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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/340174 |
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| _version_ | 1832563759216852992 |
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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. |
| format | Article |
| id | doaj-art-2d12c1e87eaa4eb3a83199574e5e77ea |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |