Synchronous Chaos in Coupled Map Lattices with General Connectivity Topology

Abstract

The purpose of the paper is to address the synchronous chaos in coupled map lattices with general connectivity topology. Our main results contain the following. First, the master stability functions also hold for general connectivity topology with coupling through a nonlinear function that needs to be exactly the individual chaotic map. Second, the synchronization curve, composed of pieces of transverse Lyapunov exponent curves, is constructed. Third, necessary and sufficient conditions on coupling strength for yielding the synchronous chaos of the system are given. Moreover, the coupling strength $d_c$ giving the fastest convergence rate of the initial values toward the synchronous state is explicitly obtained. It is also proved that such $d_c$ is independent of the choice of the individual map. Finally, our results here can be applied to address questions of wavelength bifurcations and size instability.