Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization

In this paper, we investigate the ultimate bound and positively invariant set for a new chaotic system via the generalized Lyapunov function theory. For this system, we derive a three-dimensional ellipsoidal ultimate bound and positively invariant set. In addition, the two-dimensional bound with respect to x z and y z are established. Finally, the result is applied to the study of completely chaos synchronization, an exact threshold is given with the system parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.