Global attractive sets of a novel bounded chaotic system

This paper is concerned with the boundedness of solutions of a new chaotic system. For this system, the global exponential attractive set and positively invariant set are derived based on generalized Lyapunov function theory and the extremum principle of function. Furthermore, we can conclude that the rate of the trajectories of the system going from the exterior of the attractive set ? ? to the interior of the attractive set ? ? is an exponential rate. The rate of the trajectories is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.