Multi-switching combination synchronization of spatiotemporal coupled chaotic systems with complexities

Abstract

In this paper, multi-switching combination synchronization for spatiotemporal coupled systems are studied. For the local system in spatiotemporal coupled systems, different local dynamic behaviors are taken into consideration. With the Backstepping method, synchronization controllers are designed for different possible combined errors and corresponding theorems are derived according to the Lyapunov stability theory. In the stability design, multi-switching combination synchronizations can be translated into corresponding combination projective synchronization with different projective factors. In addition, complexities including time delays are considered in the synchronization process. At last, simulation results show the robustness and effectiveness of our methods.