Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection

This paper considers the synchronization and anti-synchronization problem of N different coupled chaotic systems with ring connections. Employing the direct design method to design the synchronization and anti-synchronization controllers which can transform the error systems into a stable system with special anti-symmetric structure. Some simple stability criteria are then derived for reaching the synchronization in such systems. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical.