Anti-Synchronization of Pan and Lorenz-Lu-Liu-Cai Chaotic Systems by Active Nonlinear Control

In this paper, the authors investigate the anti-synchronization of chaotic Pan, Lorenz, and Lu systems and anti-synchronization of Liu and Cai systems. Global exponential synchronization of Pan, Lorenz, Lu, Liu, and Cai chaotic systems are established by using Lyapunov stability theory. Numerical simulations are performed to illustrate the effectiveness of the proposed synchronization schemes for Pan, Lorenz, Lu, Liu, and Cai chaotic systems. DOI: 10.4018/jalr.2012040102 16 International Journal of Artificial Life Research, 3(2), 15-25, April-June 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. the sampled-data feedback method (Murali & Lakshmanan, 2003), OGY method (Ott, Grebogi, & Yorke, 1990), back stepping method (Wu & Lu, 2003), active control method (Ho & Hung, 2002; Hagn, 1967; Li, Chlouverakis, & Xu, 2009; Liu et al., 2004; Lu et al., 2004l Lorenz & Atmos, 1963; Murali & Lakshmann, 2003; Ott, Grebogi, & Yorke, 1990; Pecora & Carrol, 1990; 1991; Pan, Xu, & Zhou, 2010; Sundarapandian, 2011a, 2011b, 2011c; Sundarapandian & Sivaperumal, 2011; Wu & Lu, 2003; Yau, 2004), etc. In this manuscript, we study the antisynchronization of non identical Pan, Lorenz, Lu, Liu and Cai chaotic systems using active nonlinear control. Explicitly, using active nonlinear control and Lyapunov stability theory, we achieve the global chaos anti-synchronization of non identical chaotic system addressed above. Numerical simulations are carried out to illustrate and validate the proposed synchronization results