Hybrid Synchronization Problem of a Class of Chaotic Systems by an Universal Control Method

Abstract

The hybrid synchronization problem of a class of chaotic systems is investigated in this paper. Firstly, the existence of hybrid synchronization problems in such systems is proved theoretically by a proposed necessary and sufficient condition. That is, the hybrid synchronization problem is equivalent to solve a group of nonlinear algebraic equations about α . It is interesting that one value of α indicates one type of synchronization. Secondly, all solutions for the hybrid synchronization problem are obtained by finding solutions of all the above equations about α . Thirdly, an universal control method is proposed to realize such hybrid synchronization problems. Finally, illustrative examples are provided to verify the validity and effectiveness of the obtained results.