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

Abstract

In this study, researchers apply control method to derive new results for the anti-synchronization of identical uncertain Lu systems, identical uncertain Pan systems and non-identical Lu 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 anti-synchronization 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. The adaptive anti-synchronization results derived in this study for uncertain Lu 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 Lu 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 study. © Medwell Journals, 2011.