Dynamics analysis of a predator-prey model with Allee effect and harvesting effort

Yichao Shao; Hengguo Yu; Chenglei Jin; Jingzhe Fang; Min Zhao; Yichao Shao; Hengguo Yu; Chenglei Jin; Jingzhe Fang; Min Zhao

doi:10.3934/era.2024263

Electronic Research Archive

2024, Volume 32, Issue 10: 5682-5716. doi: 10.3934/era.2024263

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Research article

Dynamics analysis of a predator-prey model with Allee effect and harvesting effort

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

Received: 02 September 2024 Revised: 09 October 2024 Accepted: 12 October 2024 Published: 16 October 2024

In the paper, a predator-prey model with the Allee effect and harvesting effort was proposed to explore the interaction mechanism between prey and predator. Under the framework of mathematical theory deduction, some conditions for the occurrence of transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations were derived with harvesting effort and the Allee effect as key parameters. Under the framework of bifurcation dynamics numerical simulation, the evolution process of specific bifurcation dynamics behavior was gradually visualized to reveal the influence mechanism of the Allee effect and harvesting effort. The research results indicated that the Allee effect and harvesting effort not only seriously affected the bifurcation dynamics essential characteristics of the model (1.3), but also could promote the formation of constant steady state and periodic oscillation persistent survival mode of prey and predator. Furthermore, it is worth noting that appropriate harvesting effort was beneficial for the formation of a sustainable survival cycle between prey and predator. In summary, we hoped that the research findings could contribute to the comprehensive promotion of bifurcation dynamics studies in the predator-prey model.
- predator-prey system,
- Allee effet,
- harvesting effort,
- persistent survival mode,
- evolutionary trend
Citation: Yichao Shao, Hengguo Yu, Chenglei Jin, Jingzhe Fang, Min Zhao. Dynamics analysis of a predator-prey model with Allee effect and harvesting effort[J]. Electronic Research Archive, 2024, 32(10): 5682-5716. doi: 10.3934/era.2024263

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Abstract

In the paper, a predator-prey model with the Allee effect and harvesting effort was proposed to explore the interaction mechanism between prey and predator. Under the framework of mathematical theory deduction, some conditions for the occurrence of transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations were derived with harvesting effort and the Allee effect as key parameters. Under the framework of bifurcation dynamics numerical simulation, the evolution process of specific bifurcation dynamics behavior was gradually visualized to reveal the influence mechanism of the Allee effect and harvesting effort. The research results indicated that the Allee effect and harvesting effort not only seriously affected the bifurcation dynamics essential characteristics of the model (1.3), but also could promote the formation of constant steady state and periodic oscillation persistent survival mode of prey and predator. Furthermore, it is worth noting that appropriate harvesting effort was beneficial for the formation of a sustainable survival cycle between prey and predator. In summary, we hoped that the research findings could contribute to the comprehensive promotion of bifurcation dynamics studies in the predator-prey model.

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