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By using the method of symbolic dynamics, we discuss the global synchronization and homoclinic bifurcations in a class of globally coupled systems with piecewise affine local map. We derive by virtue of admissibility condition the region of coupling strength for which the coupled system is globally synchronized. Homoclinic bifurcations are also discussed by making use of the admissibility condition...
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)=sinx. 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...
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