Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator
In this work, a Leslie-Gower model with a weak Allee effect on the prey and a fear effect on the predator is proposed. By using qualitative analyses, the local stability of the coexisting equilibrium and the existence of Turing instable are discussed. By analyzing the distribution of eigenvalues, th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023905?viewType=HTML |
| _version_ | 1827932619988271104 |
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| author | Fatao Wang Ruizhi Yang Yining Xie Jing Zhao |
| author_facet | Fatao Wang Ruizhi Yang Yining Xie Jing Zhao |
| author_sort | Fatao Wang |
| collection | DOAJ |
| description | In this work, a Leslie-Gower model with a weak Allee effect on the prey and a fear effect on the predator is proposed. By using qualitative analyses, the local stability of the coexisting equilibrium and the existence of Turing instable are discussed. By analyzing the distribution of eigenvalues, the existence of a Hopf bifurcation is studied by using the gestation time delay as a bifurcation parameter. By utilizing the normal form method and the center manifold theorem, we calculate the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. We indicate that both the weak Allee effect on the prey and fear effect on the predator have an important impact on the dynamical behaviour of the new Leslie-Gower model. We also verify the obtained results by some numerical examples. |
| first_indexed | 2024-03-13T07:11:20Z |
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| id | doaj.art-e6e96d59d66d4826a35dfa5b2f903ed3 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T07:11:20Z |
| publishDate | 2023-05-01 |
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| series | AIMS Mathematics |
| spelling | doaj.art-e6e96d59d66d4826a35dfa5b2f903ed32023-06-06T01:22:27ZengAIMS PressAIMS Mathematics2473-69882023-05-0188177191774310.3934/math.2023905Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predatorFatao Wang0Ruizhi Yang1Yining Xie2Jing Zhao3Northeast Forestry University, Harbin 150040, ChinaNortheast Forestry University, Harbin 150040, ChinaNortheast Forestry University, Harbin 150040, ChinaNortheast Forestry University, Harbin 150040, ChinaIn this work, a Leslie-Gower model with a weak Allee effect on the prey and a fear effect on the predator is proposed. By using qualitative analyses, the local stability of the coexisting equilibrium and the existence of Turing instable are discussed. By analyzing the distribution of eigenvalues, the existence of a Hopf bifurcation is studied by using the gestation time delay as a bifurcation parameter. By utilizing the normal form method and the center manifold theorem, we calculate the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. We indicate that both the weak Allee effect on the prey and fear effect on the predator have an important impact on the dynamical behaviour of the new Leslie-Gower model. We also verify the obtained results by some numerical examples.https://www.aimspress.com/article/doi/10.3934/math.2023905?viewType=HTMLpredator-preyfear effectweak allee effectnonlocal competitiondelayhopf bifurcation |
| spellingShingle | Fatao Wang Ruizhi Yang Yining Xie Jing Zhao Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator AIMS Mathematics predator-prey fear effect weak allee effect nonlocal competition delay hopf bifurcation |
| title | Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator |
| title_full | Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator |
| title_fullStr | Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator |
| title_full_unstemmed | Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator |
| title_short | Hopf bifurcation in a delayed reaction diffusion predator-prey model with weak Allee effect on prey and fear effect on predator |
| title_sort | hopf bifurcation in a delayed reaction diffusion predator prey model with weak allee effect on prey and fear effect on predator |
| topic | predator-prey fear effect weak allee effect nonlocal competition delay hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023905?viewType=HTML |
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