Hybrid Chaos Synchronization of 4-d Hyperchaotic Qi and Jia Systems by Active Nonlinear Control

This paper investigates the hybrid chaos synchronization of identical 4-D hyperchaotic Qi systems, 4-D identical hyperchaotic Jia systems and hybrid synchronization of 4-D hyperchaotic Qi and Jia systems. The hyperchaotic Qi system (2008) and hyperchaotic Jia system (2007) are important models of hyperchaotic systems. Hybrid synchronization of the 4-dimensional hyperchaotic systems addressed in this paper is achieved through complete synchronization of two pairs of states and anti-synchronization of the other two pairs of states of the underlying systems. Active nonlinear control is the method used for the hybrid synchronization of identical and different hyperchaotic Qi and Jia systems and the stability results have been established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the proposed nonlinear control method is effective and convenient to achieve hybrid synchronization of the hyperchaotic Qi and Jia systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed chaos synchronization schemes.