Estimating the bound set of a chaotic system and its application in chaos synchronization

Abstract

In this paper, we investigate the ultimate bound set for a chaotic system. Based on Lagrange multiplier method, an optimization problem has been done analytically to calculate a precise ultimate bound set of the chaotic system. Apart from that application of the bound set is also discussed and it can be used to study chaos synchronization. Synchronization has been realized between two identical chaotic systems via globally exponential approach. Resulting bound sets and synchronization are quantitatively tested to illustrate the effectiveness of the theoretical analysis.