Abstract
In this paper, we devoted to investigate a hyperelliptic estimate of the ultimate bound and positively invariant set for the new system via the Lyapunov function method. Furthermore, we obtained the global exponential attractive set , which is an exponential decay rate. The rate of the trajectories of the system going from the exterior to the interior of the set . Numerical simulations are presented to show the effectiveness and the feasibility. The theoretical results obtained will find wide applications in cascade control and chaos synchronization.
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