Bifurcations in a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges

Fengde Chen, Zhong Li, Qin Pan and Qun Zhu

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

Abstract: In this paper, we study a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges. It is shown that the model can undergo a cusp type degenerate Bogdanov–Takens bifurcation of codimension 4, focus and elliptic types degenerate Bogdanov–Takens bifurcations of codimension 3, and degenerate Hopf bifurcation of codimension 3 as the parameters vary. The model can exhibit the coexistence of multiple positive steady states, multiple limit cycles, and homoclinic loops. Our results indicate that a larger prey refuge contributes to the coexistence of both species. Numerical simulations, including three limit cycles, quadristability, a large-amplitude limit cycle enclosing three positive steady states and a homoclinic loop, two large-amplitude limit cycles enclosing three positive steady states, are presented to illustrate the theoretical results.

Keywords: Leslie–Gower predator–prey model; Strong Allee effect; Constant prey refuge; Bogdanov–Takens bifurcation; Hopf bifurcation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000074

DOI: 10.1016/j.chaos.2025.115994

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