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ALLEE EFFECT IN A RICKER TYPE DISCRETE-TIME PREDATOR–PREY MODEL WITH HOLLING TYPE-II FUNCTIONAL RESPONSE

H. EL-METWALLY

Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

E-mail Address: helmetwally@mans.edu.eg

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A. Q. KHAN

https://orcid.org/0000-0002-0278-1352

Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan

E-mail Address: abdulqadeerkhan1@gmail.com

Corresponding author.

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, and

M. Y. HAMADA

Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

E-mail Address: moe_hamada87@hotmail.com

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https://doi.org/10.1142/S0218339023500201Cited by:7 (Source: Crossref)

Abstract

In recent years, the stability of the predator–prey model subject to the Allee effect has become an interesting issue. This study investigates the effect of Allee effect on the stability of a discrete-time predator–prey model with Holling type-II functional response. Using equilibrium analysis, stability analysis and bifurcation theory, the mathematical characteristics of the proposed model are examined. Model experiences flip bifurcation and Neimark–Sacker bifurcation based on the center manifold theorem and bifurcation theory. Our analytical results are demonstrated by numerical simulations.

Keywords:

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