Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection

In this paper, we investigate the hybrid synchronization behavior in an array of coupled chaotic systems with ring connection, of which means complete synchronization (CS) and anti-synchronization (AS) could coexist. First, the anti-synchronization controllers are designed, which can transform the synchronization error dynamic system into a nonlinear system with an antisymmetric structure. Second, we investigate the complete synchronization behavior in such a chaotic system under the anti-synchronization control. After that, the stability conditions are given for reaching hybrid synchronization. Finally, numerical examples and simulation results are presented to verify and validate the hybrid synchronization behavior in coupled chaotic system.