Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect
A delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/471507 |
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| _version_ | 1832551954474074112 |
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| author | Xinhong Pan Min Zhao Chuanjun Dai Yapei Wang |
| author_facet | Xinhong Pan Min Zhao Chuanjun Dai Yapei Wang |
| author_sort | Xinhong Pan |
| collection | DOAJ |
| description | A delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the characteristic equation and identify the condition where a Hopf bifurcation can occur. Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations. |
| format | Article |
| id | doaj-art-6ed052787ca14e67b1891081ad76b157 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6ed052787ca14e67b1891081ad76b1572025-02-03T05:59:54ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/471507471507Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay EffectXinhong Pan0Min Zhao1Chuanjun Dai2Yapei Wang3School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaA delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the characteristic equation and identify the condition where a Hopf bifurcation can occur. Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations.http://dx.doi.org/10.1155/2014/471507 |
| spellingShingle | Xinhong Pan Min Zhao Chuanjun Dai Yapei Wang Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect Abstract and Applied Analysis |
| title | Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect |
| title_full | Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect |
| title_fullStr | Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect |
| title_full_unstemmed | Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect |
| title_short | Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect |
| title_sort | stability and hopf bifurcation analysis of a nutrient phytoplankton model with delay effect |
| url | http://dx.doi.org/10.1155/2014/471507 |
| work_keys_str_mv | AT xinhongpan stabilityandhopfbifurcationanalysisofanutrientphytoplanktonmodelwithdelayeffect AT minzhao stabilityandhopfbifurcationanalysisofanutrientphytoplanktonmodelwithdelayeffect AT chuanjundai stabilityandhopfbifurcationanalysisofanutrientphytoplanktonmodelwithdelayeffect AT yapeiwang stabilityandhopfbifurcationanalysisofanutrientphytoplanktonmodelwithdelayeffect |