Period-doubling Bifurcation and Stability in a Two Dimensional Discrete Prey-predator Model with Allee Effect and Immigration Parameter on Prey

Year 2022, Volume: 43 Issue: 1, 88 - 97, 30.03.2022

Figen Kangalgil Feda İlhan

https://doi.org/10.17776/csj.1026330

Cited By: 3

Abstract

This article is about the dynamics of a discrete-time prey-predator system with Allee effect and immigration parameter on prey population. Particularly, we study existence and local asymptotic stability of the unique positive fixed point. Furthermore, the conditions for the existence of bifurcation in the system are derived. In addition, it is shown that the system goes through period-doubling bifurcation by using bifurcation theory and center manifold theorem. Eventually, numerical examples are given to illustrate theoretical results.

Keywords

Prey-predator model, Stability analysis, Fixed point, Allee effect, Period-doubling bifurcation.

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