SPATIAL CHAOTIC STRUCTURE OF ATTRACTORS OF REACTION-DIFFUSION SYSTEMS

The dynamics described by a system of reaction-diffusion equations wit h a nonlinear potential exhibits complicated spatial patterns. These p atterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. T he estimates of homotopy complexity of attractors are obtained in term s of geometric characteristics of the potential and other data of the problem.