Chaos Control and Behavior Analysis of a Discrete-Time Dynamical System with Competitive Effect

Abstract

This paper is about a class of discrete-time dynamical systems with competitive effects. The local stability of the positive equilibrium point of the system and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are discussed by using the center manifold theorem and bifurcation theory. In addition, the direction of the flip bifurcation and Neimark-Sacker bifurcation is given. Furthermore, a feedback control strategy is employed to control bifurcation and chaos in the system. Finally, flip bifurcation, Neimark-Sacker bifurcation and chaos control strategy are verified with the help of numerical simulations.