On the classification of the solutions of a system of nonlinear diffusion equations in a neighborhood of a bifurcation point

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.