Dynamic behaviors of a Leslie-Gower model with strong Allee effect and fear effect in prey

Zhenliang Zhu; Yuming Chen; Zhong Li; Fengde Chen; Zhenliang Zhu; Yuming Chen; Zhong Li; Fengde Chen

doi:10.3934/mbe.2023486

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10977-10999. doi: 10.3934/mbe.2023486

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Research article

Dynamic behaviors of a Leslie-Gower model with strong Allee effect and fear effect in prey

1.
College of Mathematics and Data Science, Minjiang University, Fuzhou, 350108, Fujian, P.R. China
2.
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada
3.
College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, Fujian, P.R. China

Received: 15 February 2023 Revised: 04 April 2023 Accepted: 10 April 2023 Published: 23 April 2023

We incorporate the strong Allee effect and fear effect in prey into a Leslie-Gower model. The origin is an attractor, which implies that the ecological system collapses at low densities. Qualitative analysis reveals that both effects are crucial in determining the dynamical behaviors of the model. There can be different types of bifurcations such as saddle-node bifurcation, non-degenerate Hopf bifurcation with a simple limit cycle, degenerate Hopf bifurcation with multiple limit cycles, Bogdanov-Takens bifurcation, and homoclinic bifurcation.
- Leslie-Gower model,
- Allee effect,
- fear effect,
- limit cycle,
- bifurcation
Citation: Zhenliang Zhu, Yuming Chen, Zhong Li, Fengde Chen. Dynamic behaviors of a Leslie-Gower model with strong Allee effect and fear effect in prey[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10977-10999. doi: 10.3934/mbe.2023486

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Abstract

We incorporate the strong Allee effect and fear effect in prey into a Leslie-Gower model. The origin is an attractor, which implies that the ecological system collapses at low densities. Qualitative analysis reveals that both effects are crucial in determining the dynamical behaviors of the model. There can be different types of bifurcations such as saddle-node bifurcation, non-degenerate Hopf bifurcation with a simple limit cycle, degenerate Hopf bifurcation with multiple limit cycles, Bogdanov-Takens bifurcation, and homoclinic bifurcation.

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