Dynamics in a discrete-time predator-prey system with Allee effect
type: Item
instance of: scholarly article
title: Dynamics in a discrete-time predator-prey system with Allee effect
zbMATH Open document ID: 1269.37035
author: Xian-Wei Chen
author: Xiang-Ling Fu
author: Zhujun Jing
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2013-04-17T00:00:00Z
review text: The paper investigates the dynamics of the discrete-time predator-prey system with Allee effect. The authors prove the existence and the stability of fixed points in the system. Then, based on the bifurcation theory and the center manifold theory, they derive conditions for flip bifurcation and Hopf bifurcation. Also, the existence of chaos in the sense of Maroto is shown, using both analytical and numerical methods. The rich dynamical behaviour of the system is also illustrated here by using bifurcation diagrams, phase portraits, Lyapunov exponents and fractal dimensions. It is shown that the dynamical behaviour of the system can move from the complex unstable states to the stable states as the Allee constant increases.
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 65P20
Mathematics Subject Classification ID: 65P30
zbMATH DE Number: 6155022
zbMATH Keywords: predator-prey system
zbMATH Keywords: Allee effect
zbMATH Keywords: flip bifurcation
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Marotto's chaos
zbMATH Keywords: transient chaos
zbMATH Keywords: invariant circle
zbMATH Keywords: periodic window
reviewed by: Iulian Stoleriu
MaRDI profile type: Publication
full work available at URL: s10255-013-0207-5
OpenAlex ID: W1985826620
Wikidata QID: Q115605883
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DOI: 10.1007/S10255-013-0207-5
description: scientific article; zbMATH DE number 6155022