Some physical models of the reaction-diffusion equation, and coupled map lattices

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.