Hybrid Chaos Synchronization of Liu and Lü Systems by Active Nonlinear Control

This paper investigates the hybrid chaos synchronization of identical Liu systems, identical Lü systems, and non-identical Liu and Lü systems by active nonlinear control. Liu system (Liu

et al.

2004) and Lü system (Lü and Chen, 2002) are important models of three-dimensional chaotic systems. Hybrid synchronization of the three-dimensional chaotic systems considered in this paper are achieved through the synchronization of the first and last pairs of states and anti-synchronization of the middle pairs of the two systems. Sufficient conditions for hybrid synchronization of identical Liu, identical Lü, and non-identical Liu and Lü systems are derived using active nonlinear control and Lyapunov stability theory. Since the Lyapunov exponents are not needed for these calculations, the active nonlinear control is an effective and convenient method for the hybrid synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the proposed synchronization schemes.