Global chaos synchronization of Lü and pan systems by adaptive nonlinear control

Abstract

This paper investigates the adaptive synchronization of identical Pan systems (2010) and synchronization of non-identical Lü system (2002) and Pan system (2010). In adaptive synchronization of identical chaotic systems, the parameters of the master and slave systems are unknown and we devise feedback control laws using estimates of the system parameters. In adaptive synchronization of different chaotic systems, the parameters of the master system are known, but the parameters of the slave system are unknown and we devise feedback control laws using the estimates of the parameters of the slave system. Our adaptive synchronization results derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is effective and convenient to synchronize identical and different Lü and Pan systems. Numerical simulations are given to illustrate the effectiveness of the proposed adaptive synchronization schemes for the global chaos synchronization of chaotic systems addressed in this paper. © 2011 Springer-Verlag.