Constructive proof of globally exponentially attractive and positively invariant set of the chaotic Chen's system

In this paper, a constructive proof of the globally exponentially attractive and positively invariant set for the chaotic Chen's system is given, by using several generalized positive de nite Lyapunov functions. The problem of the existence of a globally exponentially attractive set for the chaotic Chen's system is completely solved, which is a long standing open theoretical problem. Methods provided herein can be useful for the study of other forms of chaotic systems.