Synchronization of Rikitake Chaotic Attractor via Partial System States

Abstract

This paper treats the chaotic synchronization problem for Rikitake chaotic systems via unidirectional coupling with partial systems states. Two control approaches, namely the self coupling of single state variable and nonlinear feedback controller with partial systems states, are investigated. Based on the Lyapunov stability technique, control laws based on single variable of driven system are derived such that the two identical Rikitake chaotic systems are asymptotically synchronized, where the control scheme doesn't need additional energy and it just relies on the self coupling of single state variable of the chaotic systems. Meanwhile, the complete synchronization for two identical Rikitake chaotic systems by feedback control laws with partial systems states is also derived using the conditions of asymptotical stability and exponential stability. Finally, numerical experimental results of two synchronized Rikitake chaotic systems are presented.