Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays

The purpose of this paper is to study the dynamics of a phytoplankton-zooplankton model with toxin delay. By studying the distribution of the eigenvalues of the associated characteristic equation, the pitchfork bifurcation curve of the system is obtained. Furthermore, on the pitchfork bifurcation cu...

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Main Authors: Jia-Fang Zhang, Dan Zhang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/340174
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author Jia-Fang Zhang
Dan Zhang
author_facet Jia-Fang Zhang
Dan Zhang
author_sort Jia-Fang Zhang
collection DOAJ
description The purpose of this paper is to study the dynamics of a phytoplankton-zooplankton model with toxin delay. By studying the distribution of the eigenvalues of the associated characteristic equation, the pitchfork bifurcation curve of the system is obtained. Furthermore, on the pitchfork bifurcation curve, we find that the system can undergo a Hopf bifurcation at the positive equilibrium, and we derive the critical values where Hopf-Pitchfork bifurcation occurs.
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institution Kabale University
issn 1085-3375
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publishDate 2013-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-2d12c1e87eaa4eb3a83199574e5e77ea2025-02-03T01:12:29ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/340174340174Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with DelaysJia-Fang Zhang0Dan Zhang1School of Mathematics and Information Sciences, Henan University, Kaifeng 475001, ChinaSchool of Mathematics and Information Sciences, Henan University, Kaifeng 475001, ChinaThe purpose of this paper is to study the dynamics of a phytoplankton-zooplankton model with toxin delay. By studying the distribution of the eigenvalues of the associated characteristic equation, the pitchfork bifurcation curve of the system is obtained. Furthermore, on the pitchfork bifurcation curve, we find that the system can undergo a Hopf bifurcation at the positive equilibrium, and we derive the critical values where Hopf-Pitchfork bifurcation occurs.http://dx.doi.org/10.1155/2013/340174
spellingShingle Jia-Fang Zhang
Dan Zhang
Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays
Abstract and Applied Analysis
title Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays
title_full Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays
title_fullStr Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays
title_full_unstemmed Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays
title_short Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays
title_sort hopf pitchfork bifurcation in a phytoplankton zooplankton model with delays
url http://dx.doi.org/10.1155/2013/340174
work_keys_str_mv AT jiafangzhang hopfpitchforkbifurcationinaphytoplanktonzooplanktonmodelwithdelays
AT danzhang hopfpitchforkbifurcationinaphytoplanktonzooplanktonmodelwithdelays