Abstract
We describe coupled map lattices (CMLs) of unbounded media corresponding to some well-known evolution partial differential equations (including reaction-diffusion equations and the Kuramoto-Sivashinsky, Swift-Hohenberg and Ginzburg-Landau equations). Following Kaneko we view CMLs also as phenomenological models of the medium and present the dynamical systems approach to studying the global behavior of solutions of CMLs. In particular, we establish spatio-temporal chaos associated with the set of traveling wave solutions of CMLs as well as describe the dynamics of the evolution operator on this set. Several examples are given to illustrate the appearance of Smale horseshoes and the presence of the dynamics of Morse-Smale type.
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