Chaotic patterns in coupled map lattices

In this paper we consider the existence and stability of chaotic patterns (periodic in space and chaotic in time) in coupled map lattice with local map f(x)=sin x. This is equivalent to investigating the stable chaotic set of some high-dimensional dynamical system. It is not easy in high-dimensional space to apply horseshoe technique or the theory of transversal homoclinic point and transversal cycles to show the existence of chaotic set. Motivated by the concept of anti-integrability (Aubry S. Physica D 1995;86:284–96), we prove the corresponding finite-dimensional system possesses stable chaotic set Λα in phase space RN for the nonlinearity strength α appropriately large and the coupling strength small. Consequently, there exist stable chaotic patterns in CML system.