The theorems of unsynchronizability and synchronization for coupled chaotic systems

Abstract

Chaos synchronization has been widely studied and many control methods have been presented, but up to now no criterion has been given for unsynchronizability of two coupled chaotic systems. The unsynchronizability means that the state variables of response system cannot approach to that of driving system forever. In this paper, we propose two theorems which give the criteria of unsynchronizability for two different chaotic dynamic systems and enhance a sufficient criterion for synchronization to necessary and sufficient one. Three simulated examples are given.