The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey
The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boun...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231481?viewType=HTML |
| _version_ | 1797635367086587904 |
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| author | Chengchong Lu Xinxin Liu Zhicheng Li |
| author_facet | Chengchong Lu Xinxin Liu Zhicheng Li |
| author_sort | Chengchong Lu |
| collection | DOAJ |
| description | The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management. |
| first_indexed | 2024-03-11T12:20:06Z |
| format | Article |
| id | doaj.art-b8f3586ba2de40b8b010c61afe8291e6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T12:20:06Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-b8f3586ba2de40b8b010c61afe8291e62023-11-07T01:41:47ZengAIMS PressAIMS Mathematics2473-69882023-10-01812288972892510.3934/math.20231481The dynamics and harvesting strategies of a predator-prey system with Allee effect on preyChengchong Lu0Xinxin Liu1Zhicheng Li2School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, ChinaSchool of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, ChinaSchool of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, ChinaThe study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management.https://www.aimspress.com/article/doi/10.3934/math.20231481?viewType=HTMLpredator-preyallee effecthopf bifurcationmstyoptimal harvesting |
| spellingShingle | Chengchong Lu Xinxin Liu Zhicheng Li The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey AIMS Mathematics predator-prey allee effect hopf bifurcation msty optimal harvesting |
| title | The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey |
| title_full | The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey |
| title_fullStr | The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey |
| title_full_unstemmed | The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey |
| title_short | The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey |
| title_sort | dynamics and harvesting strategies of a predator prey system with allee effect on prey |
| topic | predator-prey allee effect hopf bifurcation msty optimal harvesting |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231481?viewType=HTML |
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