Complex dynamics of a nonlinear discrete predator-prey system with Allee effect-Reference-Cited by-同舟云学术

Complex dynamics of a nonlinear discrete predator-prey system with Allee effect

Published:2024-01-01 Issue:1 Volume:22 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Wang Jing¹,Lei Ceyu²

Affiliation:

1. School of Education, Lanzhou University of Arts and Science , Lanzhou 730010 , P.R. China

2. Department of Mathematics, Northwest Normal University , Lanzhou , 730070 , P.R. China

Abstract

Abstract The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. In this article, we study a discrete predator-prey system with Holling type II functional response and Allee effect. First, the number of fixed points of the system, local stability, and global stability is discussed. The population changes of predator and prey under strong or weak Allee effects are proved using the nullclines and direction field, respectively. Second, using the bifurcation theory, the bifurcation conditions for the system to undergo transcritical bifurcation and Neimark-Sacker bifurcation at the equilibrium point are obtained. Finally, the dynamic behavior of the system is analyzed by numerical simulation of bifurcation diagram, phase diagram, and maximum Lyapunov exponent diagram. The results show that the system will produce complex dynamic phenomena such as periodic state, quasi-periodic state, and chaos.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2024-0013/pdf

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