Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey
Abstract In this paper, the dynamical behaviors of a discrete-time prey–predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark–Sacker bifurc...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2039-y |
| _version_ | 1818852085284732928 |
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| author | Figen Kangalgil |
| author_facet | Figen Kangalgil |
| author_sort | Figen Kangalgil |
| collection | DOAJ |
| description | Abstract In this paper, the dynamical behaviors of a discrete-time prey–predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark–Sacker bifurcation at the unique positive fixed point by choosing a as a bifurcation parameter. The conditions of the existence for Neimark–Sacker bifurcation and the direction of bifurcation via bifurcation theory are presented. Also, some numerical simulations are presented to support of the analytical finding. Then bifurcation diagrams and phase portraits of the model are given. |
| first_indexed | 2024-12-19T07:15:19Z |
| format | Article |
| id | doaj.art-e682edf7a8ce4b46ac29c821f663ab31 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T07:15:19Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e682edf7a8ce4b46ac29c821f663ab312022-12-21T20:31:06ZengSpringerOpenAdvances in Difference Equations1687-18472019-03-012019111210.1186/s13662-019-2039-yNeimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in preyFigen Kangalgil0Department of Mathematics, Faculty of Science, Cumhuriyet UniversityAbstract In this paper, the dynamical behaviors of a discrete-time prey–predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark–Sacker bifurcation at the unique positive fixed point by choosing a as a bifurcation parameter. The conditions of the existence for Neimark–Sacker bifurcation and the direction of bifurcation via bifurcation theory are presented. Also, some numerical simulations are presented to support of the analytical finding. Then bifurcation diagrams and phase portraits of the model are given.http://link.springer.com/article/10.1186/s13662-019-2039-yAllee effectPrey–predator modelStability |
| spellingShingle | Figen Kangalgil Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey Advances in Difference Equations Allee effect Prey–predator model Stability |
| title | Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey |
| title_full | Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey |
| title_fullStr | Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey |
| title_full_unstemmed | Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey |
| title_short | Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey |
| title_sort | neimark sacker bifurcation and stability analysis of a discrete time prey predator model with allee effect in prey |
| topic | Allee effect Prey–predator model Stability |
| url | http://link.springer.com/article/10.1186/s13662-019-2039-y |
| work_keys_str_mv | AT figenkangalgil neimarksackerbifurcationandstabilityanalysisofadiscretetimepreypredatormodelwithalleeeffectinprey |