Adaptive Coexistence of Synchronization and Anti-Synchronization for a Class of Switched Chaotic Systems

This paper addresses the problem of coexistence of synchronization and anti-synchronization (CSAS) for a class of switched chaotic systems by adaptive control method, where the switched system is realized by unified chaotic systems under arbitrary switching signal. Firstly, necessary and sufficient conditions for the CSAS of the chaotic systems are proposed from two perspectives, one is by analyzing the parity of the system expression, and the other is by decomposing the system. Secondly, according to the obtained necessary and sufficient conditions, 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 a 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.