Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect
This paper is concerned with a prey–predator system involving herd behaviour and strong Allee effect. First, the local stability analysis of all the possible equilibrium points are investigated. Second, the existence of Hopf bifurcation around the unique positive equilibrium are carried out. Finally...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2022-12-01
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| Series: | Systems Science & Control Engineering |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/21642583.2022.2079572 |
| _version_ | 1828833634938781696 |
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| author | Wenbin Yang Danqing Li |
| author_facet | Wenbin Yang Danqing Li |
| author_sort | Wenbin Yang |
| collection | DOAJ |
| description | This paper is concerned with a prey–predator system involving herd behaviour and strong Allee effect. First, the local stability analysis of all the possible equilibrium points are investigated. Second, the existence of Hopf bifurcation around the unique positive equilibrium are carried out. Finally, this paper is ended with a numerical simulation to understand the dynamics of the system. As it turns out that the ‘Allee effect constant’ plays a very important role in biological invasion mechanism, such as controlling and preventing biological invasion or invading successfully. |
| first_indexed | 2024-12-12T17:23:38Z |
| format | Article |
| id | doaj.art-85dda69ea24b4054b90a956feb972170 |
| institution | Directory Open Access Journal |
| issn | 2164-2583 |
| language | English |
| last_indexed | 2024-12-12T17:23:38Z |
| publishDate | 2022-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Systems Science & Control Engineering |
| spelling | doaj.art-85dda69ea24b4054b90a956feb9721702022-12-22T00:17:35ZengTaylor & Francis GroupSystems Science & Control Engineering2164-25832022-12-0110157258210.1080/21642583.2022.2079572Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effectWenbin Yang0Danqing Li1School of Science, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi, People's Republic of ChinaSchool of Computer Science & Technology, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi, People's Republic of ChinaThis paper is concerned with a prey–predator system involving herd behaviour and strong Allee effect. First, the local stability analysis of all the possible equilibrium points are investigated. Second, the existence of Hopf bifurcation around the unique positive equilibrium are carried out. Finally, this paper is ended with a numerical simulation to understand the dynamics of the system. As it turns out that the ‘Allee effect constant’ plays a very important role in biological invasion mechanism, such as controlling and preventing biological invasion or invading successfully.https://www.tandfonline.com/doi/10.1080/21642583.2022.2079572Prey–predatorstabilityHopf bifurcationinvasion mechanism |
| spellingShingle | Wenbin Yang Danqing Li Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect Systems Science & Control Engineering Prey–predator stability Hopf bifurcation invasion mechanism |
| title | Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect |
| title_full | Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect |
| title_fullStr | Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect |
| title_full_unstemmed | Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect |
| title_short | Dynamics analysis and numerical implementations of a diffusive predator–prey model with herd behaviour and Allee effect |
| title_sort | dynamics analysis and numerical implementations of a diffusive predator prey model with herd behaviour and allee effect |
| topic | Prey–predator stability Hopf bifurcation invasion mechanism |
| url | https://www.tandfonline.com/doi/10.1080/21642583.2022.2079572 |
| work_keys_str_mv | AT wenbinyang dynamicsanalysisandnumericalimplementationsofadiffusivepredatorpreymodelwithherdbehaviourandalleeeffect AT danqingli dynamicsanalysisandnumericalimplementationsofadiffusivepredatorpreymodelwithherdbehaviourandalleeeffect |