Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate

Abstract

In this paper, we study the stability and bifurcation analysis of a class of discrete-time dynamical system with capture rate. The local stability of the system at equilibrium points are discussed. By using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Hopf bifurcation in the interior of R+2 are proved. The numerical simulations show that the capture rate not only affects the size of the equilibrium points, but also changes the bifurcation phenomenon. It was found that the discrete system not only has flip bifurcation and Hopf bifurcation, but also has chaotic orbital sets. The complexity of dynamic behavior is verified by numerical analysis of bifurcation, phase and maximum Lyapunov exponent diagram.