Crucial impact of component Allee effect in predator-prey system
type: Item
instance of: scholarly article
title: Crucial impact of component Allee effect in predator-prey system
zbMATH Open document ID: 1543.92045
author: Kalyanashis Sahoo
author: Banshidhar Sahoo
published in: Journal of Physics A: Mathematical and Theoretical
publication date: 2024-06-27T00:00:00Z
review text: In this paper, the authors inspect the famous \NHastings and Powell (HP) model [\textit{A. Hastings} and \textit{T. Powell}, Ecology 72, No. 3, 896--903 (1991; \url{doi:10.2307/1940591})]\N incorporating component Allee effect on top predator's reproduction, and analyse the updated model with the help of both analytical and numerical phenomena. Considering cost of Allee effect, half-saturation constant of prey as the key parameters, the Hopf bifurcations are discussed. By using normal form theory introduced in \N[\textit{B. D. Hassard} et al., Theory and applications of Hopf bifurcation. Cambridge etc.: Cambridge University Press (1981; Zbl 0474.34002)], the directions of Hopf bifurcations at the critical values of Allee parameter and half-saturation constant of prey are studied as well. The formulated model indicates that the system demonstrates chaotic, periodic and stable dynamics in the variation of key parameters. The chaos can be controlled for proper application of the large values of parameter used as the cost of Allee effect and also for small values of the parameter used as the half saturation constant of prey population.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 7872289
zbMATH Keywords: predator-prey
zbMATH Keywords: Allee effect
zbMATH Keywords: chaos
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: periodic
zbMATH Keywords: stability
MaRDI profile type: Publication
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DOI: 10.1088/1751-8121/AD43CA
description: scientific article; zbMATH DE number 7872289