Bifurcation analysis of a singular bioeconomic model with allee effect and two time delays
type: Item
instance of: scholarly article
title: Bifurcation analysis of a singular bioeconomic model with allee effect and two time delays
zbMATH Open document ID: 1474.34489
DOI: 10.1155/2014/745296
author: Xue Zhang
author: Qingling Zhang
author: Zhongyi Xiang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A singular prey-predator model with time delays is formulated and analyzed. Allee effect is considered on the growth of the prey population. The singular prey-predator model is transformed into its normal form by using differential-algebraic system theory. We study its dynamics in terms of local analysis and Hopf bifurcation. The existence of periodic solutions via Hopf bifurcation with respect to two delays is established. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold argument. Finally, numerical simulations are included supporting the theoretical analysis and displaying the complex dynamical behavior of the model outside the domain of stability.
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34C40
Mathematics Subject Classification ID: 91B55
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 7022999
Wikidata QID: Q59041149
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/745296
OpenAlex ID: W2010920531
cites work: Bifurcations of a class of singular biological economic models
cites work: Hopf bifurcation for a predator-prey biological economic system with Holling type II functional response
cites work: Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting
cites work: Bifurcation and chaotic behavior of a discrete singular biological economic system
cites work: Theory of functional differential equations. 2nd ed
cites work: Introduction to functional differential equations
cites work: Delay differential equations: with applications in population dynamics
cites work: Retracted: Stability and Hopf bifurcations in a delayed Leslie-Gower predator-prey system
cites work: Theory and applications of partial functional differential equations
cites work: Dynamic behavior in a delayed stage-structured population model with stochastic fluctuation and harvesting
cites work: Dynamic behaviour of a delayed predator-prey model with harvesting
cites work: Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
cites work: Hopf bifurcation and stability for a differential-algebraic biological economic system
cites work: Bifurcation and stability analysis for a delayed Leslie-Gower predator-prey system
cites work: Effects of seasonal growth on ratio dependent delayed prey predator system
cites work: Bifurcations for a predator-prey system with two delays
cites work: Global Hopf bifurcation in the Leslie-Gower predator-prey model with two delays
cites work: Q3930015
cites work: Hopf bifurcations in a predator-prey system with a discrete delay and a distributed delay
cites work: Hopf bifurcation of a predator-prey model with time delay and stage structure for the prey
cites work: Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay
cites work: On the stability and Hopf bifurcation of a delay-induced predator-prey system with habitat complexity
description: scientific article; zbMATH DE number 7022999