Hopf bifurcation of a predator-prey system with delays and stage structure for the prey
type: Item
instance of: scholarly article
title: Hopf bifurcation of a predator-prey system with delays and stage structure for the prey
zbMATH Open document ID: 1257.92046
DOI: 10.1155/2012/282908
published in: Discrete Dynamics in Nature and Society
publication date: 2013-02-21T00:00:00Z
review text: Summary: This paper is concerned with a Holling type III predator-prey system with stage structure for the prey population and two time delays. The main result is given in terms of local stability and bifurcations. By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are also included.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 65C20
zbMATH DE Number: 6137726
Wikidata QID: Q58700447
author: Zizhen Zhang
author: Huizhong Yang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/282908
OpenAlex ID: W2168244576
cites work: Global Stability for a Class of Predator-Prey Systems
cites work: Global analyses in some delayed ratio-dependent predator-prey systems
cites work: Self-organized wave pattern in a predator-prey model
cites work: Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay
cites work: Positive solutions of a diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemes
cites work: Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response
cites work: The study of a ratio-dependent predator-prey model with stage structure in the prey
cites work: Bifurcation and stability analysis in predator-prey model with a stage-structure for predator
cites work: Global stability of a predator-prey system with stage structure for the predator
cites work: Global dynamics of a predator-prey model with time delay and stage structure for the prey
cites work: Stability and Hopf bifurcation in a delayed predator-prey system with stage structure for prey
cites work: Hopf bifurcation of a predator-prey model with time delay and stage structure for the prey
cites work: Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure
cites work: Existence and global attractivity of positive periodic solutions for a predator-prey model with modified Leslie-Gower Holling-type II schemes
cites work: Periodic solutions in a delayed predator-prey model with nonmonotonic functional response
cites work: Periodic solutions of delayed predator-prey model with the Beddington-DeAngelis functional response
cites work: Bifurcation and chaos in a ratio-dependent predator-prey system with time delay
cites work: Bifurcations in a predator-prey model with discrete and distributed time delay
cites work: Bifurcation analysis in a delayed Lotka-Volterra predator-prey model with two delays
cites work: Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predator
cites work: Complex dynamics in a prey predator system with multiple delays
cites work: Dynamic behaviour of a delayed predator-prey model with harvesting
description: scientific article; zbMATH DE number 6137726