Two theorems of generalized unsynchronization for coupled chaotic systems

Generalized chaos synchronization has been widely studied and many control methods have been presented, but up to now no criterion has been given for generalized unsynchronization. The generalized unsynchronization means that the state variables of two coupled chaotic systems cannot approach generalized synchronization. In this paper, we propose two theorems which give the criteria of generalized unsynchronization for two different chaotic dynamic systems with whatever large strength of linear coupling. Two simulated examples are also given.