Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control

In this paper, we apply control method to derive new results for the antisynchronization of identical uncertain Lü systems (2002), identical uncertain Pan systems (2010) and non-identical Lü and uncertain Pan systems. In adaptive anti-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 antisynchronization of non-identical chaotic systems, the parameters of the master system are known, but the parameters of the slave systems are unknown and we devise feedback control laws using the estimates of the parameters of the slave system. Our adaptive antisynchronization results derived in this paper for uncertain Lü and Pan systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to achieve anti-synchronization of identical and non-identical Lü and Pan chaotic systems. Numerical simulations are given to demonstrate the effectiveness of the proposed adaptive anti-synchronization schemes for the uncertain chaotic systems addressed in this paper.© EuroJournals Publishing, Inc. 2011.