April 2015, № 4 (179)

Kucherenko M.G., Kucherenko M.A. ABOUT TWO EVOLUTIONARY MODELS WITH A NONLOCAL QUADRATIC NONLINEARITYThe analysis of the properties of two well-known mathematical models of evolutionary Biophysics and physics of condensed matter, based on the differential equations of parabolic type is made. It is noted that the linearization of bilinear nonlocal member of the first model allows you to use features of the structure of the discrete spectrum of the reduced operator to analyze the dynamic mode of the explosive instability. The nonlocality of the second model included in the nonlinear operator of the Fokker-Planck, which provides spatial structuring of the system even in the absence of centers of autocatalysis. It is shown that both models do not lose their meaning and can be transferred without any significant changes in its structure in the area of methodology education processes by replacing the original biological or physical concepts equivalent concepts in the theory of knowledge. If successful broadcast of the characteristics and parameters of the overall results and conclusions of evolutionary models can be used to develop new learning strategies and original educational methods.Key words: evolutionary models, the processes of generation-destruction, explosive instability, spatial structures.

Download

References:

1. Ebеling W., Feistel R. Physik der Selbst-Organisation und Evolution.— Berlin: Akademie-Verlag, 1982.

2. Mikhailov, A. S. Critical phenomena in environments with reproduction, decay and diffusion / A. S. Mikhailov, I. V. Uporov // Usp. Fiz. Nauk. 1984. V. 144. — P. 79 — 112.

3. Zeldovich, Y. B. Intermittency of passive fields in random media / Y. B. Zeldovich, S. A. Molchanov, A. A. Ruzmaikin, D. D. Sokolov // JETP. 1985. — V. 89. — P. 2061 — 2072.

4. Zeldovich, Y. B. Intermittency in random environment / Y.B. Zeldovich, S. A. Molchanov, A.A. Ruzmaikin, D. D. Sokolov // Usp. Fiz. Nauk. 1987. -V. 152. — P. 3 — 32.

5. Vasiliev, A. Autowave processes. / V.A. Vasiliev, Yu.M. Romanovsky, V. G. Yakhno, Moscow: Nauka. Modern problems of physics. 1987.

6. Martinson, L. K. Differential equations of mathematical physics. / L. K. Martinson, Yu.I. Malov. MSTU. N. E. Bauman. 2002. — 368 p.

7. Kolmogorov, A. N. The study of the diffusion equation coupled with an increase in the amount of a substance, and its application to one biological problem / A. N. Kolmogorov, I.G. Petrovskii, N. S. Piskunov // Bulletin of Moscow state University. Series: Mathematics and mechanics. 1937. -Vol. 1. — P. 1-26.

8. Ablowitz, M.J. Explicit solutions of Fisher's equation for a special wave speed / M.J. Ablowitz, A. Zeppetella // Bull. Math. Biology. 1979. — Vol.41. — P. 835-840.

9. Fisher, R.A. The wave of advance of advantageous genes / R.A. Fisher // Annals of Eugenics. 1937. — Vol.7. — P.355-369.

10. Kucherenko, M.G. Kinetics of the static nonlinear self-quenching of luminescence in colloidal systems / M.G. Kucherenko // Coll. J. 1998. — V.60. –No 3. — P. 347-355.

11. Tikhonov, A. N., Samarskii, A. A. Equations of mathematical physics / A. N. Tikhonov and A. A. Samarskii. Moscow: Moscow state University. 1997.

12. Lifshitz, I. M. Introduction to the theory of disordered systems / I. M. Lifshits, S. A. Gredeskul, L. A. Pastur, Moscow: Nauka. 1982.

13. Sugakov, V. I. Superlattices of the exciton density / V.I. Sugakov // Solid State Physics. 1986. –V. 28. -No. 8. -P. 411-415.

14. Izvekov, S. V. Light induced dissipative superlattices of the exciton density and vector polarization in molecular crystals with impurities / S. V. Izvekov, V. I. Sugakov // Solid State Physics. 1992. -V. 34. -No. 1. -P. 103-107.

15. Kucherenko, M. G. Evolution of cognitive density field in the space of concepts / M. G. Kucherenko, M. A. Kucherenko // University complex as a region. center of education, science and culture [Electronic resource]: Proc. Scient.-method. Confer. (With international participation); Orenburg. State Univ. — Orenburg: OSU. 2015. P. 1076-1083.

16. Chernavskii, A. S. Synergetics and information. Dynamic information theory. Series synergetics: From past to future / A. S. Chernavsky // URSS. M.: 2004. — 288 p.

About this article

Authors: Kucherenko M.G., Kucherenko M.A.

Year: 2015

Editor-in-chief

Sergey Aleksandrovich
MIROSHNIKOV

© Электронное периодическое издание: ВЕСТНИК ОГУ on-line (VESTNIK OSU on-line), ISSN on-line 1814-6465
Зарегистрировано в Федеральной службе по надзору в сфере связи, информационных технологий и массовых коммуникаций
Свидетельство о регистрации СМИ: Эл № ФС77-37678 от 29 сентября 2009 г.
Учредитель: Оренбургский государственный университет (ОГУ)
Главный редактор: С.А. Мирошников
Адрес редакции: 460018, г. Оренбург, проспект Победы, д. 13, к. 2335
Тел./факс: (3532)37-27-78 E-mail: vestnik@mail.osu.ru