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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.


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About this article

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

Year: 2015

Sergey Aleksandrovich

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