食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)

This paper is concerned with a three-component model consisting of two prey and one predator with time delay and the inclusion of Holling type-Ⅱ response function incorporating a constant proportion of prey refuge. It is shown that the positive equilibrium of the system is locally asymptotically sta...

Full description

Bibliographic Details
Main Authors: ZHANGZizhen(张子振), WANGKai(汪凯)
Format: Article
Language:zho
Published: Zhejiang University Press 2014-11-01
Series:Zhejiang Daxue xuebao. Lixue ban
Subjects:
Online Access:https://doi.org/10.3785/j.issn.1008-9497.2014.06.006
_version_ 1797235965962485760
author ZHANGZizhen(张子振)
WANGKai(汪凯)
author_facet ZHANGZizhen(张子振)
WANGKai(汪凯)
author_sort ZHANGZizhen(张子振)
collection DOAJ
description This paper is concerned with a three-component model consisting of two prey and one predator with time delay and the inclusion of Holling type-Ⅱ response function incorporating a constant proportion of prey refuge. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Changes of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a critical value. Particularly, the direction of Hopf bifurcation and the stability of the periodic solutions are determined by using the normal form method and center manifold theorem. Finally, the numerical simulations are carried out to verify our theoretical findings.
first_indexed 2024-04-24T16:56:21Z
format Article
id doaj.art-cfc241fbc21e4f93a934c4fc5b9533a6
institution Directory Open Access Journal
issn 1008-9497
language zho
last_indexed 2024-04-24T16:56:21Z
publishDate 2014-11-01
publisher Zhejiang University Press
record_format Article
series Zhejiang Daxue xuebao. Lixue ban
spelling doaj.art-cfc241fbc21e4f93a934c4fc5b9533a62024-03-29T01:58:34ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972014-11-0141664264910.3785/j.issn.1008-9497.2014.06.006食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)ZHANGZizhen(张子振)0WANGKai(汪凯)1( 1.School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, Anhui Province, China)( 2.School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, Anhui Province, China)This paper is concerned with a three-component model consisting of two prey and one predator with time delay and the inclusion of Holling type-Ⅱ response function incorporating a constant proportion of prey refuge. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Changes of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a critical value. Particularly, the direction of Hopf bifurcation and the stability of the periodic solutions are determined by using the normal form method and center manifold theorem. Finally, the numerical simulations are carried out to verify our theoretical findings.https://doi.org/10.3785/j.issn.1008-9497.2014.06.006hopf bifurcationpredator-prey systemprey refugeperiodic solutiontime delay
spellingShingle ZHANGZizhen(张子振)
WANGKai(汪凯)
食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)
Zhejiang Daxue xuebao. Lixue ban
hopf bifurcation
predator-prey system
prey refuge
periodic solution
time delay
title 食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)
title_full 食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)
title_fullStr 食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)
title_full_unstemmed 食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)
title_short 食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge)
title_sort 食饵具有庇护的时滞捕食系统稳定性和hopf分支 stability and hopf bifurcation analysis for a competitive predator prey system with delay and prey refuge
topic hopf bifurcation
predator-prey system
prey refuge
periodic solution
time delay
url https://doi.org/10.3785/j.issn.1008-9497.2014.06.006
work_keys_str_mv AT zhangzizhenzhāngzizhèn shíěrjùyǒubìhùdeshízhìbǔshíxìtǒngwěndìngxìnghéhopffēnzhīstabilityandhopfbifurcationanalysisforacompetitivepredatorpreysystemwithdelayandpreyrefuge
AT wangkaiwāngkǎi shíěrjùyǒubìhùdeshízhìbǔshíxìtǒngwěndìngxìnghéhopffēnzhīstabilityandhopfbifurcationanalysisforacompetitivepredatorpreysystemwithdelayandpreyrefuge