Some physical models described by the reaction-diffusion equation, and coupled map lattices. (English. Russian original) Zbl 1160.37423

Russ. Math. Surv. 59, No. 3, 481-513 (2004); translation from Usp. Mat. Nauk 59, No. 3, 81-114 (2004).
Summary: A number of models are surveyed which appear in physics, biology, chemistry, and other areas and which are described by a reaction-diffusion equation. The corresponding coupled map lattice (CML) system is obtained by discretizing this equation. These CMLs are classified by the type of the dynamics of the local map. Several different types of behavior are observed: Morse-Smale type systems, systems with attractors, and systems with Smale horseshoes.


37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
35K57 Reaction-diffusion equations
37D15 Morse-Smale systems
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37E05 Dynamical systems involving maps of the interval
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
92E20 Classical flows, reactions, etc. in chemistry
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