Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators
In this work, we propose a predator-prey system with a Holling type Ⅱ functional response and study its dynamics when the prey exhibits vigilance behavior to avoid predation and predators exhibit cooperative hunting. We provide conditions for existence and the local and global stability of equilibri...
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| Format: | Article |
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AIMS Press
2024-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024123?viewType=HTML |
| _version_ | 1797302566720110592 |
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| author | Eric M. Takyi Charles Ohanian Margaret Cathcart Nihal Kumar |
| author_facet | Eric M. Takyi Charles Ohanian Margaret Cathcart Nihal Kumar |
| author_sort | Eric M. Takyi |
| collection | DOAJ |
| description | In this work, we propose a predator-prey system with a Holling type Ⅱ functional response and study its dynamics when the prey exhibits vigilance behavior to avoid predation and predators exhibit cooperative hunting. We provide conditions for existence and the local and global stability of equilibria. We carry out detailed bifurcation analysis and find the system to experience Hopf, saddle-node, and transcritical bifurcations. Our results show that increased prey vigilance can stabilize the system, but when vigilance levels are too high, it causes a decrease in the population density of prey and leads to extinction. When hunting cooperation is intensive, it can destabilize the system, and can also induce bi-stability phenomenon. Furthermore, it can reduce the population density of both prey and predators and also change the stability of a coexistence state. We provide numerical experiments to validate our theoretical results and discuss ecological implications. |
| first_indexed | 2024-03-07T23:39:43Z |
| format | Article |
| id | doaj.art-c34443be44724df78e1e56481aec87d3 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-03-07T23:39:43Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-c34443be44724df78e1e56481aec87d32024-02-20T01:27:44ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-01-012122768278610.3934/mbe.2024123Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predatorsEric M. Takyi0Charles Ohanian 1Margaret Cathcart2Nihal Kumar31. Department of Mathematics, Computer Science and Statistics, Ursinus College, Collegeville, PA 19426, USA2. Department of Mathematics and Computer Science, Muhlenberg College, Allentown, PA 18104, USA3. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA4. Department of Mathematics, Penn State University, State College, PA 16802, USAIn this work, we propose a predator-prey system with a Holling type Ⅱ functional response and study its dynamics when the prey exhibits vigilance behavior to avoid predation and predators exhibit cooperative hunting. We provide conditions for existence and the local and global stability of equilibria. We carry out detailed bifurcation analysis and find the system to experience Hopf, saddle-node, and transcritical bifurcations. Our results show that increased prey vigilance can stabilize the system, but when vigilance levels are too high, it causes a decrease in the population density of prey and leads to extinction. When hunting cooperation is intensive, it can destabilize the system, and can also induce bi-stability phenomenon. Furthermore, it can reduce the population density of both prey and predators and also change the stability of a coexistence state. We provide numerical experiments to validate our theoretical results and discuss ecological implications.https://www.aimspress.com/article/doi/10.3934/mbe.2024123?viewType=HTMLvigilancehunting cooperationbifurcationglobal stability |
| spellingShingle | Eric M. Takyi Charles Ohanian Margaret Cathcart Nihal Kumar Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators Mathematical Biosciences and Engineering vigilance hunting cooperation bifurcation global stability |
| title | Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators |
| title_full | Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators |
| title_fullStr | Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators |
| title_full_unstemmed | Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators |
| title_short | Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators |
| title_sort | dynamical analysis of a predator prey system with prey vigilance and hunting cooperation in predators |
| topic | vigilance hunting cooperation bifurcation global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024123?viewType=HTML |
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