Control and synchronization for a chaotic system

In this paper, based on the qualitative properties of a modified Chen system, the feedback control law is applied to suppress chaos to equilibria or limit cycles. Some sufficient conditions of chaos control are attained in terms of rigorous mathematical theory. Two different synchronization methods, such as the linear coupling technique and the adaptive active control approach, are applied to achieve the state synchronization of the two modified Chen systems. In addition, some sufficient conditions of chaos synchronization are gained. Numerical simulations verify our theory and demonstrate the feasibility and effectiveness of the proposed methods.