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

Xiongxiong Du, Xiaoling Han and Ceyu Lei
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Xiongxiong Du: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Xiaoling Han: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Ceyu Lei: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2022, vol. 10, issue 14, 1-15

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.

Keywords: predator-prey system; center manifold theorem; maximum lyapunov exponent; flip bifurcation; hopf bifurcation; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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