Dynamic analysis of a Leslie-Gower predator-prey model with the fear effect and nonlinear harvesting

Hongqiuxue Wu; Zhong Li; Mengxin He; Hongqiuxue Wu; Zhong Li; Mengxin He

doi:10.3934/mbe.2023825

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18592-18629. doi: 10.3934/mbe.2023825

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Research article

Dynamic analysis of a Leslie-Gower predator-prey model with the fear effect and nonlinear harvesting

1.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, Fujian, China
2.
College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, Fujian, China

Received: 16 July 2023 Revised: 06 September 2023 Accepted: 17 September 2023 Published: 27 September 2023

In this paper, we investigate the stability and bifurcation of a Leslie-Gower predator-prey model with a fear effect and nonlinear harvesting. We discuss the existence and stability of equilibria, and show that the unique equilibrium is a cusp of codimension three. Moreover, we show that saddle-node bifurcation and Bogdanov-Takens bifurcation can occur. Also, the system undergoes a degenerate Hopf bifurcation and has two limit cycles (i.e., the inner one is stable and the outer is unstable), which implies the bistable phenomenon. We conclude that the large amount of fear and prey harvesting are detrimental to the survival of the prey and predator.
- nonlinear harvesting,
- fear effect,
- Leslie-Gower,
- Hopf bifurcation,
- Bogdanov-Takens bifurcation
Citation: Hongqiuxue Wu, Zhong Li, Mengxin He. Dynamic analysis of a Leslie-Gower predator-prey model with the fear effect and nonlinear harvesting[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18592-18629. doi: 10.3934/mbe.2023825

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Abstract

In this paper, we investigate the stability and bifurcation of a Leslie-Gower predator-prey model with a fear effect and nonlinear harvesting. We discuss the existence and stability of equilibria, and show that the unique equilibrium is a cusp of codimension three. Moreover, we show that saddle-node bifurcation and Bogdanov-Takens bifurcation can occur. Also, the system undergoes a degenerate Hopf bifurcation and has two limit cycles (i.e., the inner one is stable and the outer is unstable), which implies the bistable phenomenon. We conclude that the large amount of fear and prey harvesting are detrimental to the survival of the prey and predator.

References

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