Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay

A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation....

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Main Authors: Shuang Guo, Weihua Jiang
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/363051
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author Shuang Guo
Weihua Jiang
author_facet Shuang Guo
Weihua Jiang
author_sort Shuang Guo
collection DOAJ
description A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.
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institution Kabale University
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publishDate 2012-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-e651b255dd5341c6bd55e2ae4704ed522025-08-20T03:26:04ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/363051363051Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with DelayShuang Guo0Weihua Jiang1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaA class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.http://dx.doi.org/10.1155/2012/363051
spellingShingle Shuang Guo
Weihua Jiang
Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
Abstract and Applied Analysis
title Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
title_full Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
title_fullStr Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
title_full_unstemmed Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
title_short Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
title_sort hopf bifurcation analysis on general gause type predator prey models with delay
url http://dx.doi.org/10.1155/2012/363051
work_keys_str_mv AT shuangguo hopfbifurcationanalysisongeneralgausetypepredatorpreymodelswithdelay
AT weihuajiang hopfbifurcationanalysisongeneralgausetypepredatorpreymodelswithdelay