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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Published inApplied mathematics in science and engineering Vol. 32; no. 1
Main Authors Javaid, Yashra, Jawad, Shireen, Ahmed, Rizwan, Ali, Ali Hasan, Rashwani, Badr
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Ltd 31.12.2024
Taylor & Francis Group
Subjects
Allee effect
Bifurcation theory
Centre manifold theory
Chaos theory
Discrete time systems
fixed point
functional response
herd behaviour
Predator-prey
Predators
prey refuge
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ISSN2769-0911
2769-0911
DOI10.1080/27690911.2024.2420953

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Summary: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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ISSN:2769-0911
2769-0911
DOI:10.1080/27690911.2024.2420953