Dynamics of a Discrete-Time Chaotic Lü System

Abstract

A discrete-time chaotic Lü system is investigated. Firstly, we give the conditions of local stability of this system around feasible fixed points. Then, we show analytically that discretized Lü system undergoes a flip-Neimark Sacker (NS) bifurcation when one of the system parameter varies near its critical value. We confirm the existence of flip-NS bifurcation via explicit Flip-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory and bifurcation theory. We carry out numerical simulations to affirm our analytical findings. Furthermore, we present Maximum Lyapunov exponents (MLEs) and Fractal dimension (FD) numerically in order to justify whether chaos exists in the system or not. At the end, we apply hybrid control strategy to eliminate chaotic trajectories of the system.