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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Main Authors: Yashra Javaid, Shireen Jawad, Rizwan Ahmed, Ali Hasan Ali, Badr Rashwani
Format: Article
Language:English
Published: Taylor & Francis Group 2024-12-01
Series:Applied Mathematics in Science and Engineering
Subjects:
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.
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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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