Hybrid Synchronization of Hyperchaotic Liu Systems via Sliding Mode Control

This paper derives new results for the hybrid synchronization of identical hyperchaotic Liu systems (Liu, Liu and Zhang, 2008) via sliding mode control. In hybrid synchronization of master and slave systems, the odd states of the two systems are completely synchronized, while their even states are antisynchronized. The stability results derived in this paper for the hybrid synchronization of identical hyperchaotic Liu systems have been proved 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 antisynchronization of the identical hyperchaotic Liu systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical hyperchaotic Liu systems.