Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour
This paper investigates the dynamics of a discrete-time predator-prey system in which the prey population is impacted by the Allee effect. Possible fixed points in the system are studied for their existence and topological categorization. Moreover, the presence and direction of period-doubling and N...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2024.2420953 |
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| author | Yashra Javaid Shireen Jawad Rizwan Ahmed Ali Hasan Ali Badr Rashwani |
| author_facet | Yashra Javaid Shireen Jawad Rizwan Ahmed Ali Hasan Ali Badr Rashwani |
| author_sort | Yashra Javaid |
| collection | DOAJ |
| description | This paper investigates the dynamics of a discrete-time predator-prey system in which the prey population is impacted by the Allee effect. Possible fixed points in the system are studied for their existence and topological categorization. Moreover, the presence and direction of period-doubling and Neimark-Sacker bifurcations at the interior fixed point are examined through the application of bifurcation theory and the centre manifold theorem. A hybrid approach is adopted to control chaotic behaviour and prevent bifurcations. Numerical examples are provided to substantiate our theoretical findings. The Allee effect has been shown to affect the dynamics of the system using numerical simulations. The moderate Allee effect stabilizes predator and prey populations, facilitating ecological cohabitation and persistence. |
| format | Article |
| id | doaj-art-dccb24402c2d4d36934458247c927d10 |
| institution | OA Journals |
| issn | 2769-0911 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj-art-dccb24402c2d4d36934458247c927d102025-08-20T02:19:34ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112024-12-0132110.1080/27690911.2024.2420953Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviourYashra Javaid0Shireen Jawad1Rizwan Ahmed2Ali Hasan Ali3Badr Rashwani4Department of Mathematics, Air University Multan Campus, Multan, PakistanDepartment of Mathematics, College of Science, University of Baghdad, Baghdad, IraqDepartment of Mathematics, Air University Multan Campus, Multan, PakistanInstitute of Mathematics, University of Debrecen, Debrecen, HungaryMathematics Department, Science Faculty, Tishreen University, Latakia, SyriaThis paper investigates the dynamics of a discrete-time predator-prey system in which the prey population is impacted by the Allee effect. Possible fixed points in the system are studied for their existence and topological categorization. Moreover, the presence and direction of period-doubling and Neimark-Sacker bifurcations at the interior fixed point are examined through the application of bifurcation theory and the centre manifold theorem. A hybrid approach is adopted to control chaotic behaviour and prevent bifurcations. Numerical examples are provided to substantiate our theoretical findings. The Allee effect has been shown to affect the dynamics of the system using numerical simulations. The moderate Allee effect stabilizes predator and prey populations, facilitating ecological cohabitation and persistence.https://www.tandfonline.com/doi/10.1080/27690911.2024.2420953Predator-preyfunctional responseherd behaviourprey refugeAllee effectfixed point |
| spellingShingle | Yashra Javaid Shireen Jawad Rizwan Ahmed Ali Hasan Ali Badr Rashwani Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour Applied Mathematics in Science and Engineering Predator-prey functional response herd behaviour prey refuge Allee effect fixed point |
| title | Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour |
| title_full | Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour |
| title_fullStr | Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour |
| title_full_unstemmed | Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour |
| title_short | Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour |
| title_sort | dynamic complexity of a discretized predator prey system with allee effect and herd behaviour |
| topic | Predator-prey functional response herd behaviour prey refuge Allee effect fixed point |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2024.2420953 |
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