Adaptive coexistence of synchronization and anti-synchronization for a class of switched chaotic systems

Abstract

This paper addresses the problem of coexistence of synchronization and anti-synchronization (CSAS) for a class of switched chaotic systems by adaptive control method. The unified chaotic system as the subsystems of the switched system is investigated. Firstly, two theorems describe the necessary and sufficient condition for the CSAS of the chaotic systems and proofed rigorously. Secondly, according to the given two theorems, two algorithms are given to search the synchronization variables and anti-synchronization variables in the chaotic systems. Thirdly, the CSAS of the switched chaotic system can be achieved by the designed adaptive global controller with only one input channel under the arbitrary switching signal. Finally, the numerical simulation results verify the validity and effectiveness of the method we obtained.