Global Chaos Synchronization of Harb and Pan Systems by Active Nonlinear Control

Since the seminal work by Pecora and Carroll in 1990, the global chaos synchronization problem has been studied extensively in the chaos literature and it has important applications in secure communications and data encryption. This paper investigates the global chaos synchronization of identical Harb systems (2002), identical Pan systems (2010) and non-identical Harb and Pan chaotic systems. Active nonlinear control is the method adopted to achieve the complete synchronization of the identical and different Harb and Pan systems. Our stability results derived in this paper are established using active control method and Lyapunov stability theory. We use a quadratic Lyapunov function for establishing global asymptotic stability of the error dynamics for the chaos synchronization problems. Since the Lyapunov exponents are not required for these calculations, the nonlinear control method is effective and convenient to synchronize the identical and different Harb and Pan systems. Numerical simulations are shown to validate and illustrate the effectiveness of the synchronization results derived in this paper.