Dynamic complexities in 2-dimensional discrete-time predator-prey systems with Allee effect in the prey
type: Item
instance of: scholarly article
title: Dynamic complexities in 2-dimensional discrete-time predator-prey systems with Allee effect in the prey
zbMATH Open document ID: 1376.92055
DOI: 10.1155/2016/4275372
author: Jie Yan
author: Xueli Chen
author: Lishun Ren
author: Chun-li Li
published in: Discrete Dynamics in Nature and Society
publication date: 2017-11-13T00:00:00Z
review text: Summary: The Allee effect is incorporated into a predator-prey model with linear functional response. Compared with the predator-prey which only takes the crowding effect and predator partially dependent on prey into consideration, it is found that the Allee effect of the prey species would increase the extinction risk of both the prey and predator. Moreover, by using a center manifold theorem and bifurcation theory, it is shown that the model with Allee effect undergoes the flip bifurcation and Hopf bifurcation in the interior of \(\mathbb R_+^2\) with different Allee effect values. In the two bifurcations, we can come to the conclusion that different Allee effect will have different bifurcation value and the increasing of the Allee effect will increase the value of bifurcation, respectively.
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6806262
zbMATH Keywords: predator-prey model
zbMATH Keywords: linear functional response
zbMATH Keywords: Allee effect
zbMATH Keywords: bifurcation
Wikidata QID: Q59123494
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/4275372
OpenAlex ID: W2507394276
cites work: Q5312212
cites work: Q5324352
cites work: Q3895297
cites work: A predator-prey model with Ivlev's functional response
cites work: Stability analysis on a predator-prey system with distributed delays
cites work: Q4429919
cites work: Modelling a predator-prey system with infected prey in polluted environment
cites work: Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey
cites work: Global Analysis of a System of Predator–Prey Equations
cites work: Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey
cites work: Bifurcation analysis of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and strong Allee effect
cites work: How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses
cites work: Global qualitative analysis of a predator-prey system with Allee effect on the prey species
cites work: Complex dynamic behaviors of a discrete-time predator-prey system
cites work: Bifurcation and chaotic behavior of a discrete-time predator-prey system
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
description: scientific article; zbMATH DE number 6806262