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

Author

Listed:
  • Chen, Fengde
  • Li, Zhong
  • Pan, Qin
  • Zhu, Qun

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.

Suggested Citation

  • Chen, Fengde & Li, Zhong & Pan, Qin & Zhu, Qun, 2025. "Bifurcations in a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000074
    DOI: 10.1016/j.chaos.2025.115994
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