Dynamics of a diffusive predator–prey model with herd behavior
This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion a...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2020-01-01
|
| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/15723 |
| _version_ | 1811275454453121024 |
|---|---|
| author | Yan Li Sanyun Li Fengrong Zhang |
| author_facet | Yan Li Sanyun Li Fengrong Zhang |
| author_sort | Yan Li |
| collection | DOAJ |
| description | This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion and the existence of Hopf bifurcation are investigated by analyzing the distribution of the eigenvalues. Furthermore, the explicit formula for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are also derived by applying the normal form theory. Next, we show the stability of positive constant equilibrium, the existence and stability of periodic solutions near positive constant equilibrium for the diffusive model. Finally, some numerical simulations are carried out to support the analytical results. |
| first_indexed | 2024-04-12T23:38:06Z |
| format | Article |
| id | doaj.art-5401143d630f4f71804017d6901563da |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-12T23:38:06Z |
| publishDate | 2020-01-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-5401143d630f4f71804017d6901563da2022-12-22T03:12:04ZengVilnius University PressNonlinear Analysis1392-51132335-89632020-01-0125110.15388/namc.2020.25.15723Dynamics of a diffusive predator–prey model with herd behaviorYan Li0Sanyun Li1Fengrong Zhang2China University of Petroleum (East China)China University of Petroleum (East China)China University of Petroleum (East China)This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion and the existence of Hopf bifurcation are investigated by analyzing the distribution of the eigenvalues. Furthermore, the explicit formula for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are also derived by applying the normal form theory. Next, we show the stability of positive constant equilibrium, the existence and stability of periodic solutions near positive constant equilibrium for the diffusive model. Finally, some numerical simulations are carried out to support the analytical results.https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/15723diffusive predator–prey modelherd behaviorstability, Leslie-Gower termHopf bifurcation |
| spellingShingle | Yan Li Sanyun Li Fengrong Zhang Dynamics of a diffusive predator–prey model with herd behavior Nonlinear Analysis diffusive predator–prey model herd behavior stability, Leslie-Gower term Hopf bifurcation |
| title | Dynamics of a diffusive predator–prey model with herd behavior |
| title_full | Dynamics of a diffusive predator–prey model with herd behavior |
| title_fullStr | Dynamics of a diffusive predator–prey model with herd behavior |
| title_full_unstemmed | Dynamics of a diffusive predator–prey model with herd behavior |
| title_short | Dynamics of a diffusive predator–prey model with herd behavior |
| title_sort | dynamics of a diffusive predator prey model with herd behavior |
| topic | diffusive predator–prey model herd behavior stability, Leslie-Gower term Hopf bifurcation |
| url | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/15723 |
| work_keys_str_mv | AT yanli dynamicsofadiffusivepredatorpreymodelwithherdbehavior AT sanyunli dynamicsofadiffusivepredatorpreymodelwithherdbehavior AT fengrongzhang dynamicsofadiffusivepredatorpreymodelwithherdbehavior |