Anti-Synchronization of Liu and Li 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 anti-synchronization of identical Liu systems (2004), identical Li systems (2009) and non-identical Liu and Li chaotic systems. Active nonlinear control is the method adopted to achieve the anti-synchronization of the identical and different Liu and Li 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 anti-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 Liu and Li systems. Numerical simulations are shown to validate and illustrate the effectiveness of the anti-synchronization results derived in this paper.