Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect
In this paper, we proposed and studied a Leslie-Gower prey-predator system which considered various ecological factors, such as the Allee effect and harvesting effect in prey populations and the hunting cooperation in predator populations. The positivity and boundedness of the system's solution...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241649 |
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| author | Na Min Hongyang Zhang Xiaobin Gao Pengyu Zeng |
| author_facet | Na Min Hongyang Zhang Xiaobin Gao Pengyu Zeng |
| author_sort | Na Min |
| collection | DOAJ |
| description | In this paper, we proposed and studied a Leslie-Gower prey-predator system which considered various ecological factors, such as the Allee effect and harvesting effect in prey populations and the hunting cooperation in predator populations. The positivity and boundedness of the system's solutions were determined. The conditions for the uniformly persistence of the system and the extinction of populations have been established. We studied the existence and type of singularities, including primary singularities and higher-order singularities. Using topological equivalent and the blow-up method, we proved that the origin was the attractor, and a defined basin of attraction was given. As the parameters change, the system may experience two saddle-node bifurcations and a Hopf bifurcation. The direction and stability of Hopf bifurcation solutions were established. Numerical simulations were given to validate the primary theoretical findings. In this paper, we found that there existed critical thresholds for Allee threshold, prey harvesting, and hunting cooperation, beyond which both predator and prey populations faced the risk of extinction. |
| format | Article |
| id | doaj-art-5b18725e57e94f79817e80f256262768 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-5b18725e57e94f79817e80f2562627682025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912346183464610.3934/math.20241649Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effectNa Min0Hongyang Zhang1Xiaobin Gao2Pengyu Zeng3School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510006, ChinaSchool of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510065, ChinaSchool of Electronics and Communication Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics, Foshan University, Foshan 528000, ChinaIn this paper, we proposed and studied a Leslie-Gower prey-predator system which considered various ecological factors, such as the Allee effect and harvesting effect in prey populations and the hunting cooperation in predator populations. The positivity and boundedness of the system's solutions were determined. The conditions for the uniformly persistence of the system and the extinction of populations have been established. We studied the existence and type of singularities, including primary singularities and higher-order singularities. Using topological equivalent and the blow-up method, we proved that the origin was the attractor, and a defined basin of attraction was given. As the parameters change, the system may experience two saddle-node bifurcations and a Hopf bifurcation. The direction and stability of Hopf bifurcation solutions were established. Numerical simulations were given to validate the primary theoretical findings. In this paper, we found that there existed critical thresholds for Allee threshold, prey harvesting, and hunting cooperation, beyond which both predator and prey populations faced the risk of extinction.https://www.aimspress.com/article/doi/10.3934/math.20241649allee effectharvesting effecthunting cooperationhigher-order singularitiessaddle-node bifurcationhopf bifurcation |
| spellingShingle | Na Min Hongyang Zhang Xiaobin Gao Pengyu Zeng Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect AIMS Mathematics allee effect harvesting effect hunting cooperation higher-order singularities saddle-node bifurcation hopf bifurcation |
| title | Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect |
| title_full | Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect |
| title_fullStr | Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect |
| title_full_unstemmed | Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect |
| title_short | Impacts of hunting cooperation and prey harvesting in a Leslie-Gower prey-predator system with strong Allee effect |
| title_sort | impacts of hunting cooperation and prey harvesting in a leslie gower prey predator system with strong allee effect |
| topic | allee effect harvesting effect hunting cooperation higher-order singularities saddle-node bifurcation hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241649 |
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