Chaotic Dynamics and Control of a Discrete-Time Chen System

Abstract

We investigate a discrete-time Chen system. First, we give the topological classifications of the fixed points of this system. Then, we analytically show that the discrete Chen system underlies a Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. We confirm the existence of a PD and NS bifurcation via the explicit PD-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory. We performed numerical simulations to confirm our analytical results. Furthermore, we use the 0-1 chaos test to quantify whether there is chaos in the system or not. At the end, the hybrid control strategy and the OGY (Ott, Grebogi, and Yorke) method are applied to eliminate chaotic trajectories of the system.