Dynamics analysis of a predator-prey model with Allee effect and harvesting effort
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-Take...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-10-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024263 |
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| author | Yichao Shao Hengguo Yu Chenglei Jin Jingzhe Fang Min Zhao |
| author_facet | Yichao Shao Hengguo Yu Chenglei Jin Jingzhe Fang Min Zhao |
| author_sort | Yichao Shao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b7dacd19ec2c4419be1f718786855aa8 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-b7dacd19ec2c4419be1f718786855aa82025-01-23T07:52:53ZengAIMS PressElectronic Research Archive2688-15942024-10-0132105682571610.3934/era.2024263Dynamics analysis of a predator-prey model with Allee effect and harvesting effortYichao Shao0Hengguo Yu1Chenglei Jin2Jingzhe Fang3Min Zhao4School of Mathematics and Physics, Wenzhou University, Wenzhou 325035, ChinaSchool of Mathematics and Physics, Wenzhou University, Wenzhou 325035, ChinaSchool of Mathematics and Physics, Wenzhou University, Wenzhou 325035, ChinaSchool of Mathematics and Physics, Wenzhou University, Wenzhou 325035, ChinaKey Laboratory for Subtropical Oceans & Lakes Environment and Biological Resources Utilization Technology of Zhejiang, Wenzhou University, Wenzhou 325035, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/era.2024263predator-prey systemallee effetharvesting effortpersistent survival modeevolutionary trend |
| spellingShingle | Yichao Shao Hengguo Yu Chenglei Jin Jingzhe Fang Min Zhao Dynamics analysis of a predator-prey model with Allee effect and harvesting effort Electronic Research Archive predator-prey system allee effet harvesting effort persistent survival mode evolutionary trend |
| title | Dynamics analysis of a predator-prey model with Allee effect and harvesting effort |
| title_full | Dynamics analysis of a predator-prey model with Allee effect and harvesting effort |
| title_fullStr | Dynamics analysis of a predator-prey model with Allee effect and harvesting effort |
| title_full_unstemmed | Dynamics analysis of a predator-prey model with Allee effect and harvesting effort |
| title_short | Dynamics analysis of a predator-prey model with Allee effect and harvesting effort |
| title_sort | dynamics analysis of a predator prey model with allee effect and harvesting effort |
| topic | predator-prey system allee effet harvesting effort persistent survival mode evolutionary trend |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024263 |
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