Abstract
We study the dynamics of coupled map lattices (CMLs) as the coupling strength c varies. Our main results are as follows. First, we show that for small c, as many snap-back repellers as possible can be obtained. Second, we study the “intermediate” range of c. In particular, the optimal range of c for getting local synchronization of CMLs can be explicitly constructed by indentifying its center, left and right radii. The center of coupling strength for local synchronization gives the fastest convergence rate of the initial values toward synchronous manifold. Moreover, we prove that the center depends on the number of nodes and the connectivity topology G, and is independent of the choice of uncoupled dynamics f