Chaos control and synchronization of a modified chaotic system

By replacing a quadratic nonlinear term in Lu system with a piecewise linear signum (PWL) function, a new simplified three-dimensional piecewise continuous autonomous system (a modified Lu system) is introduced. The qualitative properties of the modified Lu system are studied. Based on these properties, the feedback control law is applied to suppress chaos to one of the three equilibria. Several different synchronized methods, such as the active control, one way coupling by active control, and the adaptive active control are applied to achieve the state synchronization of two identical modified Lu systems. These results show that after the simplification, the modified Lu system can still keep the basic and typical nonlinear phenomena. Compared with the original Lu system, the modified Lu system has a lot of advantages, by which the modified Lu system can be more easily implemented by theoretical analysis, and more practicable made by secret communications. (C) 2006 Elsevier Ltd. All rights reserved.