Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation
In this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating...
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-09-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0474 |
| _version_ | 1811202962258657280 |
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| author | Miao Liangying He Zhiqian |
| author_facet | Miao Liangying He Zhiqian |
| author_sort | Miao Liangying |
| collection | DOAJ |
| description | In this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction-diffusion model, first it is shown that Turing instability occurs, then the direction and stability of the Hopf bifurcation is reached. Our results show that hunting cooperation plays a crucial role in the dynamics of the model, that is, it can be beneficial to the predator population and induce the rise of Turing instability. Finally, numerical simulations are performed to visualize the complex dynamic behavior. |
| first_indexed | 2024-04-12T02:46:30Z |
| format | Article |
| id | doaj.art-ac4fe5ff91214cc78f1efff470de25c6 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-12T02:46:30Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-ac4fe5ff91214cc78f1efff470de25c62022-12-22T03:51:08ZengDe GruyterOpen Mathematics2391-54552022-09-0120198699710.1515/math-2022-0474Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperationMiao Liangying0He Zhiqian1School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai, 810007, P. R. ChinaDepartment of Basic Teaching and Research, Qinghai University, Xining, Qinghai, 810016, P. R. ChinaIn this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction-diffusion model, first it is shown that Turing instability occurs, then the direction and stability of the Hopf bifurcation is reached. Our results show that hunting cooperation plays a crucial role in the dynamics of the model, that is, it can be beneficial to the predator population and induce the rise of Turing instability. Finally, numerical simulations are performed to visualize the complex dynamic behavior.https://doi.org/10.1515/math-2022-0474predator-preyhunting cooperationturing instabilityhopf bifurcationstability92d2535k5735b35 |
| spellingShingle | Miao Liangying He Zhiqian Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation Open Mathematics predator-prey hunting cooperation turing instability hopf bifurcation stability 92d25 35k57 35b35 |
| title | Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation |
| title_full | Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation |
| title_fullStr | Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation |
| title_full_unstemmed | Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation |
| title_short | Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation |
| title_sort | hopf bifurcation and turing instability in a diffusive predator prey model with hunting cooperation |
| topic | predator-prey hunting cooperation turing instability hopf bifurcation stability 92d25 35k57 35b35 |
| url | https://doi.org/10.1515/math-2022-0474 |
| work_keys_str_mv | AT miaoliangying hopfbifurcationandturinginstabilityinadiffusivepredatorpreymodelwithhuntingcooperation AT hezhiqian hopfbifurcationandturinginstabilityinadiffusivepredatorpreymodelwithhuntingcooperation |