Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay
We consider a nutrient-phytoplankton model with a Holling type II functional response and a time delay. By selecting the time delay used as a bifurcation parameter, we prove that the system is stable if the delay value is lower than the critical value but unstable when it is above this value. First,...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/939187 |
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| _version_ | 1850170983751614464 |
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| author | DeBing Mei Min Zhao Hengguo Yu Chuanjun Dai Yi Wang |
| author_facet | DeBing Mei Min Zhao Hengguo Yu Chuanjun Dai Yi Wang |
| author_sort | DeBing Mei |
| collection | DOAJ |
| description | We consider a nutrient-phytoplankton model with a Holling type II functional response and a time delay. By selecting the time delay used as a bifurcation parameter, we prove that the system is stable if the delay value is lower than the critical value but unstable when it is above this value. First, we investigate the existence and stability of the equilibria, as well as the existence of Hopf bifurcations. Second, we consider the direction, stability, and period of the periodic solutions from the steady state based on the normal form and the center manifold theory, thereby deriving explicit formulas. Finally, some numerical simulations are given to illustrate the main theoretical results. |
| format | Article |
| id | doaj-art-a3da2ce4b9a84d0ea178610fd48d2390 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a3da2ce4b9a84d0ea178610fd48d23902025-08-20T02:20:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/939187939187Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time DelayDeBing Mei0Min Zhao1Hengguo Yu2Chuanjun Dai3Yi Wang4School 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, 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, ChinaWe consider a nutrient-phytoplankton model with a Holling type II functional response and a time delay. By selecting the time delay used as a bifurcation parameter, we prove that the system is stable if the delay value is lower than the critical value but unstable when it is above this value. First, we investigate the existence and stability of the equilibria, as well as the existence of Hopf bifurcations. Second, we consider the direction, stability, and period of the periodic solutions from the steady state based on the normal form and the center manifold theory, thereby deriving explicit formulas. Finally, some numerical simulations are given to illustrate the main theoretical results.http://dx.doi.org/10.1155/2015/939187 |
| spellingShingle | DeBing Mei Min Zhao Hengguo Yu Chuanjun Dai Yi Wang Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay Discrete Dynamics in Nature and Society |
| title | Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay |
| title_full | Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay |
| title_fullStr | Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay |
| title_full_unstemmed | Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay |
| title_short | Nonlinear Dynamics of a Nutrient-Phytoplankton Model with Time Delay |
| title_sort | nonlinear dynamics of a nutrient phytoplankton model with time delay |
| url | http://dx.doi.org/10.1155/2015/939187 |
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