Analyzing bifurcation, stability, and chaos control for a discrete-time prey-predator model with Allee effect

Authors

FİGEN KANGALGİL
NİLÜFER TOPSAKAL
NİHAL ÖZTÜRK

DOI

10.55730/1300-0098.3253

Abstract

In this paper, the qualitative behavior of a discrete-time prey-predator model with Allee effect in prey population is discussed. Firstly, the existence of the fixed points and their topological classification are analyzed algebraically. Then, the conditions of existence for both period-doubling and Neimark--Sacker bifurcations arising from coexistence fixed point with the help of the center manifold theorem and bifurcation theory are investigated. OGY feedback control method is implemented to control chaos in the proposed model due to the emergence of bifurcations. Finally, numerical simulations are performed to support the theoretical findings.

Keywords

Prey-predator model, stability analysis, Allee effect, period-doubling bifurcation, Neimark--Sacker bifurcation, Chaos control

First Page

2047

Last Page

2068

Recommended Citation

KANGALGİL, FİGEN; TOPSAKAL, NİLÜFER; and ÖZTÜRK, NİHAL (2022) "Analyzing bifurcation, stability, and chaos control for a discrete-time prey-predator model with Allee effect," Turkish Journal of Mathematics: Vol. 46: No. 6, Article 1. https://doi.org/10.55730/1300-0098.3253
Available at: https://journals.tubitak.gov.tr/math/vol46/iss6/1