Chaos and bifurcations of a Leslie-Gower food chain with strong Allee effect
type: Item
instance of: scholarly article
title: Chaos and bifurcations of a Leslie-Gower food chain with strong Allee effect
zbMATH Open document ID: 1418.92143
DOI: 10.1155/2015/430985
author: Chunshan Xue
author: Xia Liu
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: Allee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect into the source. Our results show that the existence of Allee effect contributes to the occurrence of more complex dynamics of the system, including Hopf, saddle-node, transcritical, saddle-node-Hopf, period-doubling, and period-halving bifurcations and chaos.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7025360
Wikidata QID: Q59105904
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/430985
OpenAlex ID: W2181110123
cites work: Three Limit Cycles in a Leslie–Gower Predator-Prey Model with Additive Allee Effect
cites work: Dynamical complexity induced by Allee effect in a predator-prey model
cites work: Allee effect in a prey-predator system
cites work: Bifurcations and global dynamics in a predator-prey model with a strong Allee effect on the prey, and a ratio-dependent functional response
cites work: On the mechanistic underpinning of discrete-time population models with Allee effect
cites work: The stability of predator\,-\,prey systems subject to the Allee effects
cites work: Allee effect in a discrete-time predator-prey system
cites work: Bistability and an Allee effect as emergent consequences of stage-specific predation
cites work: Speeds of invasion in a model with strong or weak Allee effects
cites work: ALLEE EFFECTS: POPULATION GROWTH, CRITICAL DENSITY, AND THE CHANCE OF EXTINCTION
cites work: The evolution of phenotypic traits in a predator-prey system subject to Allee effect
cites work: Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect
cites work: Indirect Allee effect, bistability and chaotic oscillations in a predator--prey discrete model of logistic type
cites work: Bifurcation analysis of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and strong Allee effect
cites work: A Lyapunov function for Leslie-Gower predator-prey models
cites work: Retracted: Bifurcation analysis in the delayed Leslie-Gower predator-prey system
cites work: Bogdanov-Takens and triple zero bifurcations of a delayed modified Leslie-Gower predator prey system
cites work: Global stability and Hopf bifurcation in a delayed diffusive Leslie-Gower predator-prey system
cites work: Analysis of a predator-prey model with modified Holling-Tanner functional response and time delay
cites work: Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain
cites work: Criterion of Hopf bifurcations without using eigenvalues
description: scientific article; zbMATH DE number 7025360