Bifurcation analysis of Leslie-Gower predator-prey system with harvesting and fear effect

Rongjie Yu; Hengguo Yu; Chuanjun Dai; Zengling Ma; Qi Wang; Min Zhao; Rongjie Yu; Hengguo Yu; Chuanjun Dai; Zengling Ma; Qi Wang; Min Zhao

doi:10.3934/mbe.2023812

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18267-18300. doi: 10.3934/mbe.2023812

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Bifurcation analysis of Leslie-Gower predator-prey system with harvesting and fear effect

1.
Key Laboratory for Subtropical Oceans & Lakes Environment and Biological Resources Utilization Technology of Zhejiang, Wenzhou University, Wenzhou 325035, China
2.
School of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China
3.
School of Life and Environmental Science, Wenzhou University, Wenzhou 325035, China

Received: 15 August 2023 Revised: 07 September 2023 Accepted: 10 September 2023 Published: 22 September 2023

In the paper, a Leslie-Gower predator-prey system with harvesting and fear effect is considered. The existence and stability of all possible equilibrium points are analyzed. The bifurcation dynamic behavior at key equilibrium points is investigated to explore the intrinsic driving mechanisms of population interaction modes. It is shown that the system undergoes various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcations. The numerical simulation results show that harvesting and fear effect can seriously affect the dynamic evolution trend and coexistence mode. Furthermore, it is particularly worth pointing out that harvesting not only drives changes in population coexistence mode, but also has a certain degree delay. Finally, it is anticipated that these research results will be beneficial for the vigorous development of predator-prey system.
- harvesting,
- fear effect,
- existence,
- stability,
- bifurcation
Citation: Rongjie Yu, Hengguo Yu, Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao. Bifurcation analysis of Leslie-Gower predator-prey system with harvesting and fear effect[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18267-18300. doi: 10.3934/mbe.2023812

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Abstract

In the paper, a Leslie-Gower predator-prey system with harvesting and fear effect is considered. The existence and stability of all possible equilibrium points are analyzed. The bifurcation dynamic behavior at key equilibrium points is investigated to explore the intrinsic driving mechanisms of population interaction modes. It is shown that the system undergoes various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcations. The numerical simulation results show that harvesting and fear effect can seriously affect the dynamic evolution trend and coexistence mode. Furthermore, it is particularly worth pointing out that harvesting not only drives changes in population coexistence mode, but also has a certain degree delay. Finally, it is anticipated that these research results will be beneficial for the vigorous development of predator-prey system.

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