Analysis of Codimension-Two Bifurcations in a Discrete Modified Leslie-Gower System with Beddington-DeAngelis Response

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DOI: https://doi.org/10.28924/2291-8639-24-2026-71
Published: Mar 12, 2026
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Abdulaziz Almaslokh, A.A. Elsadany, A. S. Zaki, Analysis of Codimension-Two Bifurcations in a Discrete Modified Leslie-Gower System with Beddington-DeAngelis Response, Int. J. Anal. Appl., 24 (2026), 71.

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Abdulaziz Almaslokh, A.A. Elsadany, A. S. Zaki

Abstract

This paper investigates a discrete-time modified Leslie-Gower prey-predator model featuring the Beddington-DeAngelis functional response. The primary aim is to delve into the intricate dynamics of this model. Initially, we assess the existence and local stability of the model’s fixed points. Subsequently, we employ bifurcation theory and the normal form theorem to scrutinize the bifurcation behaviors of the model. Our research uncovers several co-dimension two bifurcations, such as 1:2 resonance, 1:3 resonance, and 1:4 resonance. Numerical simulations are performed to support the theoretical findings.

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