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ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
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III. ɆȺɌȿɆȺɌɂɄȺ ȼ ɈɉɂɋȺɇɂɂ ɏȺɈɋȺ ɂ ɋɂɇȿɊȽȿɌɂɑȿɋɄɂɏ ɋɂɋɌȿɆ
ȿɋɌȿɋɌȼȿɇɇɈ-ɄɈɇɋɌɊɍɄɌɂȼɂɋɌɋɄɂɃ ɉɈȾɏɈȾ Ʉ ɆɈȾȿɅɂɊɈȼȺɇɂɘ
ɆɕɒɅȿɇɂə: ȾɂɇȺɆɂɑȿɋɄȺə ɆɈȾȿɅɖ ɉɊɈɐȿɋɋȺ
ɎɈɊɆɂɊɈȼȺɇɂə ɋɂɆȼɈɅȺ
1
ɑɟɪɧɚɜɫɤɢɣ Ⱦ.ɋ., 1ɓɟɩɟɬɨɜ Ⱦ.ɋ., 1ɑɟɪɧɚɜɫɤɚɹ Ɉ.Ⱦ., 2ɇɢɤɢɬɢɧ Ⱥ.ɉ.
1
Ɏɢɡɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ ɢɦ. ɉ.ɇ. Ʌɟɛɟɞɟɜɚ ɊȺɇ, Ɇɨɫɤɜɚ
2
ɂɧɫɬɢɬɭɬ Ɉɛɳɟɣ Ɏɢɡɢɤɢ ɊȺɇ, Ɇɨɫɤɜɚ
ȼ ɪɚɦɤɚɯ ɟɫɬɟɫɬɜɟɧɧɨ-ɤɨɧɫɬɪɭɤɬɢɜɢɫɬɫɤɨɝɨ ɩɨɞɯɨɞɚ ɤ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɨɧɰɟɩɰɢɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɮɨɪɦɚɥɶɧɨɝɨ ɧɟɣɪɨɧɚ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɹɟɬ ɩɪɨɫɥɟɠɢɜɚɬɶ ɞɢɧɚɦɢɤɭ ɜɫɟɯ
ɩɪɨɰɟɫɫɨɜ, ɝɞɟ ɭɱɚɫɬɜɭɟɬ ɧɟɣɪɨɧ. ɉɪɟɞɥɚɝɚɟɬɫɹ ɛɚɡɢɪɭɸɳɚɹɫɹ ɧɚ ɷɬɨɣ ɤɨɧɰɟɩɰɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ
ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɨɜ. ɂɫɫɥɟɞɭɟɬɫɹ ɞɢɧɚɦɢɤɚ ɤɨɧɤɭɪɟɧɬɧɨɣ ɛɨɪɶɛɵ ɜ ɩɪɨɰɟɫɫɨɪɟ ɥɨɤɚɥɢɡɚɰɢɢ;
ɩɨɤɚɡɚɧɨ, ɱɬɨ ɜɚɠɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ «ɩɨɥɭ-ɜɨɡɛɭɠɞɟɧɧɵɟ» ɫɨɫɬɨɹɧɢɹ ɧɟɣɪɨɧɨɜ ɢ ɢɯ ɭɫɬɨɣɱɢɜɨɫɬɶ. Ⱥɧɚɥɢɡɢɪɭɟɬɫɹ ɜɪɟɦɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɨɛɭɱɟɧɢɹ ɦɟɠɩɥɚɫɬɢɧɧɵɯ ɫɜɹɡɟɣ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɫɚɦɨɨɪɝɚɧɢɡɨɜɚɧɧɵɣ ɯɚɪɚɤɬɟɪ ɜɫɟɝɨ ɩɪɨɰɟɫɫɚ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɧɟɣɪɨɩɪɨɰɟɫɫɨɪ, ɦɨɞɟɥɶ, ɨɛɪɚɡ, ɫɢɦɜɨɥ, ɜɧɭɬɪɢ- ɢ ɦɟɠɩɥɚɫɬɢɧɧɵɟ ɫɜɹɡɢ, ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɹ.
ȼɜɟɞɟɧɢɟ
ɉɨɞɯɨɞɵ ɤ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɦɵɲɥɟɧɢɹ
ɜ ɫɨɜɪɟɦɟɧɧɨɣ ɤɨɝɧɢɬɢɜɧɨɣ ɧɚɭɤɟ ɜɟɫɶɦɚ
ɪɚɡɧɨɨɛɪɚɡɧɵ ([3,7,13]), ɧɨ ɜɫɟ ɨɧɢ, ɬɚɤ ɢɥɢ
ɢɧɚɱɟ, ɚɩɟɥɥɢɪɭɸɬ ɤ ɧɟɣɪɨɤɨɦɩɶɸɬɢɧɝɭ.
ȼɨɡɦɨɠɧɨɫɬɢ ɧɟɣɪɨɤɨɦɩɶɸɬɟɪɨɜ ɢ ɧɟɣɪɨɫɟɬɟɣ ɞɥɹ ɪɟɲɟɧɢɹ ɤɨɧɤɪɟɬɧɵɯ ɩɪɢɤɥɚɞɧɵɯ ɡɚɞɚɱ ɛɵɥɢ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɵ ɧɟɨɞɧɨɤɪɚɬɧɨ (ɫɦ. [2] ɢ ɫɫɵɥɤɢ ɬɚɦ ɠɟ), ɩɪɢɱɟɦ ɭɩɨɪ ɞɟɥɚɥɫɹ ɧɚ ɧɚɞɟɠɧɨɫɬɶ ɢ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɷɬɢɯ ɪɟɲɟɧɢɣ. ȼ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ
ɫɬɚɧɨɜɢɬɫɹ ɜɫɟ ɛɨɥɟɟ ɹɫɧɵɦ, ɱɬɨ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɢɦɟɧɧɨ ɱɟɥɨɜɟɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ ɬɚɤɨɣ ɩɨɞɯɨɞ ɧɟ ɜɩɨɥɧɟ ɚɞɟɤɜɚɬɟɧ.
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɱɟɥɨɜɟɤ, ɫɬɚɥɤɢɜɚɹɫɶ ɫ ɪɚɡɥɢɱɧɵɦɢ ɠɢɡɧɟɧɧɵɦɢ ɫɢɬɭɚɰɢɹɦɢ, ɞɨɥɠɟɧ
ɧɚɭɱɢɬɶɫɹ ɪɟɲɚɬɶ ɫɚɦɵɟ ɪɚɡɧɵɟ, ɜ ɬɨɦ
ɱɢɫɥɟ, ɧɟɤɨɪɪɟɤɬɧɨ ɩɨɫɬɚɜɥɟɧɧɵɟ ɡɚɞɚɱɢ,
ɧɚ ɩɟɪɜɵɣ ɩɥɚɧ ɜɵɯɨɞɢɬ ɩɪɨɛɥɟɦɚ ɚɞɚɩɬɚɰɢɨɧɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ. ɉɨɷɬɨɦɭ ɱɟɥɨɜɟɱɟɫɤɨɟ ɦɵɲɥɟɧɢɟ – ɧɟ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɨ, ɱɚɫɬɨ ɧɟɩɪɟɞɫɤɚɡɭɟɦɨ ɢ ɜɫɟɝɞɚ ɢɧɞɢɜɢɞɭɚɥɶɧɨ. Ɂɚɝɚɞɤɚ ɢɧɞɢɜɢɞɭɚɥɶɧɨɫɬɢ ɦɵɲɥɟɧɢɹ — ɨɞɢɧ ɢɡ ɨɫɧɨɜɧɵɯ «ɜɵɡɨɜɨɜ» (challenge) ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ.
ȼ ɫɜɨɢɯ ɪɚɛɨɬɚɯ [4–5] ɦɵ ɢɫɩɨɥɶɡɭɟɦ
ɬ.ɧ.
«ɟɫɬɟɫɬɜɟɧɧɨ-ɤɨɧɫɬɪɭɤɬɢɜɢɫɬcɤɢɣ»
ɩɨɞɯɨɞ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ ɞɢɧɚɦɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɢɧɮɨɪɦɚɰɢɢ (ȾɌɂ, [6]), ɬɟɨɪɢɢ ɪɚɫɩɨɡɧɚɜɚɧɢɹ, ɢ ɧɟɣɪɨɤɨɦɩɶɸɬɢɧɝɟ. Ɉɞɧɚɤɨ
ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɩɨɫɥɟɞɧɹɹ
ɫɨɫɬɚɜɥɹɸɳɚɹ ɧɚɦɢ ɩɨɧɢɦɚɟɬɫɹ ɜ ɫɦɵɫɥɟ,
ɨɬɥɢɱɧɨɦ ɨɬ ɫɬɚɧɞɚɪɬɧɨɝɨ ɩɨɞɯɨɞɚ, ɜ ɱɚɫɬɧɨɫɬɢ, ɤ ɩɨɧɹɬɢɸ «ɮɨɪɦɚɥɶɧɵɣ ɧɟɣɪɨɧ».
Ɇɵ ɢɫɩɨɥɶɡɭɟɦ ɤɨɧɰɟɩɰɢɸ ɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɮɨɪɦɚɥɶɧɨɝɨ ɧɟɣɪɨɧɚ, ɤɨɬɨɪɚɹ ɨɛɫɭɠɞɚɬɶɫɹ ɧɢɠɟ.
ȼ ɪɚɛɨɬɟ [5] ɛɵɥɢ ɢɫɫɥɟɞɨɜɚɧɵ ɨɫɧɨɜɧɵɟ ɩɪɢɧɰɢɩɵ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ ɫ ɩɨɡɢɰɢɣ ȾɌɂ ɢ ɛɵɥɨ ɩɪɟɞɥɨɠɟɧɨ ɨɩɪɟɞɟɥɟɧɢɟ
ɦɵɲɥɟɧɢɹ ɤɚɤ ɫɚɦɨɨɪɝɚɧɢɡɭɸɳɟɝɨɫɹ ɩɪɨɰɟɫɫɚ ɡɚɩɢɫɢ (ɜɨɫɩɪɢɹɬɢɹ), ɫɨɯɪɚɧɟɧɢɹ, ɨɛɪɚɛɨɬɤɢ, ɚ ɬɚɤɠɟ ɝɟɧɟɪɚɰɢɢ ɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɧɨɜɨɣ ɢɧɮɨɪɦɚɰɢɢ ɛɟɡ ɜɦɟɲɚɬɟɥɶɫɬɜɚ ɢɡɜɧɟ. Ʉɨɧɟɱɧɨɣ ɰɟɥɶɸ ɧɚɲɢɯ
ɢɫɫɥɟɞɨɜɚɧɢɣ ɹɜɥɹɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɦɵɫɥɢɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ ɫɜɹɡɚɧɧɵɯ ɧɟɣɪɨɩɪɨɰɟɫɫɨɪɨɜ, ɢɥɢ Ⱥɩɩɚɪɚɬɚ Ɇɵɲɥɟɧɢɹ (ȺɆ), ɤɨɬɨɪɚɹ ɛɵɥɚ ɛɵ
ɫɩɨɫɨɛɧɚ ɜɵɩɨɥɧɹɬɶ ɩɟɪɟɱɢɫɥɟɧɧɵɟ ɜɵɲɟ
ɮɭɧɤɰɢɢ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɦɵ ɧɟ ɩɵɬɚɟɦɫɹ
ɫɤɨɧɫɬɪɭɢɪɨɜɚɬɶ ɫɢɫɬɟɦɭ, ɤɨɬɨɪɚɹ ɜɵɩɨɥɧɹɥɚ ɛɵ ɪɹɞ ɡɚɞɚɱ ɥɭɱɲɟ, ɱɟɦ ɱɟɥɨɜɟɤ. Ɇɵ
ɩɵɬɚɟɦɫɹ ɩɨɧɹɬɶ, ɤɚɤ ɦɨɠɟɬ ɷɬɨ ɞɟɥɚɬɶ ɱɟɥɨɜɟɤ, ɢ ɤɚɤ ɦɨɠɧɨ ɷɬɨɬ ɩɪɨɰɟɫɫ ɢɦɢɬɢɪɨɜɚɬɶ.
ɑɪɟɡɜɵɱɚɣɧɨ ɜɚɠɧɭɸ ɪɨɥɶ ɜ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ ɫɪɟɞɫɬɜɚɦɢ
ɧɟɣɪɨɤɨɦɩɶɸ-ɬɢɧɝɚ ɢɝɪɚɸɬ ɩɨɧɹɬɢɹ ɨɛɪɚɡ
ɢ ɫɢɦɜɨɥ. ɉɨɧɹɬɢɟ «ɨɛɪɚɡ» ɨɬɧɨɫɢɬɫɹ ɤ ɩɚɪɚɞɢɝɦɟ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɩɚɦɹɬɢ ɢ ɫɜɹɡɚɧɨ
ɫ ɩɪɨɰɟɫɫɨɪɨɦ ɏɨɩɮɢɥɞɚ [11]. ɋɱɢɬɚɟɬɫɹ,
ɱɬɨ ɨɞɢɧ ɪɟɚɥɶɧɵɣ ɩɪɟɞɴɹɜɥɟɧɧɵɣ ɨɛɴɟɤɬ
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
ɩɪɢɜɨɞɢɬ ɤ ɜɨɡɛɭɠɞɟɧɢɸ ɦɧɨɝɢɯ m >> 1
ɧɟɣɪɨɧɨɜ. ɗɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɧɚɞɟɠɧɨɫɬɶ ɢ
ɚɫɫɨɰɢɚɬɢɜɧɨɫɬɶ ɩɚɦɹɬɢ.
ɉɨɧɹɬɢɟ «ɫɢɦɜɨɥ» ɨɬɧɨɫɢɬɫɹ ɤ ɩɚɪɚɞɢɝɦɟ ɤɨɧɰɟɩɬɭɚɥɶɧɨɣ ɩɚɦɹɬɢ ɢ ɫɜɹɡɵɜɚɟɬɫɹ ɫ
ɢɦɟɧɚɦɢ Ƚɪɨɫɫɛɟɪɝɚ [9] ɢ Ʉɨɯɨɧɟɧɚ [12].
Ɂɞɟɫɶ ɨɞɧɨɦɭ ɪɟɚɥɶɧɨɦɭ ɨɛɴɟɤɬɭ ɫɬɚɜɢɬɫɹ
ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɨɞɢɧ ɜɨɡɛɭɠɞɟɧɧɵɣ ɧɟɣɪɨɧ,
ɫɢɦɜɨɥ ɞɚɧɧɨɝɨ ɨɛɪɚɡɚ. ɉɪɨɛɥɟɦɚ ɭɫɬɚɧɨɜɥɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɢɹ ɦɟɠɞɭ ɨɛɪɚɡɨɦ ɢ ɟɝɨ
ɫɢɦɜɨɥɨɦ (ɤɨɞɢɪɨɜɚɧɢɹ) ɫɬɚɜɢɥɚɫɶ ɢ ɪɟɲɚɥɚɫɶ ɜ ɪɚɡɥɢɱɧɵɯ ɨɛɥɚɫɬɹɯ ɬɟɯɧɢɱɟɫɤɨɣ
ɞɟɹɬɟɥɶɧɨɫɬɢ – ɪɚɞɢɨɮɢɡɢɤɟ, ɤɨɦɦɭɧɢɤɚɰɢɹɯ, ɢ ɬ.ɞ. ɉɪɢ ɷɬɨɦ ɝɥɚɜɧɵɦɢ ɤɚɱɟɫɬɜɚɦɢ
ɤɨɞɚ ɫɱɢɬɚɸɬɫɹ ɟɝɨ ɧɚɞɟɠɧɨɫɬɶ (ɧɟɢɫɤɚɠɟɧɢɟ) ɢ ɷɮɮɟɤɬɢɜɧɨɫɬɶ (ɫɤɨɪɨɫɬɶ ɢ
ɷɤɨɧɨɦɢɱɧɨɫɬɶ ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ). ȼ
ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɪɟɱɶ ɡɚɯɨɞɢɬ ɨ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ ɱɟɥɨɜɟɤɚ, ɦɵ
ɨɛɹɡɚɧɵ ɜɨɫɩɪɨɢɡɜɟɫɬɢ ɬɨɬ ɮɚɤɬ, ɱɬɨ ɜ ɠɢɜɵɯ ɫɢɫɬɟɦɚɯ ɫɨɨɬɜɟɬɫɬɜɢɟ ɨɛɪɚɡ l ɫɢɦɜɨɥ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɫɚɦɨ, ɜ ɩɪɨɰɟɫɫɟ ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɢ ɫɢɫɬɟɦɵ. ɉɪɢ ɷɬɨɦ ɦɵ ɨɛɹɡɚɧɵ ɜɨɫɩɪɨɢɡɜɟɫɬɢ ɢɧɞɢɜɢɞɭɚɥɶɧɨɫɬɶ
ɩɪɨɰɟɫɫɚ, ɡɚɬɟɦ ɭɠɟ ɨɰɟɧɢɜɚɬɶ ɞɪɭɝɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.
ȼ ɧɚɲɢɯ ɪɚɛɨɬɚɯ [4,5] ɷɬɚ ɩɪɨɛɥɟɦɚ ɨɛɫɭɠɞɚɥɚɫɶ ɧɟɨɞɧɨɤɪɚɬɧɨ, ɜ ɪɚɡɧɵɯ ɚɫɩɟɤɬɚɯ. ɐɟɥɶ ɞɚɧɧɨɣ ɪɚɛɨɬɵ — ɩɪɟɞɫɬɚɜɢɬɶ
ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɫɚɦɨɨɪɝɚɧɢɡɨɜɚɧɧɨɝɨ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ ɫ
ɭɱɟɬɨɦ ɜɫɟɯ ɟɝɨ ɫɬɚɞɢɣ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ
ɷɬɚ ɦɨɞɟɥɶ ɨɫɧɨɜɚɧɚ ɧɚ ɤɨɧɰɟɩɰɢɢ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɮɨɪɦɚɥɶɧɨɝɨ ɧɟɣɪɨɧɚ.
Ʉɨɧɰɟɩɰɢɹ «ɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɮɨɪɦɚɥɶɧɨɝɨ ɧɟɣɪɨɧɚ»
ɇɚɱɢɧɚɹ ɫ ɪɚɛɨɬɵ Ɇɚɤ Ʉɚɥɥɨɯɚ ɢ ɉɢɬɬɫɚ [14], ɧɟɣɪɨɤɨɦɩɶɸɬɢɧɝ ɛɚɡɢɪɭɟɬɫɹ ɧɚ
ɬɪɟɯ ɩɚɪɚɞɢɝɦɚɯ:
x ɮɨɪɦɚɥɶɧɵɣ ɧɟɣɪɨɧ ɟɫɬɶ ɞɢɯɨɬɨɦɢɱɟɫɤɢɣ ɷɥɟɦɟɧɬ, ɫɩɨɫɨɛɧɵɣ ɫɭɳɟɫɬɜɨɜɚɬɶ
ɜ ɩɚɫɫɢɜɧɨɦ ɢɥɢ ɚɤɬɢɜɧɨɦ ɫɨɫɬɨɹɧɢɢ;
x ɧɟɣɪɨɧɵ ɢ ɫɜɹɡɢ ɦɟɠɞɭ ɧɢɦɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɤɚɤ ɨɬɞɟɥɶɧɵɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɨɛɴɟɤɬɵ, ɩɪɢɱɟɦ ɢɦɟɧɧɨ ɫɜɹɡɢ ɫɩɨɫɨɛɧɵ ɨɛɭɱɚɬɶɫɹ;
x ɩɚɫɫɢɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɦɨɠɟɬ ɦɟɧɹɬɶɫɹ
(ɫɤɚɱɤɨɦ) ɧɚ ɚɤɬɢɜɧɨɟ ɩɪɢ ɜɧɟɲɧɟɦ ɜɨɡɞɟɣɫɬɜɢɢ, ɩɪɟɜɵɲɚɸɳɟɦ ɧɟɤɨɬɨɪɵɣ ɩɨɪɨɝ
ɜɨɡɛɭɠɞɟɧɢɹ.
61
ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɞɢɧɚɦɢɤɚ ɩɪɨɰɟɫɫɚ ɢ
ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɫɨɫɬɨɹɧɢɹ ɜɨ ɜɧɢɦɚɧɢɟ ɧɟ
ɩɪɢɧɢɦɚɸɬɫɹ. ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɧɟɣɪɨɮɢɡɢɨɥɨɝɢɢ ɬɚɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɹɜɥɹɟɬɫɹ, ɛɟɡɭɫɥɨɜɧɨ, ɜɭɥɶɝɚɪɧɵɦ (ɢɡɥɢɲɧɟ ɭɩɪɨɳɟɧɧɵɦ). Ɂɞɟɫɶ ɧɟɣɪɨɧ ɢ ɟɝɨ ɫɜɹɡɢ (ɚɤɫɨɧɵ,
ɫɢɧɚɩɫɵ, ɞɟɧɞɪɢɬɵ) ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɤɚɤ
ɟɞɢɧɨɟ ɰɟɥɨɟ. Ɋɟɚɥɶɧɵɣ ɧɟɣɪɨɧ  ɝɨɪɚɡɞɨ
ɛɨɥɟɟ ɫɥɨɠɧɨɟ ɭɫɬɪɨɣɫɬɜɨ, ɩɥɨɞɵ ɠɢɡɧɟɞɟɹɬɟɥɶɧɨɫɬɢ
ɤɨɬɨɪɨɝɨ
(ɦɟɬɚɛɨɥɢɬɵ)
ɜɥɢɹɸɬ ɤɚɤ ɧɚ ɦɨɡɝ, ɬɚɤ ɢ ɧɚ ɜɟɫɶ ɨɪɝɚɧɢɡɦ
([1]). Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɨɫɧɨɜɧɚɹ ɮɭɧɤɰɢɹ ɧɟɣɪɨɧɚ — ɮɨɪɦɢɪɨɜɚɬɶ ɢ ɩɪɨɜɨɞɢɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɢɦɩɭɥɶɫɵ, ɩɪɢɱɟɦ ɢɡɜɟɫɬɧɨ ɧɟɫɤɨɥɶɤɨ ɫɭɳɟɫɬɜɟɧɧɨ ɪɚɡɥɢɱɧɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ ɬɚɤɨɝɨ ɩɪɨɰɟɫɫɚ: ɨɞɢɧɨɱɧɵɣ ɢɦɩɭɥɶɫ («ɫɩɚɣɤ»), ɚɜɬɨɤɨɥɟɛɚɧɢɹ, ɩɚɤɟɬ ɢɦɩɭɥɶɫɨɜ («ɫɩɚɣɤ-ɬɪɟɣɧ») ɢ ɬ.ɩ.
Ȼɵɥɨ ɩɪɟɞɥɨɠɟɧɨ ɧɟɫɤɨɥɶɤɨ ɦɨɞɟɥɟɣ,
ɜɟɫɶɦɚ ɭɫɩɟɲɧɨ ɨɩɢɫɵɜɚɸɳɢɯ ɞɢɧɚɦɢɤɭ
ɦɟɦɛɪɚɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɧɟɣɪɨɧɚ (ɫɦ. [1] ɢ
ɫɫɵɥɤɢ ɬɚɦ ɠɟ). Ⱦɨ ɫɢɯ ɩɨɪ ɧɚɢɛɨɥɟɟ ɛɢɨɥɨɝɢɱɟɫɤɢ-ɪɟɥɟɜɚɧɬɧɨɣ ɫɱɢɬɚɟɬɫɹ ɦɨɞɟɥɶ
ɏɨɞɠɤɢɧɚ-ɏɚɤɫɥɢ [10], ɨɞɧɚɤɨ ɫɪɚɜɧɢɬɟɥɶɧɚɹ ɫɥɨɠɧɨɫɬɶ ɷɬɨɣ ɦɨɞɟɥɢ (ɤɚɠɞɵɣ
ɧɟɣɪɨɧ ɨɩɢɫɵɜɚɟɬɫɹ ɱɟɬɵɪɶɦɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ) ɨɝɪɚɧɢɱɢɜɚɟɬ ɟɟ
ɩɪɢɦɟɧɟɧɢɟ ɩɪɢ ɫɢɦɭɥɹɰɢɢ ɞɢɧɚɦɢɤɢ ɧɟɣɪɨɧɧɵɯ ɫɟɬɟɣ.
ɉɨɡɠɟ ɷɬɚ ɦɨɞɟɥɶ ɛɵɥɚ ɪɟɞɭɰɢɪɨɜɚɧɚ (ɫ
ɩɨɬɟɪɟɣ ɧɟɤɨɬɨɪɵɯ ɧɸɚɧɫɨɜ) ɞɨ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ ɜ ɪɚɛɨɬɚɯ Ɏɢɬɰɏɶɸ ɢ ɇɚɝɭɦɨ [8,
15]. Ɋɚɫɫɦɨɬɪɢɦ ɷɬɭ ɦɨɞɟɥɶ ɩɨɞɪɨɛɧɟɟ.
Ɉɫɧɨɜɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɟɪɟɦɟɧɧɨɣ
ɹɜɥɹɟɬɫɹ ɦɟɦɛɪɚɧɧɵɣ ɩɨɬɟɧɰɢɚɥ V, ɧɨ ɞɥɹ
ɚɞɟɤɜɚɬɧɨɝɨ ɨɩɢɫɚɧɢɹ ɫɥɨɠɧɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ ɧɟɨɛɯɨɞɢɦɨ ɜɜɟɫɬɢ ɟɳɟ ɨɞɧɭ
ɜɧɭɬɪɟɧɧɸɸ ɩɟɪɟɦɟɧɧɭɸ Y, ɤɨɬɨɪɚɹ ɨɛɟɫɩɟɱɢɜɚɟɬ ɫɬɚɛɢɥɢɡɚɰɢɸ ɪɟɠɢɦɨɜ ɱɟɪɟɡ ɨɬɪɢɰɚɬɟɥɶɧɭɸ ɨɛɪɚɬɧɭɸ ɫɜɹɡɶ:
dV 1
{a1V a2V 2 a3V 3 a0 b0Y ,ext}, (1)
V
dt W
dY
1
{b1V b 2Y },
(2)
dt W Y
ɝɞɟ ɚ0,1,2,3 ɢ b0,1,2 — ɩɚɪɚɦɟɬɪɵ, WV, WY — ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ ɚɤɬɢɜɚɰɢɢ; Iext —
ɜɧɟɲɧɟɟ ɜɨɡɞɟɣɫɬɜɢɟ. Ʉɭɛɢɱɟɫɤɚɹ ɧɟɥɢɧɟɣɧɨɫɬɶ ɜ (1) ɜ ɩɪɢɧɰɢɩɟ ɩɨɡɜɨɥɹɟɬ ɜɨɫɩɪɨɢɡɜɟɫɬɢ ɜɫɟ ɭɩɨɦɹɧɭɬɵɟ ɧɟɬɪɢɜɢɚɥɶɧɵɟ
ɪɟɠɢɦɵ. ɉɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɜɵɛɨɪɟ ɩɚɪɚ-
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
ɦɟɬɪɨɜ (ɚ0 =ɚ2 =E, ɚ1 = ɚ3 = 1; b0,1,2 = 0) ɢ
ɡɚɦɟɧɟ ɜɧɟɲɧɟɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɫɭɦɦɚɪɧɵɣ ɫɢɝɧɚɥ ɨɬ ɫɨɫɟɞɧɢɯ ɧɟɣɪɨɧɨɜ, ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɦɟɦɛɪɚɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ (1) ɮɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɟɬ ɫ ɭɪɚɜɧɟɧɢɟɦ ɬɢɩɚ ɏɨɩɮɢɥɞɚ ɜ ɟɝɨ ɤɨɧɬɢɧɭɚɥɶɧɨɦ (ɚ ɧɟ ɞɢɫɤɪɟɬɧɨɦ) ɩɪɟɞɫɬɚɜɥɟɧɢɢ:
n
dHi (t) 1
2
3
{[
H
E
(
H
1
)
H
]
:ijHj } (3)
¦
i
i
i
i
dt
Wi H
jzi
ɉɪɢ ɷɬɨɦ ɫɚɦ ɧɟɣɪɨɧ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ
ɛɢɫɬɚɛɢɥɶɧɵɣ ɷɥɟɦɟɧɬ, ɚ ɩɚɪɚɦɟɬɪ E ɨɬɧɨɫɢɬɫɹ ɤ ɩɨɪɨɝɭ ɟɝɨ ɜɨɡɛɭɠɞɟɧɢɢ. ɂɦɟɧɧɨ ɜ
ɬɚɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɞɟɥɢ Ɏɢɬɰɏɶɸɇɚɝɭɦɨ [8, 15] ɧɟɣɪɨɧ ɧɚɢɛɨɥɟɟ ɛɥɢɡɨɤ ɤ
ɮɨɪɦɚɥɶɧɨɦɭ ɧɟɣɪɨɧɭ Ɇɚɤ Ʉɚɥɥɨɯɚɉɢɬɬɫɚ [14]. Ⱦɚɥɟɟ ɢɦɟɧɧɨ ɬɚɤɨɣ ɧɟɣɪɨɧ
ɦɵ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɦ ɮɨɪɦɚɥɶɧɵɦ ɧɟɣɪɨɧɨɦ.
Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɨɫɧɨɜɧɵɦ
ɪɟɠɢɦɨɦ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɧɟɣɪɨɧɚ ɹɜɥɹɟɬɫɹ ɧɟ ɛɢɫɬɚɛɢɥɶɧɵɣ, ɚ ɢɦɩɭɥɶɫɧɵɣ ɪɟɠɢɦ (ɫɩɚɣɤ), ɤɨɬɨɪɵɣ ɧɟ ɫɜɨɞɢɬɫɹ ɤ ɫɦɟɧɟ
ɩɨɤɨɹ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɧɟɣɪɨɧɚ ɩɪɢ ɩɪɟɜɵɲɟɧɢɢ ɩɨɪɨɝɚ ɜɧɟɲɧɟɝɨ ɜɨɡɞɟɣɫɬɜɢɹ.
62
ɛɭɞɟɦ ɭɱɢɬɵɜɚɬɶ ɞɥɢɬɟɥɶɧɨɫɬɶ ɮɚɡ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢ.
Ɇɨɞɟɥɶ ɩɪɨɰɟɫɫɨɪɚ ɥɨɤɚɥɢɡɚɰɢɢ
ɉɪɨɰɟɫɫɨɪ ɥɨɤɚɥɢɡɚɰɢɢ ɨɛɪɚɡɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɥɚɫɬɢɧɭ, ɧɚɫɟɥɟɧɧɭɸ n
ɮɨɪɦɚɥɶɧɵɦɢ ɞɢɧɚɦɢɱɟɫɤɢɦɢ ɧɟɣɪɨɧɚɦɢ,
ɬ.ɟ. ɞɢɧɚɦɢɱɟɫɤɢɦɢ ɛɢɫɬɚɛɢɥɶɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ (ɫɦ. ɜɵɲɟ), ɫɩɨɫɨɛɧɵɦɢ ɩɟɪɟɤɥɸɱɚɬɶ ɞɪɭɝ ɞɪɭɝɚ ɜ ɚɤɬɢɜɧɨɟ ɢɥɢ ɩɚɫɫɢɜɧɨɟ
ɫɨɫɬɨɹɧɢɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɫɥɨɜɢɣ ɨɛɭɱɟɧɢɹ. ɉɪɢɧɰɢɩ ɪɚɛɨɬɵ ɫɥɟɞɭɸɳɢɣ: ɩɪɢ
ɚɤɬɢɜɚɰɢɢ m ɧɟɣɪɨɧɨɜ (m<n), ɜ ɪɟɡɭɥɶɬɚɬɟ
ɢɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɜɵɠɢɜɚɟɬ ɬɨɥɶɤɨ ɨɞɢɧ
ɢɡ ɧɢɯ, ɤɨɬɨɪɵɣ ɢ ɫɬɚɧɨɜɢɬɫɹ ɫɢɦɜɨɥɨɦ
ɞɚɧɧɨɝɨ ɧɚɛɨɪɚ ɧɟɣɪɨɧɨɜ (ɨɛɪɚɡɚ) — ɤɚɤ ɢ
ɜ [12], «ɩɨɛɟɞɢɬɟɥɶ ɩɨɥɭɱɚɟɬ ɜɫɟ». ȿɫɬɟɫɬɜɟɧɧɨ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ
ɧɟɣɪɨɧɨɜ ɞɨɥɠɧɨ ɛɵɬɶ ɤɨɧɤɭɪɟɧɬɧɵɦ (ɩɨɞɚɜɥɹɸɳɢɦ).
ȼ ɧɚɲɢɯ ɪɚɛɨɬɚɯ [4,5] ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ
ɫɥɟɞɭɸɳɚɹ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɨɪɚ ɥɨɤɚɥɢɡɚɰɢɢ:
dGkV (t) 1
(Dk 1) ˜GkV Dk ˜ (GkV )2 (GkV )3
dt WG
>
@
, (4)
V V
¦*kl ˜ Gk Gl Z(t)[k (t)
lzk
Ɋɢɫ. 1. ȼɪɟɦɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɦɛɪɚɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɧɟɣɪɨɧɚ ɜ ɪɟɠɢɦɟ
ɫɩɚɣɤɚ.
ɇɚ ɪɢɫ. 1 ɩɪɟɞɫɬɚɜɥɟɧɚ ɞɢɧɚɦɢɤɚ ɩɨɜɟɞɟɧɢɹ ɦɟɦɛɪɚɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ V ɧɟɣɪɨɧɚ
ɜ ɦɨɞɟɥɢ (1–2) ɜ ɪɟɠɢɦɟ ɫɩɚɣɤɚ. Ɂɞɟɫɶ,
ɤɪɨɦɟ ɮɚɡ ɩɨɤɨɹ ɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɫɭɳɟɫɬɜɭɟɬ ɟɳɟ ɢ ɮɚɡɚ ɪɟɮɪɚɤɬɟɪɧɨɫɬɢ, ɜ ɤɨɬɨɪɨɣ
ɧɟɣɪɨɧ ɧɟ ɜɨɡɛɭɠɞɚɟɬɫɹ ɧɢ ɩɪɢ ɤɚɤɨɦ
ɜɧɟɲɧɟɦ ɜɨɡɞɟɣɫɬɜɢɢ. ɉɪɢ ɷɬɨɦ ɜɪɟɦɟɧɧɚɹ
ɲɤɚɥɚ, ɬ.ɟ. ɞɥɢɬɟɥɶɧɨɫɬɶ ɷɬɢɯ ɮɚɡ (Trest,
Tex, Tref ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ) ɡɚɜɢɫɢɬ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ai ɢ bi ɢ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɧɨɣ ɞɥɹ ɪɚɡɧɵɯ ɧɟɣɪɨɧɨɜ. ɇɢɠɟ, ɜ ɪɚɦɤɚɯ ɤɨɧɰɟɩɰɢɢ
ɛɢɫɬɚɛɢɥɶɧɨɝɨ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɟɣɪɨɧɚ, ɦɵ
ɝɞɟ GkV — ɩɟɪɟɦɟɧɧɵɟ ɮɨɪɦɚɥɶɧɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɧɟɣɪɨɧɨɜ ɬɢɩɚ Ƚɪɨɫɫɛɟɪɝɚ;
k = 1…n. ɋɬɚɰɢɨɧɚɪɧɵɟ ɫɨɫɬɨɹɧɢɹ ɧɟɣɪɨɧɨɜ ɜ ɞɚɧɧɨɦ ɩɪɟɞɫɬɚɜɥɟɧɢɢ: ɚɤɬɢɜɧɨɟ
(G = +1) ɢ ɩɚɫɫɢɜɧɨɟ (G = 0). ɉɚɪɚɦɟɬɪɵ
ɩɪɟɞɫɬɚɜɥɹɸɬ: WG — ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɚɤɬɢɜɚɰɢɢ, ɢ Dk — ɩɨɪɨɝ ɚɤɬɢɜɚɰɢɢ (ɫɬɚɰɢɨɧɚɪɧɵɟ
ɫɨɫɬɨɹɧɢɹ
ɫɭɳɟɫɬɜɭɸɬ
ɩɪɢ
1 < Dk < 2 ɢ ɪɚɜɧɨɩɪɚɜɧɵ ɩɪɢ Dk =1,5). Ɉɬɦɟɬɢɦ, ɱɬɨ ɜ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɤɨɧɤɭɪɟɧɬɧɨɟ (ɱɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɡɧɚɤɨɦ «ɦɢɧɭɫ» ɩɟɪɟɞ ɩɨɫɥɟɞɧɢɦ ɱɥɟɧɨɦ) ɢ
ɧɟɥɢɧɟɣɧɨɟ.
ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɫɢɦɜɨɥ, ɜɵɛɪɚɧɧɵɣ
ɛɥɚɝɨɞɚɪɹ ɤɨɧɤɭɪɟɧɬɧɨɦɭ ɜɡɚɢɦɨɞɟɣɫɬɜɢɸ,
ɞɨɥɠɟɧ ɛɵɬɶ ɡɚɩɨɦɧɟɧ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɜ
ɪɟɡɭɥɶɬɚɬɟ ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ Ƚ, ɩɪɢ ɩɨɜɬɨɪɧɨɣ ɚɤɬɢɜɚɰɢɢ ɬɨɝɨ ɠɟ ɧɚɛɨɪɚ ɧɟɣɪɨɧɨɜ,
ɞɨɥɠɟɧ ɩɨɛɟɠɞɚɬɶ ɬɨɬ ɠɟ ɫɚɦɵɣ ɧɟɣɪɨɧɫɢɦɜɨɥ. ɗɬɨɬ ɷɮɮɟɤɬ ɞɨɫɬɢɝɚɟɬɫɹ ɩɭɬɟɦ
ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ Ƚ, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ⱦɨ ɨɛɭɱɟɧɢɹ
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
ɜɫɟ ɫɜɹɡɢ ɫɢɦɦɟɬɪɢɱɧɵ ɢ ɪɚɜɧɵ Ƚkl= Ƚlk=
Ƚ(0)= Ƚ0. ȼ ɩɪɨɰɟɫɫɟ ɨɛɭɱɟɧɢɹ ɫɜɹɡɢ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɡɚɤɨɧɭ:
dī kl (t )
1
Ƚ {Gk ˜ Gl (Gk Gl )} , (5)
dt
W
ɝɞɟ WȽ — ɜɪɟɦɟɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɨɛɭɱɟɧɢɹ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɫɨɝɥɚɫɧɨ (5) ɨɛɭɱɟɧɢɟ (ɢɡɦɟɧɟɧɢɟ ɫɜɹɡɟɣ) ɩɪɟɤɪɚɳɚɟɬɫɹ, ɤɨɝɞɚ ɨɞɢɧ ɢɡ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɧɟɣɪɨɧɨɜ
ɫɬɚɧɨɜɢɬɫɹ ɩɚɫɫɢɜɟɧ.
Ɉɬɦɟɬɢɦ, ɱɬɨ ɤɚɤ ɜɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ,
ɬɚɤ ɢ ɜ ɨɛɭɱɟɧɢɢ ɩɪɢɧɢɦɚɸɬ ɭɱɚɫɬɢɟ ɬɨɥɶɤɨ ɚɤɬɢɜɧɵɟ ɧɟɣɪɨɧɵ. ɗɬɨ ɡɧɚɱɢɬ, ɱɬɨ ɨɛɳɟɟ ɱɢɫɥɨ ɧɟɣɪɨɧɨɜ ɧɚ ɩɥɚɫɬɢɧɟ ɪɨɥɢ ɧɟ
ɢɝɪɚɟɬ, ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɱɢɫɥɨ
ɧɟɣɪɨɧɨɜ m, ɫɨɫɬɚɜɥɹɸɳɢɯ ɨɛɪɚɡ.
ɂɫɫɥɟɞɨɜɚɧɢɹ ɦɨɞɟɥɢ (4) ɩɨɤɚɡɚɥɢ, ɱɬɨ ɜ
ɫɢɦɦɟɬɪɢɱɧɨɦ ɫɥɭɱɚɟ, ɬ.ɟ. ɩɪɢ Dk = D ɢ
Ƚlk =Ƚkl =Ƚ(0) = Ƚ0, ɩɪɨɰɟɫɫ ɜɵɛɨɪɚ ɫɢɦɜɨɥɚ
ɧɟɭɫɬɨɣɱɢɜ. ɗɬɨ ɡɧɚɱɢɬ, ɱɬɨ ɩɪɢ ɚɤɬɢɜɚɰɢɢ
ɨɛɪɚɡɚ ɢɡ m ɧɟɣɪɨɧɨɜ Gm(0) = 1, k = 1...m, ɜ
ɪɟɡɭɥɶɬɚɬɟ ɧɟɥɢɧɟɣɧɨɝɨ ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ
ɜɢɞɚ (5), ɦɚɥɟɣɲɟɟ (ɫɥɭɱɚɣɧɨɟ!) ɩɪɟɢɦɭɳɟɫɬɜɨ ɨɞɧɨɝɨ ɢɡ ɧɢɯ ɩɪɨɜɨɰɢɪɭɟɬ ɟɝɨ ɷɤɫɩɚɧɫɢɸ ɢ ɩɨɞɚɜɥɟɧɢɟ ɨɫɬɚɥɶɧɵɯ.
ɂɫɫɥɟɞɨɜɚɧɢɹ ɦɨɞɟɥɢ ɩɪɨɜɨɞɢɥɢɫɶ ɤɚɤ
ɚɧɚɥɢɬɢɱɟɫɤɢ, ɬɚɤ ɢ ɦɟɬɨɞɨɦ ɜɵɱɢɫɥɢɬɟɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ. Ⱦɟɬɚɥɶɧɨɟ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɜ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ m = 2. Ⱦɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ
ɫɬɪɨɢɥɫɹ ɮɚɡɨɜɵɣ ɩɨɪɬɪɟɬ ɫɢɫɬɟɦɵ, ɚɧɚɥɢɡɢɪɨɜɚɥɢɫɶ ɜɨɡɦɨɠɧɵɟ ɪɟɠɢɦɵ ɩɨɜɟɞɟɧɢɹ,
ɩɪɨɜɨɞɢɥɫɹ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɢ ɨɩɪɟɞɟɥɟɧɢɟ ɛɢɮɭɪɤɚɰɢɨɧɧɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ Ƚ0 ɢ D.
ȼ ɫɥɭɱɚɟ m >> 2 ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɜɵɜɨɞɵ
ɦɨɝɭɬ ɛɵɬɶ ɬɨɥɶɤɨ ɨɛɨɛɳɟɧɵ, ɚ ɨɫɧɨɜɧɵɦ
ɪɟɡɭɥɶɬɚɬɨɦ ɹɜɥɹɟɬɫɹ ɤɨɦɩɶɸɬɟɪɧɵɣ ɷɤɫɩɟɪɢɦɟɧɬ.
Ⱥɧɚɥɢɡ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ
ɨɛɪɚɡɚ ɢɡ ɞɜɭɯ ɧɟɣɪɨɧɨɜ
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɞɟɥɶ (4) ɫɜɨɞɢɬɫɹ ɤ
ɞɜɭɦ ɭɪɚɜɧɟɧɢɹɦ ɞɥɹ ɩɟɪɟɦɟɧɧɵɯ G1 ɢ G2;
ɡɚɞɚɱɚ ɫɢɦɦɟɬɪɢɱɧɚ: D1 = D2 = D ɢ
Ƚ12 = Ƚ21 =Ƚ (0) =Ƚ0. ȼ ɧɚɱɚɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ {1,1} ɨɛɚ ɧɟɣɪɨɧɚ ɚɤɬɢɜɧɵ; ɨɧɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɛɪɚɡɭ. ȼ ɩɪɨɰɟɫɫɟ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ ɞɨɥɠɟɧ ɩɨɛɟɞɢɬɶ ɨɞɢɧ ɢɡ ɧɢɯ,
ɢ ɤɨɧɟɱɧɵɦ ɫɨɫɬɨɹɧɢɟɦ ɞɨɥɠɧɨ ɛɵɬɶ {1,0}
ɢɥɢ {0,1}.
63
ɂɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɩɨɷɬɚɩɧɨ.
ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɚɧɚɥɢɡɢɪɨɜɚɥɫɹ ɮɚɡɨɜɵɣ
ɩɨɪɬɪɟɬ ɫɢɫɬɟɦɵ ɛɟɡ ɭɱɟɬɚ ɨɛɭɱɟɧɢɹ.
Ɍɨɩɨɥɨɝɢɹ ɮɚɡɨɜɨɝɨ ɩɨɪɬɪɟɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɜɟɞɟɧɢɟɦ ɢɡɨɤɥɢɧ. ȼɟɪɬɢɤɚɥɶɧɵɟ
ɢɡɨɤɥɢɧɵ (d/dtG1 = 0) ɡɚɞɚɸɬɫɹ ɭɫɥɨɜɢɹɦɢ:
G1 0; G2 (D 1) DG1 G12 Ƚ 0 ˜ G1 (6)
ɂɡɨɤɥɢɧɵ ɝɨɪɢɡɨɧɬɚɥɟɣ (dG2/dt = 0)
ɢɦɟɸɬ ɜɢɞ:
2
G2 0; G1 (D 1) DG2 G2 Ƚ 0 ˜ G2 (7)
Ɍɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɢɡɨɤɥɢɧ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɫɬɚɰɢɨɧɚɪɧɵɦ ɫɨɫɬɨɹɧɢɹɦ. ɉɪɢ ɷɬɨɦ
ɜɵɪɨɠɞɟɧɧɵɟ ɢɡɨɤɥɢɧɵ G1 = 0 ɢ G2 = 0 ɩɨɪɨɠɞɚɸɬ ɬɪɢɜɢɚɥɶɧɵɟ, ɢɥɢ «ɱɢɫɬɵɟ» ɫɬɚɰɢɨɧɚɪɵ {1,0}, {0,1} ɢ {0,0} (ɧɚ ɪɢɫ. 2 ɨɧɢ
ɩɨɦɟɱɟɧɵ “1”, “2”, “3” ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ),
ɤɨɬɨɪɵɟ ɜɫɟɝɞɚ ɹɜɥɹɸɬɫɹ ɭɫɬɨɣɱɢɜɵɦɢ ɭɡɥɚɦɢ. ɉɟɪɟɫɟɱɟɧɢɹ ɩɚɪɚɛɨɥɢɱɟɫɤɢɯ ɢɡɨɤɥɢɧ ɩɨɪɨɠɞɚɸɬ ɢ ɞɪɭɝɢɟ ɫɬɚɰɢɨɧɚɪɵ ɫɨɫɬɨɹɧɢɹ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɧɟɬɪɢɜɢɚɥɶɧɵɦ
ɷɮɮɟɤɬɚɦ. ɂɡ ɭɪɚɜɧɟɧɢɣ (6) ɢ (7) ɫɥɟɞɭɟɬ,
ɱɬɨ ɫɢɦɦɟɬɪɢɱɧɵɟ ɫɨɫɬɨɹɧɢɹ G* ɪɚɜɧɵ
*
G1 G2 {G, 1/2(DȽ0)r (DȽ0)2 / 4(D1) , (8)
ɬ.ɟ. ɫɭɳɟɫɬɜɭɸɬ ɜ ɬɨɣ ɨɛɥɚɫɬɢ ɩɚɪɚɦɟɬɪɨɜ,
ɝɞɟ ɞɢɫɤɪɢɦɢɧɚɧɬ ɫɢɫɬɟɦɵ D ɧɟ ɨɬɪɢɰɚɬɟɥɟɧ:
D (D Ƚ 0 ) 2 4 ˜ (D 1) t 0.
(9)
ɗɬɨ ɭɫɥɨɜɢɟ ɧɚɤɥɚɞɵɜɚɟɬ ɞɨɜɨɥɶɧɨ ɫɢɥɶɧɨɟ ɨɝɪɚɧɢɱɟɧɢɟ ɧɚ ɩɚɪɚɦɟɬɪ Ƚ0:
Ƚ 0 d D 2 ˜ D 1.
(10)
Ⱦɪɭɝɚɹ ɩɚɪɚɦɟɬɪɢɱɟɫɤɚɹ ɛɢɮɭɪɤɚɰɢɹ ɫɜɹɡɚɧɚ ɫ ɭɫɬɨɣɱɢɜɨɫɬɶɸ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɨɹɧɢɣ. Ɇɟɧɶɲɢɣ ɫɬɚɰɢɨɧɚɪ ɜɫɟɝɞɚ ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɵɦ ɫɟɞɥɨɦ; ɭɫɬɨɣɱɢɜɨɫɬɶ
ɛɨɥɶɲɟɝɨ ɫɬɚɰɢɨɧɚɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɚɦɢ Ʌɹɩɭɧɨɜɚ:
Omax (D 1) 2 ˜ (D Ƚ0 ) ˜ G* 3˜ (G* )2 , (11)
Omin
Omax 2 ˜ Ƚ 0 ˜ G* .
(12)
Ɇɟɧɶɲɟɟ ɢɡ ɧɢɯ Omin ɜɫɟɝɞɚ ɨɬɪɢɰɚɬɟɥɶɧɨ, ɧɨ Omax ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɪɚɡɥɢɱɧɵɟ ɡɧɚɱɟɧɢɹ. ɇɚ Ɋɢɫ. 2ɚ–ɜ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɬɪɢ ɜɨɡɦɨɠɧɵɯ ɜɚɪɢɚɧɬɚ ɬɨɩɨɥɨɝɢɢ ɮɚɡɨɜɨɝɨ ɩɨɪɬɪɟɬɚ. Ɋɚɫɫɦɨɬɪɢɦ ɢɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ.
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
Ɋɢɫ. 2. Ɏɚɡɨɜɵɣ ɩɨɪɬɪɟɬ ɫɢɫɬɟɦɵ (4) ɩɪɢ
ɪɚɡɥɢɱɧɵɯ ɫɨɨɬɧɨɲɟɧɢɹɯ ɩɚɪɚɦɟɬɪɨɜ (ɫɦ.
ɜ ɬɟɤɫɬɟ). ɋɩɥɨɲɧɵɟ ɥɢɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɬ
ɢɡɨɤɥɢɧɚɦ, ɫɬɪɟɥɤɚɦɢ ɭɤɚɡɚɧɨ ɧɚɩɪɚɜɥɟɧɢɟ
ɞɜɢɠɟɧɢɹ ɢɡɨɛɪɚɠɚɸɳɟɣ ɬɨɱɤɢ
I. ȼ ɨɛɥɚɫɬɢ {D d 0} ɩɚɪɚɛɨɥɢɱɟɫɤɢɟ
ɢɡɨɤɥɢɧɵ ɧɟ ɩɟɪɟɫɟɤɚɸɬɫɹ ɜɨɨɛɳɟ. ɋɨɫɬɨɹɧɢɹ «1» ɢ «2» ɹɜɥɹɸɬɫɹ ɱɢɫɬɵɦɢ, ɬ.ɟ. ɜ
ɧɢɯ ɜɨɡɛɭɠɞɟɧ ɬɨɥɶɤɨ ɨɞɢɧ ɧɟɣɪɨɧ. ɗɬɢ
ɫɨɫɬɨɹɧɢɹ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɭɫɬɨɣɱɢɜɵɟ
ɭɡɥɵ. Ɉɛɥɚɫɬɢ ɩɪɢɬɹɠɟɧɢɹ ɢɯ ɪɚɡɞɟɥɟɧɵ
ɫɟɩɚɪɚɬɪɢɫɨɣ, ɤɨɬɨɪɚɹ ɜ ɫɢɥɭ ɫɢɦɦɟɬɪɢɢ
ɹɜɥɹɟɬɫɹ ɛɢɫɫɟɤɬɪɢɫɨɣ.
64
ɋɨɫɬɨɹɧɢɟ “3” ɬɚɤɠɟ ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɵɦ ɭɡɥɨɦ; ɜ ɧɟɦ ɜɫɟ ɧɟɣɪɨɧɵ ɩɚɫɫɢɜɧɵ.
ɋɨɫɬɨɹɧɢɹ “4” ɢ “5” ɹɜɥɹɸɬɫɹ ɫɟɞɥɚɦɢ,
ɱɟɪɟɡ ɧɢɯ ɩɪɨɯɨɞɹɬ ɫɟɩɚɪɚɬɪɢɫɵ (ɧɚ ɪɢɫɭɧɤɟ ɧɟ ɩɨɤɚɡɚɧɵ), ɨɬɞɟɥɹɸɳɢɟ ɨɛɥɚɫɬɢ
ɩɪɢɬɹɠɟɧɢɹ ɫɨɫɬɨɹɧɢɣ “1” ɢ “2” ɨɬ ɨɛɥɚɫɬɢ
ɩɪɢɬɹɠɟɧɢɹ ɫɨɫɬɨɹɧɢɹ “3”.
ɇɚɱɚɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ G1 = G2 = 1 (ɨɛɪɚɡ)
ɧɚɯɨɞɢɬɫɹ ɜ ɨɛɥɚɫɬɢ ɩɪɢɬɹɠɟɧɢɹ ɫɬɚɰɢɨɧɚɪɚ “3”. ɂɡɨɛɪɚɠɚɸɳɚɹ ɬɨɱɤɚ ɢɡ ɧɚɱɚɥɶɧɨɝɨ
ɫɨɫɬɨɹɧɢɹ ɛɵɫɬɪɨ ɞɜɢɠɟɬɫɹ ɩɨ ɛɢɫɫɟɤɬɪɢɫɟ
ɤ ɬɨɱɤɟ {0,0} ɢ ɨɫɬɚɟɬɫɹ ɜ ɧɟɣ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɪɟɞɴɹɜɥɟɧɧɵɣ ɨɛɪɚɡ «ɝɚɫɧɟɬ» ɢ
ɫɢɦɜɨɥ ɧɟ ɨɛɪɚɡɭɟɬɫɹ.
ɋɥɭɱɚɣ D = 0 ɹɜɥɹɟɬɫɹ ɩɪɟɞɟɥɶɧɵɦ: ɩɚɪɚɛɨɥɢɱɟɫɤɢɟ ɢɡɨɤɥɢɧɵ ɧɟ ɩɟɪɟɫɟɤɚɸɬɫɹ,
ɧɨ ɤɚɫɚɸɬɫɹ ɜ ɬɨɱɤɟ G*=1/2(D –Ƚ0). ɗɬɚ
ɬɨɱɤɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɥɨɠɧɭɸ ɛɢɮɭɪɤɚɰɢɸ «ɫɟɞɥɨ-ɭɡɟɥ» ɢ ɧɟ ɦɨɠɟɬ ɨɛɟɫɩɟɱɢɬɶ
ɜɵɛɨɪ ɫɢɦɜɨɥɚ.
II. ȼ ɨɛɥɚɫɬɢ ɩɚɪɚɦɟɬɪɨɜ {D > 0,
Omax< 0} ɜɨɡɧɢɤɚɟɬ ɫɪɚɡɭ ɧɟɫɤɨɥɶɤɨ ɧɨɜɵɯ
ɫɬɚɰɢɨɧɚɪɨɜ, ɨɬɦɟɱɟɧɧɵɯ ɧɚ ɪɢɫ. 2ɛ ɰɢɮɪɚɦɢ “6”–“9”. ɉɪɢ ɷɬɨɦ ɫɨɫɬɨɹɧɢɹ “8” ɢ
“9”, ɜ ɤɨɬɨɪɵɯ ɩɟɪɟɦɟɧɧɵɟ G1 ɢ G2 ɢɦɟɸɬ
ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɡɧɚɱɟɧɢɹ, ɹɜɥɹɸɬɫɹ ɫɟɞɥɚɦɢ. ɋɢɦɦɟɬɪɢɱɧɨɟ ɫɨɫɬɨɹɧɢɟ “7”, ɜ ɤɨɬɨɪɨɦ G1 = G2 = G*+, ɨɩɪɟɞɟɥɟɧɧɨɟ ɮɨɪɦɭɥɨɣ
(8), ɫɬɚɧɨɜɢɬɫɹ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɭɫɬɨɣɱɢɜɵɦ
ɭɡɥɨɦ, ɜ ɨɛɥɚɫɬɶ ɩɪɢɬɹɠɟɧɢɟ ɤɨɬɨɪɨɝɨ ɩɨɩɚɞɚɟɬ ɧɚɱɚɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ {1,1} (ɬ.ɟ. ɨɛɪɚɡ). ɂɡɨɛɪɚɠɚɸɳɚɹ ɬɨɱɤɚ ɞɜɢɠɟɬɫɹ ɩɨ ɫɟɩɚɪɚɬɪɢɫɟ ɤ ɫɨɫɬɨɹɧɢɸ “7” ɢ ɬɚɦ ɨɫɬɚɟɬɫɹ.
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɢɦɜɨɥ ɧɟ ɨɛɪɚɡɭɟɬɫɹ, ɚ
ɜɫɟ ɧɟɣɪɨɧɵ, ɫɨɫɬɚɜɥɹɸɳɢɟ ɨɛɪɚɡ, ɩɟɪɟɯɨɞɹɬ ɜ ɩɨɥɭ-ɜɨɡɛɭɠɞɟɧɧɨɟ («ɩɚɬɨɥɨɝɢɱɟɫɤɨɟ») ɫɨɫɬɨɹɧɢɟ.
III. ȼ ɞɨɜɨɥɶɧɨ ɭɡɤɨɣ ɨɛɥɚɫɬɢ ɩɚɪɚɦɟɬɪɨɜ {D > 0, Omax > 0}, ɝɞɟ D ɢ Omax ɨɩɪɟɞɟɥɹɸɬɫɹ ɮɨɪɦɭɥɚɦɢ (9) ɢ (11), ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ (ɪɢɫ. 2ɜ). Ɂɞɟɫɶ ɮɚɡɨɜɵɣ ɩɨɪɬɪɟɬ
ɩɪɢɨɛɪɟɬɚɟɬ ɢɦɟɧɧɨ ɬɟ ɫɜɨɣɫɬɜɚ, ɤɨɬɨɪɵɟ
ɧɟɨɛɯɨɞɢɦɵ ɞɥɹ ɩɪɨɰɟɫɫɚ ɜɵɛɨɪɚ ɫɢɦɜɨɥɚ.
ɋɨɫɬɨɹɧɢɹ “7”, “8”, “9” ɫɥɢɜɚɸɬɫɹ, ɢ “7”
ɫɬɚɧɨɜɢɬɫɹ ɧɟɭɫɬɨɣɱɢɜɵɦ ɫɟɞɥɨɦ. ȼ ɬɚɤɨɦ
ɪɟɠɢɦɟ ɢɡɨɛɪɚɠɚɸɳɚɹ ɬɨɱɤɚ ɢɡ ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ {1,1} ɛɵɫɬɪɨ ɞɜɢɠɟɬɫɹ ɩɨ
ɛɢɫɫɟɤɬɪɢɫɟ ɤ ɡɧɚɱɟɧɢɸ G1 = G2 = G*+, ɝɞɟ
«ɡɚɫɬɪɟɜɚɟɬ». ɋɥɭɱɚɣɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɩɪɢɜɨɞɢɬ ɟɟ ɜ ɨɛɥɚɫɬɶ ɩɪɢɬɹɠɟɧɢɹ ɫɨɫɬɨɹɧɢɣ
“1” ɢɥɢ “2”. ȼ ɤɨɦɩɶɸɬɟɪɧɨɦ ɷɤɫɩɟɪɢɦɟɧ-
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
ɬɟ ɫɱɢɬɚɥɚɫɶ ɡɚɜɢɫɢɦɨɫɬɶ G1(t) ɜ ɩɪɨɰɟɫɫɟ
ɜɵɛɨɪɚ ɫɢɦɜɨɥɚ-ɩɨɛɟɞɢɬɟɥɹ ɩɪɢ ɧɟɫɤɨɥɶɤɢɯ ɩɪɟɞɴɹɜɥɟɧɢɹɯ ɨɛɪɚɡɚ (ɜ ɫɢɥɭ ɫɢɦɦɟɬɪɢɢ ɡɚɞɚɱɢ G2(t) ɜɟɞɟɬ ɫɟɛɹ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɨ). Ȼɵɥɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɜ 50% ɪɟɚɥɢɡɚɰɢɣ ɢɡɨɛɪɚɠɚɸɳɚɹ ɬɨɱɤɚ ɢɡ ɧɚɱɚɥɶɧɨɝɨ
ɩɨɥɨɠɟɧɢɹ {1,1} ɭɯɨɞɢɬ ɜ ɫɬɚɰɢɨɧɚɪ {0,1}
(ɱɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɨɛɟɞɢɥ G2(t)), ɚ ɜ ɞɪɭɝɢɯ 50% — ɜ ɫɬɚɰɢɨɧɚɪ {1,0}.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɵ ɡɚɤɥɸɱɚɟɦ, ɱɬɨ ɪɟɠɢɦ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɣ ɮɨɪɦɢɪɨɜɚɧɢɟ ɫɢɦɜɨɥɚ, ɜ ɩɚɪɚɦɟɬɪɢɱɟɫɤɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɡɚɧɢɦɚɟɬ ɭɡɤɭɸ ɨɛɥɚɫɬɶ ɦɟɠɞɭ ɪɟɠɢɦɚɦɢ,
ɩɪɢ ɤɨɬɨɪɵɯ ɫɢɦɜɨɥ ɨɛɪɚɡɨɜɚɬɶɫɹ ɧɟ ɦɨɠɟɬ. ɋɦɵɫɥ ɷɬɨɝɨ ɪɟɡɭɥɶɬɚɬɚ ɜ ɬɨɦ, ɱɬɨ ɩɪɢ
ɫɥɚɛɨɦ ɜɡɚɢɦɧɨɦ ɩɨɞɚɜɥɟɧɢɢ (ɦɚɥɵɯ Ƚ0)
ɜɵɠɢɜɚɸɬ ɜɫɟ ɧɟɣɪɨɧɵ ɨɛɪɚɡɚ, ɯɨɬɹ ɢ ɜ
ɩɨɥɭ-ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ɉɪɢ ɫɥɢɲɤɨɦ ɫɢɥɶɧɨɦ ɜɡɚɢɦɧɨɦ ɩɨɞɚɜɥɟɧɢɢ ɝɚɫɧɭɬ
ɜɨɨɛɳɟ ɜɫɟ ɧɟɣɪɨɧɵ. Ɍɨɥɶɤɨ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɫɨɨɬɧɨɲɟɧɢɢ ɩɚɪɚɦɟɬɪɨɜ Ƚ0 ɢ D
ɜɵɛɨɪ ɫɢɦɜɨɥɚ ɜɨɡɦɨɠɟɧ.
ɇɢɠɟ ɛɭɞɟɬ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɭɱɟɬ ɨɛɭɱɟɧɢɹ
ɫɜɹɡɟɣ Ƚ ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (5) ɡɧɚɱɢɬɟɥɶɧɨ
ɪɚɫɲɢɪɹɟɬ ɬɭ ɨɛɥɚɫɬɶ ɩɚɪɚɦɟɬɪɨɜ, ɝɞɟ ɩɪɨɰɟɫɫ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ ɜɨɡɦɨɠɟɧ.
ɋɚɦɨ ɩɨ ɫɟɛɟ ɨɛɭɱɟɧɢɟ ɫɜɹɡɟɣ ɧɟɨɛɯɨɞɢɦɨ
ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɜɵɛɪɚɧɧɵɣ ɫɢɦɜɨɥ ɡɚɩɨɦɧɢɥɫɹ ɢ ɩɪɢ ɫɥɟɞɭɸɳɟɦ ɩɪɟɞɴɹɜɥɟɧɢɢ ɬɨɝɨ
ɠɟ ɨɛɪɚɡɚ ɚɤɬɢɜɢɪɨɜɚɥɫɹ ɛɵ ɫɪɚɡɭ (ɦɢɧɭɹ
ɫɬɚɞɢɸ ɜɵɛɨɪɚ). Ɂɚɦɟɬɢɦ, ɱɬɨ, ɫɨɝɥɚɫɧɨ
(5), ɨɛɭɱɟɧɢɟ ɫɜɹɡɟɣ Ƚ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɨ,
ɬɚɤ ɱɬɨ ɫɨɛɥɸɞɚɟɬɫɹ ɭɫɥɨɜɢɟ Ƚ12+Ƚ21=2Ƚ0;
ɢɧɚɱɟ ɝɨɜɨɪɹ, ɷɬɢ ɫɜɹɡɢ ɨɛɭɱɚɸɬɫɹ ɧɟ ɧɟɡɚɜɢɫɢɦɨ. ɋɨɝɥɚɫɧɨ ɚɧɚɥɢɡɭ, ɩɪɨɜɟɞɟɧɧɨɦɭ
ɜɵɲɟ, ɨɛɭɱɟɧɢɟ ɫɥɟɞɭɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ
ɩɪɨɰɟɫɫ, ɨɞɧɨɜɪɟɦɟɧɧɵɣ ɫ ɜɵɛɨɪɨɦ ɫɢɦɜɨɥɚ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɨɫɤɨɥɶɤɭ ɧɚɱɚɥɶɧɨɟ
ɫɨɫɬɨɹɧɢɟ {1,1} (ɨɛɪɚɡ) ɩɨɩɚɞɚɟɬ ɜ ɨɛɥɚɫɬɶ
ɩɪɢɬɹɠɟɧɢɹ ɫɟɞɥɚ “7”, ɫɢɫɬɟɦɚ ɛɵɫɬɪɨ ɞɨɫɬɢɝɚɟɬ ɷɬɨɣ ɬɨɱɤɢ ɢ ɡɚɬɟɦ ɞɨɥɝɨɟ ɜɪɟɦɹ
ɩɪɨɜɨɞɢɬ ɜ ɟɟ ɨɤɪɟɫɬɧɨɫɬɢ. ɗɬɨ ɞɚɟɬ ɧɚɦ
ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɟɞɫɬɚɜɢɬɶ ɩɟɪɟɦɟɧɧɵɟ ɜ
ɜɢɞɟ:
G1=G*+ + [, G2 =G*+ + K , Ƚ = Ƚ0+G, ɢ ɢɫɫɥɟɞɨɜɚɬɶ ɦɚɥɵɟ ɨɬɤɥɨɧɟɧɢɹ [, K ɢ G ɨɬ
ɫɬɚɰɢɨɧɚɪɧɵɯ ɡɧɚɱɟɧɢɣ. Ʌɟɝɤɨ ɩɨɤɚɡɚɬɶ,
ɱɬɨ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɨɬɤɥɨɧɟɧɢɣ ɢɦɟɸɬ ɜɢɞ
d[
v (Omax Ƚ0G* )[ Ƚ0G*K (G* )2G ; (13)
dt
65
dK
v (Omax Ƚ0G* )K Ƚ0G*[ (G* )2 G (14)
dt
dG
v F ˜ (G*[ G*K)
(15)
dt
*
ɝɞɟ G + ɢ Omax ɡɚɞɚɧɵ ɭɪɚɜɧɟɧɢɹɦɢ (8) ɢ
(11) ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; ɩɚɪɚɦɟɬɪ F=WG/WȽ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ. Ʌɟɝɤɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɞɟɬɟɪɦɢɧɚɧɬ ɷɬɨɣ
ɫɢɫɬɟɦɵ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɤ ɜɢɞɭ:
[O(Oma[ 2Ƚ0 ˜G*)]˜[O˜(OOmax)2F˜(G*)4]. (16)
ɂɡ (16) ɫɥɟɞɭɟɬ, ɱɬɨ ɨɞɧɨ ɢɡ ɬɪɟɯ ɱɢɫɟɥ Ʌɹɩɭɧɨɜɚ O = Omax–2Ƚ0G*=Omin ɨɬɪɢɰɚɬɟɥɶɧɨ
ɢ ɫɨɜɩɚɞɚɟɬ ɫ ɬɚɤɨɜɵɦ ɜ ɨɬɫɭɬɫɬɜɢɟ ɨɛɭɱɟɧɢɹ (12). Ⱦɜɚ ɞɪɭɝɢɯ ɨɩɪɟɞɟɥɹɸɬɫɹ ɢɡ ɭɫɥɨɜɢɹ:
1
1
˜ Omax r ˜ O2max 8 ˜ F ˜ (G* ) 4 , (17)
2
2
ɬ.ɟ. ɨɞɧɨ ɜɫɟɝɞɚ ɨɬɪɢɰɚɬɟɥɶɧɨ, ɜɬɨɪɨɟ ɠɟ
ɜɫɟɝɞɚ ɩɨɥɨɠɢɬɟɥɶɧɨ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ,
ɩɪɢ ɨɞɧɨɜɪɟɦɟɧɧɨɦ ɜɵɛɨɪɟ ɫɢɦɜɨɥɚ ɢ ɨɛɭɱɟɧɢɢ ɫɜɹɡɟɣ, ɫɨɫɬɨɹɧɢɟ G+* ɜɫɸɞɭ ɜ ɨɛɥɚɫɬɢ ɟɝɨ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɫɟɞɥɨɦ,
ɬ.ɟ. ɧɟɭɫɬɨɣɱɢɜɨ.
Ɏɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɷɬɨɝɨ ɩɪɨɫɬ: ɭɱɟɬ
ɨɛɭɱɟɧɢɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɜɵɛɨɪɨɦ ɫɢɦɜɨɥɚ ɜɤɥɸɱɚɟɬ ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɨɛɪɚɬɧɭɸ
ɫɜɹɡɶ ɦɚɥɨɝɨ ɨɬɤɥɨɧɟɧɢɹ ɢɡɨɛɪɚɠɚɸɳɟɣ
ɬɨɱɤɢ ɨɬ ɛɢɫɫɟɤɬɪɢɫɵ, ɱɬɨ ɭɫɭɝɭɛɥɹɟɬ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɢ ɩɪɢɜɨɞɢɬ ɤ ɛɵɫɬɪɨɦɭ ɜɵɛɨɪɭ ɚɬɬɪɚɤɬɨɪɚ (ɭɫɬɨɣɱɢɜɨɝɨ ɭɡɥɚ). ȼɪɟɦɹ
ɚɤɬɢɜɚɰɢɢ ɜɵɛɪɚɧɧɨɝɨ ɫɢɦɜɨɥɚ ɩɪɢ ɷɬɨɦ
ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɞɨ ɨɛɭɱɟɧɢɹ.
ɗɬɢ ɜɵɜɨɞɵ ɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɢɬɶ ɢ
ɧɚ ɫɥɭɱɚɣ ɨɛɪɚɡɚ ɢɡ m >> 1 ɧɟɣɪɨɧɨɜ. Ⱥɧɚɥɢɬɢɱɟɫɤɢɟ ɜɵɱɢɫɥɟɧɢɹ ɩɪɢ ɷɬɨɦ ɡɚɬɪɭɞɧɢɬɟɥɶɧɵ, ɧɨ ɤɚɱɟɫɬɜɟɧɧɵɟ ɜɵɜɨɞɵ ɨɫɬɚɸɬɫɹ ɜ ɫɢɥɟ. Ɉɫɧɨɜɧɨɣ ɜɵɜɨɞ ɡɚɤɥɸɱɚɟɬɫɹ
ɜ ɬɨɦ, ɱɬɨ ɩɪɨɰɟɫɫɨɪ, ɫɩɨɫɨɛɧɵɣ ɩɪɟɨɛɪɚɡɨɜɵɜɚɬɶ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɟ ɨɛɪɚɡɵ
m >> 1, ɞɨɥɠɟɧ ɨɛɥɚɞɚɬɶ ɨɩɪɟɞɟɥɟɧɧɨɣ
«ɷɥɚɫɬɢɱɧɨɫɬɶɸ», ɬ.ɟ. ɧɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ
ɫɢɥɵ ɫɜɹɡɢ Ƚ0 ɞɨɥɠɧɵ ɛɵɬɶ ɦɚɥɵ.
Ɉɬɦɟɬɢɦ, ɱɬɨ ɜɪɟɦɹ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ
ɜɵɛɨɪɚ ɧɟɣɪɨɧɚ-ɩɨɛɟɞɢɬɟɥɹ, ɡɚɜɢɫɢɬ, ɪɚɡɭɦɟɟɬɫɹ, ɨɬ ɩɚɪɚɦɟɬɪɚ F, ɧɨ, ɤɪɨɦɟ ɬɨɝɨ,
ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɫɥɨɠɧɨɫɬɢ ɨɛɪɚɡɚ,
ɬ.ɟ. ɱɢɫɥɚ (m–1).
Or
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɜɫɟɝɨ ɩɪɨɰɟɫɫɚ
ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ
Ʉɨɧɫɬɪɭɤɰɢɹ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɦɵɫɥɢɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ ȺɆ ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɜ ɪɚɛɨɬɚɯ [5]. ȿɟ ɜɚɠɧɵɦ ɷɥɟɦɟɧɬɨɦ ɹɜɥɹɟɬɫɹ
ɛɥɨɤ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ ɬɢɩɢɱɧɨɝɨ
ɨɛɪɚɡɚ. Ɉɬɜɥɟɤɚɹɫɶ ɨɬ ɞɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ
ɤɨɧɫɬɪɭɤɰɢɢ, ɪɚɫɫɦɨɬɪɢɦ ɩɨɞɪɨɛɧɨ ɦɨɞɟɥɶ, ɫɩɨɫɨɛɧɭɸ ɨɩɢɫɚɬɶ ɷɬɨɬ ɩɪɨɰɟɫɫ.
ɋɚɦɨɨɪɝɚɧɢɡɨɜɚɧɧɵɣ ɩɪɨɰɟɫɫ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ ɬɢɩɢɱɧɨɝɨ ɨɛɪɚɡɚ ɩɪɨɢɫɯɨɞɢɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɧɟɫɤɨɥɶɤɨ ɫɬɚɞɢɣ
(ɫɦ. ɪɢɫ. 3).
66
ɞɨɥɠɧɵ ɢɫɱɟɡɧɭɬɶ, ɢɧɚɱɟ ɫɜɹɡɶ ɫ ɫɢɦɜɨɥɨɦ
ɛɭɞɟɬ ɢɫɤɚɠɟɧɚ.
ɇɚɤɨɧɟɰ, ɧɚ ɩɨɫɥɟɞɧɟɣ ɫɬɚɞɢɢ ɞɨɥɠɧɚ
ɩɪɨɢɫɯɨɞɢɬɶ ɫɩɟɰɢɚɥɢɡɚɰɢɹ ɧɟɣɪɨɧɚɫɢɦɜɨɥɚ: ɧɟɣɪɨɧ, ɫɬɚɜɲɢɣ ɫɢɦɜɨɥɨɦ ɞɚɧɧɨɝɨ ɨɛɪɚɡɚ, ɧɟ ɞɨɥɠɟɧ ɭɱɚɫɬɜɨɜɚɬɶ ɜ ɤɨɧɤɭɪɟɧɬɧɨɣ ɛɨɪɶɛɟ ɡɚ ɩɪɚɜɨ ɫɬɚɬɶ ɫɢɦɜɨɥɨɦ
ɞɪɭɝɨɝɨ. ɗɬɨɬ ɷɮɮɟɤɬ ɦɨɠɟɬ ɛɵɬɶ ɨɛɟɫɩɟɱɟɧ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢ, ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ
ɩɚɪɚɦɟɬɪɚ D (ɬ.ɟ. ɭɜɟɥɢɱɟɧɢɹ ɩɨɪɨɝɚ ɜɨɡɛɭɠɞɟɧɢɹ) ɧɟɣɪɨɧɚ, ɜɵɛɪɚɧɧɨɝɨ ɧɚ ɪɨɥɶ
ɫɢɦɜɨɥɚ – ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɧɤɭɪɟɧɬɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɞɚɧɧɨɝɨ ɧɟɣɪɨɧɚ ɩɚɞɚɟɬ.
ȼɫɟ ɫɬɚɞɢɢ ɩɪɨɰɟɫɫɚ ɦɨɠɧɨ ɨɩɢɫɚɬɶ
ɞɜɭɦɹ ɫɜɹɡɚɧɧɵɦɢ ɧɚɛɨɪɚɦɢ ɭɪɚɜɧɟɧɢɣ
ɜɢɞɚ:
dGk0 (t )
dt
1
WG
{(D (t ) 1) ˜ Gk0 D (t ) ˜ (Gk0 ) 2 , (18)
(Gk0 ) 3 ¦ *kl ˜ Gk0 Gl0 Z (t )[ k (t ) l zk
\ kk H k
typ
m
¦ <ki H ityp }
k
Ɋɢɫ.3. ɋɬɚɞɢɢ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ
ɫɢɦɜɨɥɚ (ɫɦ. ɜ ɬɟɤɫɬɟ).
ɇɚ ɩɟɪɜɨɣ ɫɬɚɞɢɢ (ɪɢɫ. 3ɚ) ɨɛɪɚɡ, ɬ.ɟ.
ɧɚɛɨɪ m ɚɤɬɢɜɧɵɯ ɧɟɣɪɨɧɨɜ ɫ ɩɥɚɫɬɢɧɵ
ɬɢɩɢɱɧɵɯ ɨɛɪɚɡɨɜ Htyp (ɬɢɩɚ ɏɨɩɮɢɥɞɚ),
ɩɟɪɟɞɚɟɬɫɹ ɩɪɹɦɵɦɢ ɦɟɠɩɥɚɫɬɢɧɧɵɦɢ ɫɜɹɡɹɦɢ \ ɧɚ ɩɥɚɫɬɢɧɭ ɬɢɩɚ Ƚɪɨɫɫɛɟɪɝɚ G0,
ɬ.ɟ. ɜɨɡɛɭɠɞɚɟɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ (ɬɨɬ ɠɟ
ɫɚɦɵɣ) ɧɚɛɨɪ ɧɟɣɪɨɧɨɜ ɜ ɩɪɨɰɟɫɫɨɪɟ ɥɨɤɚɥɢɡɚɰɢɢ. ɇɚɱɚɥɨ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ ɩɪɢɦɟɦ ɡɚ
ɬɨɱɤɭ ɨɬɫɱɟɬɚ (t = 0).
ɇɚ ɜɬɨɪɨɣ ɫɬɚɞɢɢ (ɪɢɫ. 3ɛ) ɩɪɨɢɫɯɨɞɢɬ
ɤɨɧɤɭɪɟɧɬɧɚɹ ɛɨɪɶɛɚ ɢ ɨɛɭɱɟɧɢɟ ɜɧɭɬɪɢɩɥɚɫɬɢɧɧɵɯ ɫɜɹɡɟɣ ɜ ɩɪɨɰɟɫɫɨɪɟ ɥɨɤɚɥɢɡɚɰɢɢ Ƚ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɨɣ ɩɨɛɟɠɞɚɟɬ (ɨɫɬɚɟɬɫɹ ɚɤɬɢɜɧɵɦ) ɬɨɥɶɤɨ ɨɞɢɧ ɧɟɣɪɨɧ, ɜɵɛɪɚɧɧɵɣ ɫɥɭɱɚɣɧɨ. ɂɦɟɧɧɨ ɷɬɨɬ ɧɟɣɪɨɧ
ɫɬɚɧɨɜɢɬɫɹ ɫɢɦɜɨɥɨɦ ɨɛɪɚɡɚ, ɤɚɤ ɪɚɫɫɦɨɬɪɟɧɨ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ. ɇɨ ɷɬɨɝɨ ɧɟɞɨɫɬɚɬɨɱɧɨ: ɫɢɦɜɨɥ ɞɨɥɠɟɧ ɨɛɥɚɞɚɬɶ ɫɩɨɫɨɛɧɨɫɬɶɸ ɞɟɤɨɦɩɨɡɢɰɢɢ, ɬ.ɟ. ɚɤɬɢɜɢɪɨɜɚɬɶ
ɢɦɟɧɧɨ ɫɜɨɣ ɨɛɪɚɡ ɧɚ ɩɥɚɫɬɢɧɟ Htyp.
ɇɚ ɬɪɟɬɶɟɣ ɫɬɚɞɢɢ (ɪɢɫ. 3ɜ) ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɦɟɠɩɥɚɫɬɢɧɧɵɟ (ɫɟɦɚɧɬɢɱɟɫɤɢɟ)
ɫɜɹɡɢ <, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɞɟɤɨɦɩɨɡɢɰɢɸ ɢ
ɭɫɬɨɣɱɢɜɭɸ ɫɜɹɡɶ ɫɢɦɜɨɥlɨɛɪɚɡ. Ʉ ɷɬɨɦɭ
ɦɨɦɟɧɬɭ ɩɪɹɦɵɟ ɦɟɠɩɥɚɫɬɢɧɧɵɟ ɫɜɹɡɢ \
typ
i
dH (t) 1
{ Hityp Ei ˜ ((Hityp)2 1) (Hityp)3 H
dt
W
. (19)
>
@
n
m
iz j
k
typ
¦:typ
ij H j ¦<ik Gk }
ɑɥɟɧ Z(t)]k(t) ɜ (18) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɱɟɬɭ
ɫɥɭɱɚɣɧɨɝɨ ɮɚɤɬɨɪɚ («ɲɭɦɚ»): Z(t) ɟɫɬɶ
ɚɦɩɥɢɬɭɞɚ ɲɭɦɚ, ]k(t) – ɫɥɭɱɚɣɧɚɹ ɮɭɧɤɰɢɹ
(0d ] d1).
Ɉɛɭɱɟɧɢɟ ɩɪɹɦɵɯ ɦɟɠɩɥɚɫɬɢɧɧɵɯ ɫɜɹɡɟɣ \ ɞɨɥɠɧɨ ɩɪɢɜɨɞɢɬɶ ɤ ɢɯ ɭɝɚɫɚɧɢɸ ɤ
ɬɨɦɭ ɜɪɟɦɟɧɢ, ɤɨɝɞɚ ɧɚɱɧɟɬɫɹ ɤɨɧɤɭɪɟɧɬɧɚɹ ɛɨɪɶɛɚ, ɬ.ɟ. ɞɨɫɬɚɬɨɱɧɨ ɛɵɫɬɪɨ:
d\ kk
dt
1
\ kkGk (Hk 1) ,
2W \
(20)
ɝɞɟ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɭɫɥɨɜɢɟ W\ <WȽ, WG.
Ɉɛɭɱɟɧɢɟ ɫɜɹɡɟɣ Ƚ ɩɪɨɢɫɯɨɞɢɬ ɫɨɝɥɚɫɧɨ
(5).
ɉɨɫɥɟ ɨɤɨɧɱɚɧɢɹ ɩɪɨɰɟɫɫɚ ɤɨɧɤɭɪɟɧɰɢɢ
ɧɟɣɪɨɧɨɜ ɧɚ ɩɥɚɫɬɢɧɟ G0 ɢ ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ
Ƚ ɞɨɥɠɟɧ ɧɚɱɚɬɶɫɹ ɩɪɨɰɟɫɫ ɮɨɪɦɢɪɨɜɚɧɢɹ
ɫɟɦɚɧɬɢɱɟɫɤɢɯ ɦɟɠɩɥɚɫɬɢɧɧɵɯ ɫɜɹɡɟɣ <ik,
ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
d<ik
1
<ik (<max <ik )Gk ( Hi 1) , (21)
dt
2W <
ɩɪɢɱɟɦ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɭɫɥɨɜɢɟ
W<>WȽ, W\.
ɇɚɤɨɧɟɰ, ɩɨɫɥɟ ɭɫɢɥɟɧɢɹ ɫɜɹɡɟɣ < ɞɨ
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɨɝɨ ɭɪɨɜɧɹ (<a<max),
ɞɨɥɠɧɚ ɛɵɬɶ ɨɛɟɫɩɟɱɟɧɚ ɫɩɟɰɢɚɥɢɡɚɰɢɹ
ɧɟɣɪɨɧɚ-ɫɢɦɜɨɥɚ: ɧɟɣɪɨɧ, ɜɵɛɪɚɧɧɵɣ ɧɚ
ɪɨɥɶ ɫɢɦɜɨɥɚ ɞɚɧɧɨɝɨ ɨɛɪɚɡɚ, ɜ ɞɚɥɶɧɟɣɲɟɦ ɧɟ ɞɨɥɠɟɧ ɭɱɚɫɬɜɨɜɚɬɶ ɜ ɤɨɧɤɭɪɟɧɬɧɨɣ ɛɨɪɶɛɟ ɡɚ ɩɪɚɜɨ ɫɬɚɬɶ ɫɢɦɜɨɥɨɦ ɤɚɤɨɝɨ-ɥɢɛɨ ɞɪɭɝɨɝɨ ɨɛɪɚɡɚ. Ɉɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɜɚɪɢɚɧɬɨɜ ɨɛɭɱɟɧɢɹ ɩɚɪɚɦɟɬɪɚ Dk. ɇɚ
ɫɬɚɞɢɢ ɜɵɛɨɪɚ ɫɢɦɜɨɥɚ ɜɫɟ ɩɨɪɨɝɢ ɚɤɬɢɜɚɰɢɢ D ɞɨɥɠɧɵ ɛɵɬɶ ɧɟ ɜɟɥɢɤɢ, ɢɧɚɱɟ ɧɚɪɭɲɚɟɬɫɹ ɭɫɥɨɜɢɟ (10): ɩɪɢ D = 2 ɩɪɨɰɟɫɫ
ɜɵɛɨɪɚ ɫɢɦɜɨɥɚ ɫɬɚɧɨɜɢɬɫɹ ɧɟɜɨɡɦɨɠɟɧ
(Ƚ0 d 0). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɟɫɥɢ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɩɪɨɰɟɫɫɚ ɜɵɛɨɪɚ ɩɚɪɚɦɟɬɪ Dk ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ ɫɜɨɟɦɭ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ, ɬɚɤɨɣ ɫɢɦɜɨɥ ɛɨɥɟɟ ɧɟɤɨɧɤɭɪɟɧɬɨɫɩɨɫɨɛɟɧ. ɉɪɨɰɟɫɫ ɨɛɭɱɟɧɢɹ ɩɚɪɚɦɟɬɪɚ
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
d'D k
1
'D k ('D max 'D k ),
(22)
WD
dt
ɝɞɟ 'Dk — ɨɬɤɥɨɧɟɧɢɟ ɩɚɪɚɦɟɬɪɚ Dk ɨɬ ɟɝɨ
ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ D0, WD — ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɨɛɭɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ D. ɗɬɨ
ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɹɜɧɨɟ ɪɟɲɟɧɢɟ:
' D max
' D k (t )
T t
1 exp[ ' D max D
]
WD
, (23)
WD
' D max
ɌD
ln
' D ma [
' D in
Ɂɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɞɨɥɠɧɵ ɛɵɬɶ ɨɝɪɚɧɢɱɟɧɵ ɭɫɥɨɜɢɹɦɢ:
ɜɟɥɢɱɢɧɚ 'Din ɦɚɥɚ, ɧɚ ɭɪɨɜɧɟ ɮɥɸɤɬɭɚɰɢɣ, ɧɟ ɩɪɟɩɹɬɫɬɜɭɸɳɢɯ ɨɛɪɚɡɨɜɚɧɢɸ
ɫɢɦɜɨɥɚ (ɜ ɤɨɦɩɶɸɬɟɪɧɵɯ ɪɚɫɱɟɬɚɯ — ɧɚ
ɭɪɨɜɧɟ ɬɨɱɧɨɫɬɢ).
ɜɟɥɢɱɢɧɚ 'Dmax ɜɟɥɢɤɚ, ɬɚɤ, ɱɬɨ ɜɵɜɨɞɢɬ ɫɢɦɜɨɥ ɢɡ ɤɨɧɤɭɪɟɧɬɧɨɣ ɛɨɪɶɛɵ ɩɪɢ
ɩɪɟɞɴɹɜɥɟɧɢɢ ɞɪɭɝɨɝɨ ɨɛɪɚɡɚ.
ɜɪɟɦɹ TD ɛɨɥɶɲɟ ɜɪɟɦɟɧɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ, ɧɨ ɦɟɧɶɲɟ ɜɪɟɦɟɧɢ ɟɝɨ ɡɚɬɭɯɚɧɢɹ (ɩɨɫɥɟɞɧɟɟ ɜ ɦɨɞɟɥɢ ɫɤɨɥɶ ɭɝɨɞɧɨ
ɜɟɥɢɤɨ); ɷɬɨ ɨɝɪɚɧɢɱɢɜɚɟɬ ɜɟɥɢɱɢɧɭ WD ɫɧɢɡɭ.
ȼɪɟɦɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɫɜɹɡɟɣ \, Ƚ, < ɢ
ɩɚɪɚɦɟɬɪɚ D ɩɪɨɢɥɥɸɫɬɪɢɪɨɜɚɧɚ ɧɚ ɪɢɫ. 4.
ɉɪɢ t t T* ɜɟɫɶ ɩɪɨɰɟɫɫ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɡɚɜɟɪɲɟɧɧɵɦ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɪɚɜɧɟɧɢɹ (18-23) ɩɪɟɞ-
67
ɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɚɦɤɧɭɬɭɸ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɜ ɞɚɧɧɨɣ ɦɨɞɟɥɢ
ɫɚɦɨɨɪɝɚɧɢɡɚɰɢɹ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ
ɫɦɟɧɚ ɫɬɚɞɢɣ ɜɫɟɝɨ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ ɧɟ ɩɨɞɪɚɡɭɦɟɜɚɟɬ ɜɤɥɸɱɟɧɢɹ/ɜɵɤɥɸɱɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɚ ɩɪɨɢɫɯɨɞɢɬ ɡɚ
ɫɱɟɬ ɪɚɡɥɢɱɢɹ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧ ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ ɪɚɡɧɨɝɨ ɬɢɩɚ, ɬ.ɟ. ɩɚɪɚɦɟɬɪɨɜ W\,
WȽ, W< ɢ TD.
Ɋɢɫ. 4. Ⱦɢɧɚɦɢɤɚ ɨɛɭɱɟɧɢɹ ɫɜɹɡɟɣ \, Ƚ, < ɢ
ɩɚɪɚɦɟɬɪɚ D.
Ɂɚɤɥɸɱɟɧɢɟ
ȿɫɬɟɫɬɜɟɧɧɨ-ɤɨɧɫɬɪɭɤɬɢɜɢɫɬɫɤɢɣ ɩɨɞɯɨɞ ɤ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ
ɢɦɟɟɬ ɧɟɫɤɨɥɶɤɨ ɫɭɳɟɫɬɜɟɧɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ. ɋɪɟɞɢ ɧɢɯ ɧɚɢɛɨɥɟɟ ɜɚɠɧɵɦɢ ɹɜɥɹɸɬɫɹ:
x ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɨɧɬɢɧɭɚɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɧɟɣɪɨɩɪɨɰɟɫɫɨɪɨɜ;
x ɨɩɟɪɢɪɨɜɚɧɢɟ ɨɛɪɚɡɧɨɣ ɢ ɫɢɦɜɨɥɶɧɨɣ
ɢɧɮɨɪɦɚɰɢɟɣ;
x ɭɱɟɬ ɫɥɭɱɚɣɧɨɝɨ ɮɚɤɬɨɪɚ (ɲɭɦɚ).
ɂɦɟɧɧɨ ɷɬɢ ɨɫɨɛɟɧɧɨɫɬɢ ɩɨɡɜɨɥɹɸɬ
ɩɪɟɞɥɚɝɚɬɶ ɪɚɡɥɢɱɧɵɟ ɜɚɪɢɚɧɬɵ ɦɨɞɟɥɟɣ, ɜ
ɱɚɫɬɧɨɫɬɢ, ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɢɦɜɨɥɚ. Ɋɚɫɫɦɨɬɪɟɧɧɵɣ ɜɚɪɢɚɧɬ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ
ɞɚɧɧɨɣ ɪɚɛɨɬɟ, ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɦɨɠɟɬ ɨɛɟɫɩɟɱɢɬɶ ɩɪɨɰɟɫɫ ɜɵɛɨɪɚ ɢ ɡɚɩɨɦɢɧɚɧɢɹ
ɫɢɦɜɨɥɚ, ɩɪɢɱɟɦ ɥɢɲɶ ɜ ɨɩɪɟɞɟɥɟɧɧɨɣ ɨɛɥɚɫɬɢ ɩɚɪɚɦɟɬɪɨɜ. ɗɬɨɬ ɮɚɤɬ ɩɨɡɜɨɥɹɟɬ
ɨɛɟɫɩɟɱɢɬɶ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢ ɢ ɫɩɟɰɢɚɥɢɡɚɰɢɸ ɧɟɣɪɨɧɨɜ-ɫɢɦɜɨɥɨɜ, ɬ.ɟ. ɟɝɨ ɫɜɹɡɶ
ɬɨɥɶɤɨ ɫ ɨɞɧɢɦ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɟɦɭ, ɨɛɪɚɡɨɦ.
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
Ɉɫɧɨɜɧɵɦ ɫɜɨɣɫɬɜɨɦ ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ
ɦɨɞɟɥɢ ɹɜɥɹɟɬɫɹ ɬɨɬ ɮɚɤɬ, ɱɬɨ ɩɪɨɰɟɫɫ ɜɵɛɨɪɚ ɫɢɦɜɨɥɚ ɧɟɭɫɬɨɣɱɢɜ, ɢ ɩɨɷɬɨɦɭ ɪɟɡɭɥɶɬɚɬ ɫɥɭɱɚɟɧ. ɂɦɟɧɧɨ ɷɮɮɟɤɬ ɫɥɭɱɚɣɧɨɝɨ ɜɵɛɨɪɚ ɜ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɫɢɫɬɟɦɚɯ ɦɨɠɟɬ ɢɦɢɬɢɪɨɜɚɬɶ ɷɮɮɟɤɬ ɢɧɞɢɜɢɞɭɚɥɶɧɨɫɬɢ ɠɢɜɵɯ ɫɢɫɬɟɦ.
ȼɚɠɧɨ, ɱɬɨ ɷɬɢ ɪɟɡɭɥɶɬɚɬɵ ɩɨɥɭɱɟɧɵ ɧɚ
ɨɫɧɨɜɟ ɤɨɧɰɟɩɰɢɢ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɮɨɪɦɚɥɶɧɨɝɨ ɧɟɣɪɨɧɚ ɢ ɤɨɧɬɢɧɭɚɥɶɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɦɨɞɟɥɢ, ɜ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɞɟɬɚɥɶɧɨ ɩɪɨɫɥɟɞɢɬɶ ɩɭɬɶ ɩɟɪɟɯɨɞɚ ɧɟɣɪɨɧɚ
ɢɡ ɨɞɧɨɝɨ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ, ɭɱɢɬɵɜɚɹ ɩɨɜɟɞɟɧɢɟ ɩɪɨɰɟɫɫɨɪɚ ɜ
ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɫɨɫɬɨɹɧɢɹɯ 0 < G < 1. ȼ
ɞɢɫɤɪɟɬɧɵɯ ɫɢɫɬɟɦɚɯ ɞɢɧɚɦɢɱɟɫɤɢɣ ɚɧɚɥɢɡ
ɧɟɜɨɡɦɨɠɟɧ.
Ʌɢɬɟɪɚɬɭɪɚ
1. Ⱥɧɨɯɢɧ Ʉ.ȼ., Ȼɭɪɰɟɜ Ɇ.ɋ., ɂɥɶɢɧ ȼ.Ⱥ.,
Ʉɢɫɟɥɟɜ ɂ.ɂ., Ʉɭɤɢɧ Ʉ.Ⱥ., Ʌɚɯɦɚɧ Ʉ.ȼ.,
ɉɚɪɚɫɤɟɜɢɱ Ⱥ.ȼ., Ɋɵɛɤɚ Ɋ.Ȼ. ɋɨɜɪɟɦɟɧɧɵɟ ɩɨɞɯɨɞɵ ɤ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɚɤɬɢɜɧɨɫɬɢ ɤɭɥɶɬɭɪ ɧɟɣɪɨɧɨɜ in vitro. // Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɛɢɨɥɨɝɢɹ ɢ ɛɢɨɢɧɮɨɪɦɚɬɢɤɚ. 2012. –Ɍ.7. –ʋ2. –ɫ. 372-397.
2. ȿɠɨɜ Ⱥ.Ⱥ., ɒɭɦɫɤɢɣ ɋ.Ⱥ. ɇɟɣɪɨɤɨɦɩɶɸɬɢɧɝ ɢ ɟɝɨ ɩɪɢɦɟɧɟɧɢɹ. Ɇ.: ɆɂɎɂ.
2008. – 222 ɫ.
3. ɋɬɚɧɤɟɜɢɱ Ʌ.Ⱥ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɤɨɝɧɢɬɢɜɧɵɯ ɮɭɧɤɰɢɣ ɧɚɜɢɝɚɰɢɨɧɧɨɝɨ ɩɨɜɟɞɟɧɢɹ ɜ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɪɨɛɨɬɚ.// Ɍɪɭɞɵ 3-ɣ ɤɨɧɮɟɪɟɧɰɢɢ «ɇɟɥɢɧɟɣɧɚɹ ɞɢɧɚɦɢɤɚ ɜ ɤɨɝɧɢɬɢɜɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ», ɇɢɠɧɢɣ ɇɨɜɝɨɪɨɞ, 2013. –
ɫ. 159-161.
4. ɑɟɪɧɚɜɫɤɚɹ Ɉ.Ⱦ., ɑɟɪɧɚɜɫɤɢɣ Ⱦ.ɋ.,
Ʉɚɪɩ ȼ.ɉ., ɇɢɤɢɬɢɧ Ⱥ.ɉ. Ɉ ɪɨɥɢ ɩɨɧɹɬɢɣ «ɨɛɪɚɡ» ɢ «ɫɢɦɜɨɥ» ɜ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ ɫɪɟɞɫɬɜɚɦɢ
ɧɟɣɪɨɤɨɦɩɶɸɬɢɧɝɚ // ɂɡɜɟɫɬɢɹ ɜɭɡɨɜ.
ɉɪɢɤɥɚɞɧɚɹ ɇɟɥɢɧɟɣɧɚɹ Ⱦɢɧɚɦɢɤɚ.
2011. – Ɍ.19. – ʋ 6. – ɫ. 5–20.
5. ɑɟɪɧɚɜɫɤɚɹ Ɉ.Ⱦ., ɑɟɪɧɚɜɫɤɢɣ Ⱦ.ɋ.,
Ʉɚɪɩ ȼ.ɉ., ɇɢɤɢɬɢɧ Ⱥ.ɉ., Ɋɨɠɢɥɨ ə.Ⱥ.
ɉɪɨɰɟɫɫ ɦɵɲɥɟɧɢɹ ɜ ɤɨɧɬɟɤɫɬɟ ɞɢɧɚɦɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɢɧɮɨɪɦɚɰɢɢ. ɑɚɫɬɶ I:
Ɉɫɧɨɜɧɵɟ ɰɟɥɢ ɢ ɡɚɞɚɱɢ ɦɵɲɥɟɧɢɹ //
ɋɥɨɠɧɵɟ ɋɢɫɬɟɦɵ. 2012. – ʋ 1. – ɋ.
25-41; ɑɚɫɬɶ II: ɉɨɧɹɬɢɹ «ɨɛɪɚɡ» ɢ
«ɫɢɦɜɨɥ» ɤɚɤ ɢɧɫɬɪɭɦɟɧɬɵ ɦɨɞɟɥɢɪɨ-
68
ɜɚɧɢɹ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ ɫɪɟɞɫɬɜɚɦɢ
ɧɟɣɪɨɤɨɦɩɶɸɬɢɧɝɚ // ɋɥɨɠɧɵɟ ɋɢɫɬɟɦɵ. 2012. – ʋ2. – ɋ. 47-67; ɑɚɫɬɶ III:
Ɉɞɢɧ ɢɡ ɜɚɪɢɚɧɬɨɜ ɤɨɧɫɬɪɭɤɰɢɢ ɧɟɣɪɨɩɪɨɰɟɫɫɨɪɨɜ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɪɨɰɟɫɫɚ ɦɵɲɥɟɧɢɹ // ɋɥɨɠɧɵɟ ɋɢɫɬɟɦɵ.
2012. – ʋ3. – ɋ. 25-36.
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NATURAL-CONSTRUCTIVE APPROACH IN THINKING MODELLING:
DYNAMIC MODEL OF SYMBOL GEN-
ʪ.ˁ. ˋ̡̛̖̬̦̭̜̌̏ / ˁ̨̨̣̙̦̭̯̽. ˀ̱̥̌̚. ʿ̨̡̡̛̭̯̦̖̣̭̭̌̌. – 2013 – ζ 4 – ˁ. 60-69
ERATION5
Chernavsky D.S., Schepetov D.S., Chernavskaya O.D., Nikitin A.P.
Within the framework of the naturalconstructive approach in thinking modelling
we consider the conception of dynamic formal
neuron that allows tracing the dynamics of all
processes with a neuron. The mathematical
model of symbol generation based on the conception is proposed. The dynamics of the
competitive activity in location is researched.
Moreover, ‘semi-firing’ neurons and their
stability play an important role. Time dependence of interlamellar bonding providing selforganization of the process is analyzed.
Keywords: neuroprocessor, model, image,
symbol, inner- and interlamellar bonding,
self-organization.
5
ɋɬɚɬɶɹ ɩɨɞɝɨɬɨɜɥɟɧɚ ɤ ɩɭɛɥɢɤɚɰɢɢ ɩɨ ɢɬɨɝɚɦ
ɬɪɟɬɶɟɣ ɜɫɟɪɨɫɫɢɣɫɤɨɣ ɤɨɧɮɟɪɟɧɰɢɢ «ɇɟɥɢɧɟɣɧɚɹ
ɞɢɧɚɦɢɤɚ ɜ ɤɨɝɧɢɬɢɜɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ» ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɨɩɨɥɧɟɧɧɵɣ ɩɨ ɢɬɨɝɚɦ ɞɢɫɤɭɫɫɢɢ
ɞɨɤɥɚɞ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɧɚ ɷɬɨɣ ɤɨɧɮɟɪɟɧɰɢɢ.
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