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Classification of solutions of a system of nonlinear diffusion equations in a neighborhood of a bifurcation point

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Abstract

The theory of reaction-diffusion systems in a neighborhood of a bifurcation point is considered. The basic types of space-time ordering, diffusion chaos in such systems, and sequences of bifurcations leading to complication of solutions are studied. A detailed discussion is given of a hierarchy of simplified models (one- and two-dimensional mappings, systems of ordinary differential equations, and others) which make it possible to carry out a qualitative analysis of the problem studied in the case of small regions. A number of generalizations of the equations studied and the simplest types of ordering in the two-dimensional case are described.

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Authors
  1. T. S. Akhromeeva
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  2. S. P. Kurdyumov
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  3. G. G. Malinetskii
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  4. A. A. Samarskii
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 28, 207–313, 1986.

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Akhromeeva, T.S., Kurdyumov, S.P., Malinetskii, G.G. et al. Classification of solutions of a system of nonlinear diffusion equations in a neighborhood of a bifurcation point. J Math Sci 41, 1292–1356 (1988). https://doi.org/10.1007/BF01098786

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