Global Synchronization of Coupled Map Lattices

Abstract

Global synchronization of coupled map lattices are investigated in this paper. A sufficient condition for global synchronization is derived. Unlike other approaches, the coupled lattices is not linearized in this paper. Instead, the sufficient condition for the synchronization is obtained here by introducing a reference state along with Lyapunov function method, and this condition is simply given in terms of the maximum absolute value of eigenvalues of the coupling matrices those are not equal to one. Moreover, we give how to construct the coupling matrix to guarantee global synchronization of coupled map lattices based on two comparing matrices, which is very convenient to use. A typical example of coupled map lattices with chaotic nodes is finally used to verify the theoretical results and the effectiveness of the proposed synchronization scheme.