The Sliding Mode Controller Design for Hybrid Synchronization of Pan Systems

This paper investigates the hybrid synchronization of identical Pan systems (Pan, Xu and Zhou, 2010) by sliding mode control. In hybrid synchronization of chaotic systems, one part of the master and slave systems is completely synchronized, while the other part is anti-synchronized. The co-existence of complete and anti-synchronization enhances the security of the communication devices using chaotic systems. The stability results derived in this paper for the hybrid synchronization of identical Pan systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve hybrid synchronization of the identical Pan systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical Pan systems.