɟɪ Ʌɚɣɧ», 2002. – 384 ɫ. 70.

Ɋɵɠɢɤɨɜ

ɘ.ɂ.

ɂɦɢɬɚɰɢɨɧɧɨɟ

ɦɨɞɟɥɢɪɨɜɚɧɢɟ:

Ɍɟɨɪɢɹ

ɢ

ɡɚɞɚɱ

ɧɚ

ɬɟɯɧɨɥɨɝɢɢ. – ɋɉɛ.: Ʉɨɪɨɧɚ ɩɪɢɧɬ; Ɇ.: Ⱥɥɶɬɟɤɫ-Ⱥ, 2004. – 384 ɫ. 71.

Ɋɵɠɢɤɨɜ

ɘ.ɂ.

Ɋɟɲɟɧɢɟ

ɧɚɭɱɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ

ɩɟɪɫɨɧɚɥɶɧɨɦ ɤɨɦɩɶɸɬɟɪɟ. – ɋɉɛ.: Ʉɨɪɨɧɚ ɩɪɢɧɬ, 2000. – 272 ɫ. 72.

ɋɚɜɨɫɬɢɰɤɢɣ

ɘ.Ⱥ.

Ɉɰɟɧɤɚ

ɧɟɨɛɯɨɞɢɦɨɝɨ

ɱɢɫɥɚ

ɥɢɧɢɣ

ɨɛɫɥɭɠɢɜɚɧɢɹ ɩɪɢ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɨɦ ɨɛɨɫɧɨɜɚɧɢɢ ɦɧɨɝɨɤɚɧɚɥɶɧɵɯ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯ ɫɢɫɬɟɦ //ɗɤɨɧɨɦɢɤɚ ɢ ɩɪɨɢɡɜɨɞɫɬɜɨ. – 2002. - ʋ 10 – ɋ. 1621. 73.

ɋɚɥɦɚɧɨɜ Ɉ.ɇ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɷɤɨɧɨɦɢɤɚ ɫ ɩɪɢɦɟɧɟɧɢɟɦ Mathɫad

ɢ Excel. – ɋɉɛ.: Ȼɏȼ-ɉɟɬɟɪɛɭɪɝ, 2003. – 464 ɫ.: ɢɥ. 74.

ɋɚɦɭɷɥɶɫɨɧ ɉ. ɗɤɨɧɨɦɢɤɚ. Ɇ.: ȻɂɇɈɆ, 1997. – ɫ. 800.

75.

ɋɚɧɢɧ Ⱥ.Ʌ. ɋɬɪɭɤɬɭɪɵ ɢ ɯɚɨɫ – ɩɪɨɛɥɟɦɵ ɮɢɡɢɤɢ. Ʌ.: Ɂɧɚɧɢɟ, 1985.

– 32 ɫ. 76.

ɋɚɬɜɚɥɞɢɟɜ Ⱥ.Ⱥ. ɍɩɪɚɜɥɟɧɢɟ ɡɚɧɹɬɨɫɬɶɸ ɧɚɫɟɥɟɧɢɹ ɜ Ɋɟɫɩɭɛɥɢɤɟ

ɍɡɛɟɤɢɫɬɚɧ: Ⱥɜɬɨɪɟɮ. ɞɢɫɫ. … ɞɨɤɬ. ɷɤɨɧ. ɧɚɭɤ. ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝ. 1993. 117

77.

ɋɟɦɟɧɟɧɤɨ Ɇ.Ƚ. ȼɜɟɞɟɧɢɟ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ. Ɇ.:

ɋɈɅɈɇ-Ɋ, 2002. – 112 ɫ. 78.

ɋɟɦɟɧɱɢɧ

ȿ.Ⱥ.,

Ɂɚɣɰɟɜɚ

ɂ.ȼ.

ȼɟɪɨɹɬɧɨɫɬɧɚɹ

ɦɨɞɟɥɶ

ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ // ȼɟɫɬɧɢɤ ɋɬɚɜɪɨɩɨɥɶɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. – 2004. - ȼɵɩɭɫɤ 38. - ɋ. 58-60. 79.

ɋɟɦɟɧɱɢɧ ȿ.Ⱥ., Ɂɚɣɰɟɜɚ ɂ.ȼ. ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɪɚɛɨɬɵ ɛɢɪɠɢ

ɬɪɭɞɚ// Ɉɛɨɡɪɟɧɢɟ ɩɪɢɤɥɚɞɧɨɣ ɢ ɩɪɨɦɵɲɥɟɧɧɨɣ ɦɚɬɟɦɚɬɢɤɢ, 2005. - Ɍ.12. ɜ.2. – ɋ. 508 - 509. 80.

ɋɟɦɟɧɱɢɧ ȿ.Ⱥ., Ɂɚɣɰɟɜɚ ɂ.ȼ. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ

ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ // Ɉɛɨɡɪɟɧɢɟ ɩɪɢɤɥɚɞɧɨɣ ɢ ɩɪɨɦɵɲɥɟɧɧɨɣ ɦɚɬɟɦɚɬɢɤɢ. – 2004. - Ɍ.11. ɜ.2. - ɋ. 398-399. 81.

ɋɟɦɟɧɱɢɧ

ȿ.Ⱥ.,

Ɂɚɣɰɟɜɚ

ɂ.ȼ.

Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ

ɦɨɞɟɥɶ

ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɜɭɯɨɬɪɚɫɥɟɜɨɣ ɷɤɨɧɨɦɢɤɢ: ɋɛɨɪɧɢɤ ɬɪɭɞɨɜ ɬɪɟɬɶɟɣ ɪɟɝɢɨɧɚɥɶɧɨɣ ɧɚɭɱɧɨɣ ɤɨɧɮɟɪɟɧɰɢɢ. – ɋɬɚɜɪɨɩɨɥɶ: ɋɟɜɄɚɜȽɌɍ, 2003. – 239 ɫ. 82.

ɋɟɦɟɧɱɢɧ

ȿ.Ⱥ.,

Ɂɚɣɰɟɜɚ

ɂ.ȼ.

Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ

ɦɨɞɟɥɶ

ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɞɜɭɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ // ɗɤɨɧɨɦɢɤɚ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ. – 2004. – Ɍ. 40. ʋ 4. – ɋ. 137-139. 83.

ɋɟɦɟɧɱɢɧ

ȿ.Ⱥ.,

Ɂɚɣɰɟɜɚ

ɂ.ȼ.

Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ

ɦɨɞɟɥɶ

ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ // Ɉɛɨɡɪɟɧɢɟ ɩɪɢɤɥɚɞɧɨɣ ɢ ɩɪɨɦɵɲɥɟɧɧɨɣ ɦɚɬɟɦɚɬɢɤɢ, 2003. - Ɍ.10. ɜ.3. - ɋ.740-741. 84.

ɋɟɦɟɧɱɢɧ

ȿ.Ⱥ.,

Ɂɚɣɰɟɜɚ

ɂ.ȼ.

Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ

ɦɨɞɟɥɶ

ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɪɵɧɤɚ ɬɪɭɞɚ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɨɬɪɚɫɥɟɣ ɷɤɨɧɨɦɢɤɢ: Ɇɚɬɟɪɢɚɥɵ ȼɨɪɨɧɟɠɫɤɨɣ ɜɟɫɟɧɧɟɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɲɤɨɥɵ «ɉɨɧɬɪɹɝɢɧɫɤɢɟ ɱɬɟɧɢɹ – XIV». – ȼɨɪɨɧɟɠ: ȼɨɪɨɧɟɠɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ, 2003. – 177 ɫ. 85.

ɋɟɦɟɧɨɜ ȼ.ȼ., ɉɚɧɬɟɥɟɟɜ Ⱥ.ȼ., Ȼɨɪɬɚɧɨɜɫɤɢɣ Ⱥ.ɋ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ

ɬɟɨɪɢɹ ɭɩɪɚɜɥɟɧɢɹ ɜ ɩɪɢɦɟɪɚɯ ɢ ɡɚɞɚɱɚɯ. – Ɇ.: ɂɡɞ-ɜɨ ɆȺɂ, 1997. 261 ɫ.: ɢɥ., ɬɚɛɥ. 86.

ɋɢɦɨɧɨɜɢɱ ɋ.ȼ., ȿɜɫɟɟɜ Ƚ.Ⱥ., Ⱥɥɟɤɫɟɟɜ Ⱥ.Ƚ. ɋɩɟɰɢɚɥɶɧɚɹ

ɢɧɮɨɪɦɚɬɢɤɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ. – Ɇ.: ȺɋɌ-ɉɊȿɋɋ; ɂɧɮɨɪɤɨɦ-ɉɪɟɫɫ, 1999. – 118

480 ɫ. 87.

ɋɧɚɩɟɥɟɜ ɘ.Ɇ., ɋɬɚɪɨɫɟɥɶɫɤɢɣ ȼ.Ⱥ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɢ ɭɩɪɚɜɥɟɧɢɟ

ɜ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦɚɯ. – Ɇ.: ɋɨɜɟɬɫɤɨɟ ɪɚɞɢɨ, 1974. – 264 ɫ. 88.

ɋɨɜɟɬɨɜ Ȼ.ə. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦ. ɉɪɚɤɬɢɤɭɦ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ

ɞɥɹ ɜɭɡɨɜ/ Ȼ.ə. ɋɨɜɟɬɨɜ, ɋ.Ⱥ. əɤɨɜɥɟɜ. – 2-ɟ ɢɡɞ., ɩɟɪɟɪɚɛ. ɢ ɞɨɩ. – Ɇ.: ȼɵɫɲ. ɲɤ., 2003. – 295 ɫ.:ɢɥ. 89.

ɋɨɜɟɬɨɜ Ȼ.ə., əɤɨɜɥɟɜ ɋ.Ⱥ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦ: ɭɱɟɛɧɢɤ ɞɥɹ

ɜɭɡɨɜ. – Ɇ.: ȼɵɫɲ. ɲɤ., 2001. – 395 ɫ. 90.

Ɍɨɦɚɲɟɜɫɤɢɣ ȼ.ɇ., ɀɞɚɧɨɜɚ ȿ.Ƚ. ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɜ

ɫɪɟɞɟ GPSS. – Ɇ.: Ȼɟɫɬɫɟɥɥɟɪ, 2003. – 416 ɫ. 91.

Ɍɭɬɭɛɚɥɢɧ ȼ.ɇ. Ɍɟɨɪɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɫɥɭɱɚɣɧɵɯ ɩɪɨɰɟɫɫɨɜ: ɍɱɟɛ.

ɉɨɫɨɛɢɟ. – Ɇ.: ɂɡɞ-ɜɨ ɆȽɍ, 1992. – 400 ɫ. 92.

Ɍɸɪɢɧ ɘ.ɇ., Ɇɚɤɚɪɨɜ Ⱥ.Ⱥ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɞɚɧɧɵɯ ɧɚ

ɤɨɦɩɶɸɬɟɪɟ. – Ɇ.: ɂɧɮɚ-Ɇ, 1998. – 528 ɫ. 93.

ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɨ GPSS World. /ɉɟɪɟɜɨɞ ɫ ɚɧɝɥɢɣɫɤɨɝɨ/. - Ʉɚɡɚɧɶ:

ɂɡɞ-ɜɨ «Ɇɚɫɬɟɪ Ʌɚɣɧ», 2002. – 270 ɫ. 94.

Ɏɚɞɞɟɟɜ Ⱦ.Ʉ., Ɏɚɞɞɟɟɜɚ ȼ.ɇ. ȼɵɱɢɫɥɢɬɟɥɶɧɵɟ ɦɟɬɨɞɵ ɥɢɧɟɣɧɨɣ

ɚɥɝɟɛɪɵ. – 2-ɟ ɢɡɞ., ɞɨɩ. – Ɇ.: ɎɂɁɆȺɌȽɂɁ, 1963. – 736 ɫ. 95.

ɏɚɪɜɟɣ Ƚ. Excel 97 ɞɥɹ Windows ɞɥɹ «ɱɚɣɧɢɤɨɜ» / ɉɟɪ. ɫ ɚɧɝɥ. – Ɇ.:

ɂɡɞɚɬ. Ⱦɨɦ «ȼɢɥɶɹɦɫ», 2000. – 386 ɫ. 96.

ɒɚɩɨɬ Ⱦ.ȼ., Ʉɚɪɛɨɜɫɤɢɣ ɂ.Ʉ., Ʌɭɤɚɰɤɢɣ Ⱥ.Ɇ., Ɏɟɞɨɪɨɜɚ Ƚ.ȼ.

ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɷɤɨɧɨɦɢɱɟɫɤɨɝɨ ɩɨɜɟɞɟɧɢɹ ɩɪɨɢɡɜɨɞɢɬɟɥɟɣ ɬɨɜɚɪɨɜ ɢ ɭɫɥɭɝ // ɗɤɨɧɨɦɢɤɚ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ. - 2004. Ɍɨɦ 40. ʋ 3. - ɋ. 88-102. 97.

ɒɟɜɰɨɜ Ƚ.ɋ. Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ: ɬɟɨɪɢɹ ɢ ɩɪɢɤɥɚɞɧɵɟ ɚɫɩɟɤɬɵ:

ɍɱɟɛ. ɩɨɫɨɛɢɟ. – Ɇ.: Ɏɢɧɚɧɫɵ ɢ ɫɬɚɬɢɫɬɢɤɚ, 2003. – 576 ɫ. 98.

ɒɪɚɣɛɟɪ Ƚ.Ⱦɠ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɧɚ GPSS.- Ɇ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ,

1980. – 592 ɫ. 99.

ɗɤɨɧɨɦɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɢ ɩɪɢɤɥɚɞɧɵɟ ɦɨɞɟɥɢ / ɉɨɞ

ɪɟɞ. ȼ.ȼ. Ɏɟɞɨɫɟɟɜɚ. - Ɇ.: ɘɇɂɌɂ, 1999. – 391 ɫ. 100. ɗɫɤɟɪɨɜ Ⱦ.Ȼ. ɋɨɰɢɚɥɶɧɨ - ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɩɪɨɛɥɟɦɵ ɮɨɪɦɢɪɨɜɚɧɢɹ 119

ɪɵɧɤɚ ɬɪɭɞɚ ɢ ɭɩɪɚɜɥɟɧɢɹ ɡɚɧɹɬɨɫɬɶɸ ɜ ɞɟɩɪɟɫɫɢɜɧɨ-ɬɪɭɞɧɨɢɡɛɵɬɨɱɧɨɦ ɪɟɝɢɨɧɟ (ɧɚ ɩɪɢɦɟɪɟ Ⱦɚɝɟɫɬɚɧɚ): Ⱥɜɬɨɪɟɮ. ɞɢɫɫ. … ɞɨɤɬ. ɷɤɨɧ. ɧɚɭɤ. ɋɚɧɤɬɉɟɬɟɪɛɭɪɝ. 1999. 101. ɘɮɟɪɟɜɚ Ʌ.ȿ. Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɮɨɪɦɢɪɨɜɚɧɢɹ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɬɪɭɞɨɜɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɜ ɭɫɥɨɜɢɹɯ ɪɵɧɤɚ ɬɪɭɞɚ (ɧɚ ɩɪɢɦɟɪɟ ȼɨɫɬɨɱɧɨɣ ɋɢɛɢɪɢ ɢ Ⱦɚɥɶɧɟɝɨ ȼɨɫɬɨɤɚ): Ⱥɜɬɨɪɟɮ. ɞɢɫɫ. … ɞɨɤɬ. ɷɤɨɧ. ɧɚɭɤ. Ɇ. 1992.

120

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Ɉɬɞɟɥɵ ɛɢɪɠɢ ɬɪɭɞɚ

Ȼɢɪɠɚ ɬɪɭɞɚ

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Ȝ2

ɇ1 ɋ1

ȝ1 ɇ2

124

ɋ2

ȝ2

Q-ɫɯɟɦɚ ɛɢɪɠɢ ɬɪɭɞɚ

ɇ5

ɇ4

ɇ3

Ʉ

ȝ4

Ɉɛ

ȝ5

Ɋ

ȝ3

ɉɪɢɥɨɠɟɧɢɟ Ƚ Ʉɨɦɩɥɟɤɫ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ ɜ ɫɢɫɬɟɦɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GPSS World

Ȼɥɨɤ-ɞɢɚɝɪɚɦɦɚ ɦɨɞɟɥɢ ɛɢɪɠɢ ɬɪɭɞɚ

Ʌɢɫɬɢɧɝ ɦɨɞɭɥɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɛɢɪɠɢ ɬɪɭɞɚ ɧɚ ɹɡɵɤɟ GPSS World ; Ɉɩɪɟɞɟɥɟɧɢɟ ɬɚɛɥɢɰ VrSp1 Table M1,10,5,5 VrSp2 Table M1,10,5,5 VrKon Table M1,10,5,5 VrOb Table M1,10,5,5 VrRab Table M1,10,5,5 ;Ɉɩɪɟɞɟɥɟɧɢɟ ɮɭɧɤɰɢɢ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Post FUNCTION RN1,D7 .4,1/.5,2/.6,3/.7,4/.8,5/.9,6/1,8 ;Ɂɚɞɚɧɢɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ VrMod EQU 480 ; Ɉɩɢɫɚɧɢɟ ɚɪɢɮɦɟɬɢɱɟɫɤɢɯ ɜɵɪɚɠɟɧɢɣ ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Sp1 VerObrSp1 FVARIABLE N$ObrZapSp1/N$KolZap ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Sp2 VerObrSp2 FVARIABLE N$ObrZapSp2/N$Met2 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Rab VerObrRab FVARIABLE N$ObrZapRab/N$Met4 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Kon VerObrKon FVARIABLE N$ObrZapKon/N$Met5 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Ob VerObrOb FVARIABLE N$ObrZapOb/N$Met6 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ VerBirga FVARIABLE (V$VerObrSp1+V$VerObrSp2+V$VerObrRab+V$VerObrKon+V$VerObrOb)/5 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɬɪɟɛɨɜɚɧɢɹ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ VOtk FVARIABLE 1-X$VerBirga ;ȼɟɪɨɹɬɧɨɫɬɶ ɛɟɡɨɬɤɚɡɧɨɣ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ VerOtk FVARIABLE (AC1-X$VOtk)/AC1 ;ɋɟɝɦɟɧɬ ɢɦɢɬɚɰɢɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Sp1 KolZap GENERATE FN$Post ; ɉɨɫɬɭɩɥɟɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ Met1 QUEUE SpQ1 ; ȼɫɬɚɬɶ ɜ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Sp1 SEIZE Sp1 ; Ɂɚɧɹɬɶ ɨɬɞɟɥ Sp1 DEPART SpQ1 ; ɉɨɤɢɧɭɬɶ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Sp1 ADVANCE (Exponential(2,0,5)) ; Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɟ Sp1 RELEASE Sp1 ; Ɉɫɜɨɛɨɞɢɬɶ Sp1 ObrZapSp1 TABULATE VrSp1 ; Ⱦɚɧɧɵɟ ɨɛ ɨɬɞɟɥɟ Sp1 ɜ ɬɚɛɥɢɰɭ ;ɋɟɝɦɟɧɬ ɢɦɢɬɚɰɢɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Sp2 TRANSFER .73,Met2,Met7 ; Ɉɛɫɥɭɠɟɧɧɵɟ ɜ ɨɬɞɟɥɟ Sp2 KolZapVtor GENERATE (Exponential(3,0,10)) ; ɉɨɫɬɭɩɥɟɧɢɟ ɬɪɟɛɨɜɚɧɢɣ ɨɬ ɛɟɡɪɚɛɨɬɧɵɯ Met2 QUEUE SpQ2 ; ȼɫɬɚɬɶ ɜ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Sp2 SEIZE Sp2 ; Ɂɚɧɹɬɶ ɨɬɞɟɥ Sp2 DEPART SpQ2 ; ɉɨɤɢɧɭɬɶ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Sp2 ADVANCE 7,3 ; Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɟ Sp2 RELEASE Sp2 ; Ɉɫɜɨɛɨɞɢɬɶ Sp2 ObrZapSp2 TABULATE VrSp2 ; Ⱦɚɧɧɵɟ ɨɛ ɨɬɞɟɥɟ Sp2 ɜ ɬɚɛɥɢɰɭ TRANSFER 0.63,Met3,Met4 ; ɍɯɨɞ ɢɡ ɨɬɞɟɥɚ Met3 TRANSFER 0.1,Met5,Met6 ; ɍɯɨɞ ɢɡ ɨɬɞɟɥɚ ;ɋɟɝɦɟɧɬ ɢɦɢɬɚɰɢɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Rab Met4 QUEUE RabQ ; ȼɫɬɚɬɶ ɜ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Rab SEIZE Rab ; Ɂɚɧɹɬɶ ɨɬɞɟɥ ɨɬɞɟɥ Rab DEPART RabQ ; ɉɨɤɢɧɭɬɶ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Rab ADVANCE 5,3 ;Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɟ Rab RELEASE Rab ; Ɉɫɜɨɛɨɞɢɬɶ Rab ObrZapRab TABULATE VrRab ; Ⱦɚɧɧɵɟ ɨɛ ɨɬɞɟɥɟ Rab TRANSFER 0.3,Met2,Met7 ; ɍɯɨɞ ɢɡ ɨɬɞɟɥɚ Rab ;ɋɟɝɦɟɧɬ ɢɦɢɬɚɰɢɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Ps Met5 QUEUE KonQ ; ȼɫɬɚɬɶ ɜ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Kon SEIZE Kon ; Ɂɚɧɹɬɶ ɨɬɞɟɥ ɨɬɞɟɥ Kon DEPART KonQ ; ɉɨɤɢɧɭɬɶ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Kon ADVANCE 5,3 ; Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɟ Kon

126

Kon ; Ɉɫɜɨɛɨɞɢɬɶ Kon TABULATE VrKon ; Ⱦɚɧɧɵɟ ɨɛ ɨɬɞɟɥɟ Kon TRANSFER 0.1,Met2,Met7 ; ɍɯɨɞ ɢɡ ɨɬɞɟɥɚ Kon ;ɋɟɝɦɟɧɬ ɢɦɢɬɚɰɢɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɜ ɨɬɞɟɥɟ Ob Met6 QUEUE ObQ ; ȼɫɬɚɬɶ ɜ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Ob SEIZE Ob ; Ɂɚɧɹɬɶ ɨɬɞɟɥ ɨɬɞɟɥ Ob DEPART ObQ ; ɉɨɤɢɧɭɬɶ ɨɱɟɪɟɞɶ ɜ ɨɬɞɟɥ Ob ADVANCE 5,3 ; Ɉɛɫɥɭɠɢɜɚɧɢɟ ɜ ɨɬɞɟɥɟ Ob RELEASE Ob ; Ɉɫɜɨɛɨɞɢɬɶ Ob ObrZapOb TABULATE VrOb ; Ⱦɚɧɧɵɟ ɨɛ ɨɬɞɟɥɟ Ob TRANSFER 0.1,Met2,Met7 ; ɍɯɨɞ ɢɡ ɨɬɞɟɥɚ Ob Met7 TERMINATE ; Ɉɛɫɥɭɠɟɧɧɵɟ ɬɪɟɛɨɜɚɧɢɹ ;ɋɟɝɦɟɧɬ ɡɚɞɚɧɢɹ ɜɪɟɦɟɧɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ GENERATE VrMod SAVEVALUE VerObrSp1,V$VerObrSp1 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥɟ Sp1 SAVEVALUE VerObrSp2,V$VerObrSp2 ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥɟ Sp2 SAVEVALUE VerObrRab,V$VerObrRab ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥɟ Rab SAVEVALUE VerObrKon,V$VerObrKon ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥɟ Kon SAVEVALUE VerObrOb,V$VerObrOb ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɜ ɨɬɞɟɥɟ Ob SAVEVALUE VerBirga,V$VerBirga ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ SAVEVALUE VOtk,V$VOtk ;ȼɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɜ ɨɛɫɥɭɠɢɜɚɧɢɹ ɬɪɟɛɨɜɚɧɢɹ ɧɚ ɛɢɪɠɟ ɬɪɭɞɚ SAVEVALUE VerOtk,V$VerOtk ;ȼɟɪɨɹɬɧɨɫɬɶ ɛɟɡɨɬɤɚɡɧɨɣ ɪɚɛɨɬɵ ɛɢɪɠɢ ɬɪɭɞɚ TERMINATE 1 RELEASE

ObrZapKon

127

Ʌɢɫɬɢɧɝ ɫɬɚɧɞɚɪɬɧɨɝɨ ɨɬɱɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚ ʋ 1 START TIME 0.000

END TIME 480.000

NAME INTZAP KOLZAP KOLZAPVTOR KON KONQ MET1 MET2 MET3 MET4 MET5 MET6 MET7 OB OBQ OBRZAPKON OBRZAPOB OBRZAPRAB OBRZAPSP1 OBRZAPSP2 POST RAB RABQ SP1 SP2 SPQ1 SPQ2 VERBIRGA VEROBRKON VEROBROB VEROBRRAB VEROBRSP1 VEROBRSP2 VEROTK VOTK VRKON VRMOD VROB VRRAB VRSP1 VRSP2

LABEL KOLZAP MET1

OBRZAPSP1 KOLZAPVTOR MET2

LOC 1 2 3 4 5 6 7 8 9 10 11 12

BLOCKS 49

FACILITIES 5

STORAGES 0

VALUE 5.000 1.000 9.000 10023.000 10022.000 2.000 10.000 17.000 18.000 25.000 32.000 39.000 10025.000 10024.000 30.000 37.000 23.000 7.000 15.000 10005.000 10021.000 10020.000 10017.000 10019.000 10016.000 10018.000 10013.000 10011.000 10012.000 10010.000 10008.000 10009.000 10015.000 10014.000 10002.000 480.000 10003.000 10004.000 10000.000 10001.000

BLOCK TYPE GENERATE QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER GENERATE QUEUE SEIZE DEPART

ENTRY COUNT CURRENT COUNT RETRY 132 0 0 132 55 0 77 0 0 77 0 0 77 1 0 76 0 0 76 0 0 76 0 0 47 0 0 123 52 0 71 0 0 71 0 0

128

OBRZAPSP2 MET3 MET4

OBRZAPRAB MET5

OBRZAPKON MET6

OBRZAPOB MET7

FACILITY DELAY SP1 55 SP2 52 RAB 0 KON 0 OB 0

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

ADVANCE RELEASE TABULATE TRANSFER TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER TERMINATE GENERATE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE TERMINATE

ENTRIES

UTIL.

71 70 70 70 28 42 42 42 42 42 42 42 25 25 25 25 25 25 25 3 3 3 3 3 3 3 70 1 1 1 1 1 1 1 1 1 1

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

AVE. TIME AVAIL. OWNER PEND INTER RETRY

77

0.977

6.091

1

106

0

0

0

71

0.986

6.667

1

64

0

0

0

42

0.416

4.751

1

0

0

0

0

25

0.249

4.787

1

0

0

0

0

3

0.036

5.804

1

0

0

0

0

QUEUE RETRY SPQ1 SPQ2 RABQ KONQ OBQ

MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME

TABLE CUM.%

MEAN

55 52 1 1 1

55 52 0 0 0

132 123 42 25 3

3 1 39 22 3

STD.DEV.

29.185 29.436 0.015 0.007 0.000

RANGE

129

106.126 114.872 0.170 0.135 0.000

AVE.(-0) 108.594 115.814 2.385 1.128 0.000

RETRY FREQUENCY

0 0 0 0 0

VRSP1

94.140

68.383

0 _

-

10.000

13

10.000

-

15.000

3

15.000

-

20.000

2

20.000

-

25.000

5

25.000

-

_

-

10.000

1

10.000

-

15.000

2

15.000

-

20.000

1

20.000

-

25.000

1

25.000

-

20.000

-

25.000

-

_

25.000

-

_

10.000

-

15.000

2

15.000

-

20.000

1

20.000

-

25.000

0

25.000

-

17.11 21.05 23.68 30.26 100.00 VRSP2

168.498

_

53

107.424

0

1.43 4.29 5.71 7.14 100.00 VRKON

180.642

_

65

103.714

0 25.000

1

4.00 100.00 VROB

110.177

100.00 VRRAB

173.702

24

47.936

0 3

112.765

0

4.76 7.14 7.14 _

39

100.00

SAVEVALUE VEROBRSP1 VEROBRSP2 VEROBRRAB VEROBRKON VEROBROB VERBIRGA VOTK VEROTK

FEC XN 181 106 64 182 183

PRI 0 0 0 0 0

RETRY 0 0 0 0 0 0 0 0

BDT 482.000 482.635 483.707 493.155 960.000

VALUE 0.576 0.569 1.000 1.000 1.000 0.829 0.171 1.000

ASSEM 181 106 64 182 183

CURRENT 0 5 13 0 0

130

NEXT 1 6 14 9 40

PARAMETER

VALUE

Ʌɢɫɬɢɧɝ ɫɬɚɧɞɚɪɬɧɨɝɨ ɨɬɱɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚ ʋ 2 START TIME 0.000

END TIME 480.000

NAME INTZAP KOLZAP KOLZAPVTOR KON KONQ MET1 MET2 MET3 MET4 MET5 MET6 MET7 OB OBQ OBRZAPKON OBRZAPOB OBRZAPRAB OBRZAPSP1 OBRZAPSP2 POST RAB RABQ SP1 SP2 SPQ1 SPQ2 VERBIRGA VEROBRKON VEROBROB VEROBRRAB VEROBRSP1 VEROBRSP2 VEROTK VOTK VRKON VRMOD VROB VRRAB VRSP1 VRSP2

LABEL KOLZAP MET1

OBRZAPSP1 KOLZAPVTOR MET2

LOC 1 2 3 4 5 6 7 8 9 10 11

BLOCKS 49

FACILITIES 5

STORAGES 0

VALUE 5.000 1.000 9.000 10023.000 10022.000 2.000 10.000 17.000 18.000 25.000 32.000 39.000 10025.000 10024.000 30.000 37.000 23.000 7.000 15.000 10005.000 10021.000 10020.000 10017.000 10019.000 10016.000 10018.000 10013.000 10011.000 10012.000 10010.000 10008.000 10009.000 10015.000 10014.000 10002.000 480.000 10003.000 10004.000 10000.000 10001.000

BLOCK TYPE GENERATE QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER GENERATE QUEUE SEIZE

ENTRY COUNT CURRENT COUNT RETRY 146 0 0 146 78 0 68 0 0 68 0 0 68 1 0 67 0 0 67 0 0 67 0 0 47 0 0 126 45 0 81 0 0

131

OBRZAPSP2 MET3 MET4

OBRZAPRAB MET5

OBRZAPKON MET6

OBRZAPOB MET7

FACILITY DELAY SP1 78 SP2 45 RAB 0 KON 1 OB 0

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

DEPART ADVANCE RELEASE TABULATE TRANSFER TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER TERMINATE GENERATE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE TERMINATE

ENTRIES

UTIL.

81 81 80 80 80 31 49 49 49 49 49 49 49 27 26 26 26 25 25 25 4 4 4 4 4 4 4 66 1 1 1 1 1 1 1 1 1 1

0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

AVE. TIME AVAIL. OWNER PEND INTER RETRY

68

0.982

6.929

1

94

0

0

0

81

0.984

5.830

1

130

0

0

0

49

0.501

4.903

1

0

0

0

0

26

0.280

5.176

1

123

0

0

0

4

0.041

4.925

1

0

0

0

0

QUEUE RETRY SPQ1 SPQ2 RABQ KONQ OBQ

MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME

TABLE

MEAN

79 46 1 1 1

78 45 0 1 0

146 126 49 27 4

3 1 38 21 4

STD.DEV.

37.949 22.929 0.039 0.023 0.000

RANGE

132

124.763 87.347 0.381 0.417 0.000

AVE.(-0) 127.381 88.046 1.699 1.876 0.000

RETRY FREQUENCY

0 0 0 0 0

CUM.% VRSP1

119.159

81.888

0 _

-

10.000

5

10.000

-

15.000

1

15.000

-

20.000

5

20.000

-

25.000

5

25.000

-

_

-

10.000

1

10.000

-

15.000

2

15.000

-

20.000

1

20.000

-

25.000

2

25.000

-

20.000

-

25.000

-

_

25.000

-

_

15.000

-

20.000

2

20.000

-

25.000

2

25.000

-

7.46 8.96 16.42 23.88 100.00 VRSP2

145.891

_

51

102.304

0

1.25 3.75 5.00 7.50 100.00 VRKON

147.152

_

74

89.840

0 25.000

1

4.00 100.00 VROB

141.769

100.00 VRRAB

147.788

24

86.775

0 4

104.615

0

4.08 8.16 _

45

100.00

SAVEVALUE VEROBRSP1 VEROBRSP2 VEROBRRAB VEROBRKON VEROBROB VERBIRGA VOTK VEROTK

FEC XN 123 195 94 130 196 197

PRI 0 0 0 0 0 0

RETRY 0 0 0 0 0 0 0 0

BDT 481.256 482.000 484.286 484.453 493.155 960.000

VALUE 0.459 0.635 1.000 0.926 1.000 0.804 0.196 1.000

ASSEM 123 195 94 130 196 197

CURRENT 28 0 5 13 0 0

133

NEXT 29 1 6 14 9 40

PARAMETER

VALUE

Ʌɢɫɬɢɧɝ ɫɬɚɧɞɚɪɬɧɨɝɨ ɨɬɱɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚ ʋ 3 START TIME 0.000

END TIME 480.000

NAME KOLZAP KOLZAPVTOR KON KONQ MET1 MET2 MET3 MET4 MET5 MET6 MET7 OB OBQ OBRZAPKON OBRZAPOB OBRZAPRAB OBRZAPSP1 OBRZAPSP2 POST RAB RABQ SP1 SP2 SPQ1 SPQ2 VERBIRGA VEROBRKON VEROBROB VEROBRRAB VEROBRSP1 VEROBRSP2 VEROTK VOTK VRKON VRMOD VROB VRRAB VRSP1 VRSP2

LABEL KOLZAP MET1

OBRZAPSP1 KOLZAPVTOR MET2

LOC 1 2 3 4 5 6 7 8 9 10 11 12 13 14

BLOCKS 49

FACILITIES 5

STORAGES 0

VALUE 1.000 9.000 10022.000 10021.000 2.000 10.000 17.000 18.000 25.000 32.000 39.000 10024.000 10023.000 30.000 37.000 23.000 7.000 15.000 10005.000 10020.000 10019.000 10016.000 10018.000 10015.000 10017.000 10012.000 10010.000 10011.000 10009.000 10007.000 10008.000 10014.000 10013.000 10002.000 480.000 10003.000 10004.000 10000.000 10001.000

BLOCK TYPE GENERATE QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER GENERATE QUEUE SEIZE DEPART ADVANCE RELEASE

ENTRY COUNT CURRENT COUNT RETRY 154 0 0 154 91 0 63 0 0 63 0 0 63 1 0 62 0 0 62 0 0 62 0 0 47 0 0 120 39 0 81 0 0 81 0 0 81 1 0 80 0 0

134

OBRZAPSP2 MET3 MET4

OBRZAPRAB MET5

OBRZAPKON MET6

OBRZAPOB MET7

FACILITY DELAY SP1 91 SP2 39 RAB 0 KON 0 OB 0

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

TABULATE TRANSFER TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER TERMINATE GENERATE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE TERMINATE

ENTRIES

UTIL.

80 80 32 48 48 48 48 48 48 48 30 30 30 30 30 30 30 2 2 2 2 2 2 2 69 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

AVE. TIME AVAIL. OWNER PEND INTER RETRY

63

0.998

7.603

1

86

0

0

0

81

0.982

5.822

1

9

0

0

0

48

0.528

5.279

1

0

0

0

0

30

0.273

4.362

1

0

0

0

0

2

0.020

4.885

1

0

0

0

0

QUEUE RETRY SPQ1 SPQ2 RABQ KONQ OBQ

MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME

TABLE CUM.% VRSP1

MEAN

93 39 2 1 1

139.882

91 39 0 0 0

154 120 48 30 2

1 1 32 28 2

STD.DEV.

46.341 21.840 0.104 0.003 0.000

144.439 87.360 1.045 0.043 0.000

RANGE

AVE.(-0) 145.384 88.095 3.134 0.648 0.000

RETRY FREQUENCY

94.120

0 _

135

-

10.000

5

0 0 0 0 0

8.06 10.000

-

15.000

0

15.000

-

20.000

1

20.000

-

25.000

0

25.000

-

_

-

10.000

1

10.000

-

15.000

1

15.000

-

20.000

2

20.000

-

25.000

0

25.000

-

20.000

-

25.000

-

_

25.000

-

_

_

-

10.000

1

10.000

-

15.000

0

15.000

-

20.000

1

20.000

-

25.000

1

25.000

-

8.06 9.68 9.68 100.00 VRSP2

153.745

_

56

95.779

0

1.25 2.50 5.00 5.00 100.00 VRKON

141.951

_

76

81.271

0 25.000

1

3.33 100.00 VROB

132.048

100.00 VRRAB

171.300

29

96.653

0 2

104.693

0

2.08 2.08 4.17 6.25 _

45

100.00

SAVEVALUE VEROBRSP1 VEROBRSP2 VEROBRRAB VEROBRKON VEROBROB VERBIRGA VOTK VEROTK

RETRY 0 0 0 0 0 0 0 0

VALUE 0.403 0.667 1.000 1.000 1.000 0.814 0.186 1.000

CEC XN 203

PRI 0

M1 480.000

ASSEM 203

CURRENT 0

NEXT 1

PARAMETER

VALUE

FEC XN 86 9 204 205

PRI 0 0 0 0

BDT 480.510 482.352 493.155 960.000

ASSEM 86 9 204 205

CURRENT 5 13 0 0

NEXT 6 14 9 40

PARAMETER

VALUE

136

Ʌɢɫɬɢɧɝ ɫɬɚɧɞɚɪɬɧɨɝɨ ɨɬɱɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚ ʋ 4 START TIME 0.000

END TIME 480.000

NAME KOLZAP KOLZAPVTOR KON KONQ MET1 MET2 MET3 MET4 MET5 MET6 MET7 OB OBQ OBRZAPKON OBRZAPOB OBRZAPRAB OBRZAPSP1 OBRZAPSP2 POST RAB RABQ SP1 SP2 SPQ1 SPQ2 VERBIRGA VEROBRKON VEROBROB VEROBRRAB VEROBRSP1 VEROBRSP2 VEROTK VOTK VRKON VRMOD VROB VRRAB VRSP1 VRSP2

LABEL KOLZAP MET1

OBRZAPSP1 KOLZAPVTOR MET2

LOC 1 2 3 4 5 6 7 8 9 10 11 12 13

BLOCKS 49

FACILITIES 5

STORAGES 0

VALUE 1.000 9.000 10022.000 10021.000 2.000 10.000 17.000 18.000 25.000 32.000 39.000 10024.000 10023.000 30.000 37.000 23.000 7.000 15.000 10005.000 10020.000 10019.000 10016.000 10018.000 10015.000 10017.000 10012.000 10010.000 10011.000 10009.000 10007.000 10008.000 10014.000 10013.000 10002.000 480.000 10003.000 10004.000 10000.000 10001.000

BLOCK TYPE GENERATE QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER GENERATE QUEUE SEIZE DEPART ADVANCE

ENTRY COUNT CURRENT COUNT RETRY 162 0 0 162 106 0 56 0 0 56 0 0 56 1 0 55 0 0 55 0 0 55 0 0 47 0 0 116 47 0 69 0 0 69 0 0 69 1 0

137

OBRZAPSP2 MET3 MET4

OBRZAPRAB MET5

OBRZAPKON MET6

OBRZAPOB MET7

FACILITY DELAY SP1 106 SP2 47 RAB 0 KON 0 OB 0

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

RELEASE TABULATE TRANSFER TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER TERMINATE GENERATE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE TERMINATE

ENTRIES

UTIL.

68 68 68 23 45 45 45 45 44 44 44 22 22 22 22 22 22 22 1 1 1 1 1 1 1 53 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

AVE. TIME AVAIL. OWNER PEND INTER RETRY

56

0.998

8.554

1

76

0

0

0

69

0.972

6.763

1

41

0

0

0

45

0.511

5.450

1

134

0

0

0

22

0.229

4.988

1

0

0

0

0

1

0.014

6.948

1

0

0

0

0

QUEUE RETRY SPQ1 SPQ2 RABQ KONQ OBQ

MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME

TABLE CUM.% VRSP1

MEAN

107 48 1 1 1

106 47 0 0 0

168.477

162 116 45 22 1

1 2 32 21 1

STD.DEV.

56.344 23.414 0.045 0.001 0.000

RANGE

113.666

166.946 96.886 0.482 0.027 0.000

167.983 98.586 1.668 0.604 0.000

RETRY FREQUENCY 0

138

AVE.(-0) 0 0 0 0 0

_

-

10.000

5

10.000

-

15.000

0

15.000

-

20.000

0

20.000

-

25.000

1

25.000

-

_

-

10.000

2

10.000

-

15.000

1

15.000

-

20.000

2

20.000

-

25.000

0

25.000

-

20.000

-

25.000

-

_

25.000

-

_

_

-

10.000

1

10.000

-

15.000

0

15.000

-

20.000

1

20.000

-

25.000

1

25.000

-

9.09 9.09 9.09 10.91 100.00 VRSP2

164.711

_

49

108.769

0

2.94 4.41 7.35 7.35 100.00 VRKON

179.128

_

63

96.266

0 25.000

1

4.55 100.00 VROB

71.397

100.00 VRRAB

167.585

21

0.000

0 1

116.351

0

2.27 2.27 4.55 6.82 _

41

100.00

SAVEVALUE VEROBRSP1 VEROBRSP2 VEROBRRAB VEROBRKON VEROBROB VERBIRGA VOTK VEROTK

FEC XN 212 76 134 41 211 213

PRI 0 0 0 0 0 0

RETRY 0 0 0 0 0 0 0 0

BDT 481.000 483.433 483.806 488.656 493.155 960.000

VALUE 0.340 0.586 0.978 1.000 1.000 0.781 0.219 1.000

ASSEM 212 76 134 41 211 213

CURRENT 0 5 21 13 0 0

139

NEXT 1 6 22 14 9 40

PARAMETER

VALUE

Ʌɢɫɬɢɧɝ ɫɬɚɧɞɚɪɬɧɨɝɨ ɨɬɱɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚ ʋ 5 START TIME 0.000

END TIME 480.000

NAME KOLZAP KOLZAPVTOR KON KONQ MET1 MET2 MET3 MET4 MET5 MET6 MET7 OB OBQ OBRZAPKON OBRZAPOB OBRZAPRAB OBRZAPSP1 OBRZAPSP2 POST RAB RABQ SP1 SP2 SPQ1 SPQ2 VERBIRGA VEROBRKON VEROBROB VEROBRRAB VEROBRSP1 VEROBRSP2 VEROTK VOTK VRKON VRMOD VROB VRRAB VRSP1 VRSP2

LABEL KOLZAP MET1

OBRZAPSP1 KOLZAPVTOR MET2

LOC 1 2 3 4 5 6 7 8 9 10 11 12 13

BLOCKS 49

FACILITIES 5

STORAGES 0

VALUE 1.000 9.000 10022.000 10021.000 2.000 10.000 17.000 18.000 25.000 32.000 39.000 10024.000 10023.000 30.000 37.000 23.000 7.000 15.000 10005.000 10020.000 10019.000 10016.000 10018.000 10015.000 10017.000 10012.000 10010.000 10011.000 10009.000 10007.000 10008.000 10014.000 10013.000 10002.000 480.000 10003.000 10004.000 10000.000 10001.000

BLOCK TYPE GENERATE QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER GENERATE QUEUE SEIZE DEPART ADVANCE

ENTRY COUNT CURRENT COUNT RETRY 152 0 0 152 103 0 49 0 0 49 0 0 49 1 0 48 0 0 48 0 0 48 0 0 47 0 0 99 34 0 65 0 0 65 0 0 65 1 0

140

OBRZAPSP2 MET3 MET4

OBRZAPRAB MET5

OBRZAPKON MET6

OBRZAPOB MET7

FACILITY DELAY SP1 103 SP2 34 RAB 0 KON 0 OB 0

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

RELEASE TABULATE TRANSFER TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER QUEUE SEIZE DEPART ADVANCE RELEASE TABULATE TRANSFER TERMINATE GENERATE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE SAVEVALUE TERMINATE

ENTRIES

UTIL.

64 64 64 21 43 43 43 43 42 42 42 19 19 19 19 19 19 19 2 2 2 2 2 2 2 59 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

AVE. TIME AVAIL. OWNER PEND INTER RETRY

49

0.998

9.776

1

69

0

0

0

65

0.968

7.145

1

41

0

0

0

43

0.554

6.189

1

123

0

0

0

19

0.244

6.153

1

0

0

0

0

2

0.021

5.143

1

0

0

0

0

QUEUE RETRY SPQ1 SPQ2 RABQ KONQ OBQ

MAX CONT. ENTRY ENTRY(0) AVE.CONT. AVE.TIME

TABLE CUM.% VRSP1

MEAN

103 34 1 1 1

103 34 0 0 0

159.837

152 99 43 19 2

1 2 31 17 2

STD.DEV.

52.827 19.695 0.058 0.008 0.000

RANGE

116.551

166.824 95.492 0.650 0.208 0.000

167.928 97.461 2.330 1.977 0.000

RETRY FREQUENCY 0

141

AVE.(-0) 0 0 0 0 0

_

-

10.000

3

10.000

-

15.000

2

15.000

-

20.000

0

20.000

-

25.000

0

25.000

-

_

-

10.000

1

10.000

-

15.000

0

15.000

-

20.000

1

20.000

-

25.000

3

25.000

-

20.000

-

25.000

-

_

25.000

-

_

10.000

-

15.000

1

15.000

-

20.000

0

20.000

-

25.000

0

25.000

-

6.25 10.42 10.42 10.42 100.00 VRSP2

148.273

_

43

96.292

0

1.56 1.56 3.13 7.81 100.00 VRKON

146.674

_

59

92.281

0 25.000

1

5.26 100.00 VROB

241.957

100.00 VRRAB

153.460

18

111.999

0 2

98.959

0

2.38 2.38 2.38 _

41

100.00

SAVEVALUE VEROBRSP1 VEROBRSP2 VEROBRRAB VEROBRKON VEROBROB VERBIRGA VOTK VEROTK

FEC XN 41 69 123 201 202 203

PRI 0 0 0 0 0 0

RETRY 0 0 0 0 0 0 0 0

BDT 481.211 481.781 481.841 482.000 493.155 960.000

VALUE 0.316 0.646 0.977 1.000 1.000 0.788 0.212 1.000

ASSEM 41 69 123 201 202 203

CURRENT 13 5 21 0 0 0

142

NEXT 14 6 22 1 9 40

PARAMETER

VALUE

Математическое моделирование самоорганизующихся экономич. процессов(Диссертация)

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