Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control
We investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pair of semicontinuous systems with biological and artificial control. First, the existence of an order-1 periodic solution to the system is analyzed using a Poincaré map and a geometric method. The stab...
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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: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/914647 |
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| _version_ | 1832556181884764160 |
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| author | Yapei Wang Min Zhao Xinhong Pan Chuanjun Dai |
| author_facet | Yapei Wang Min Zhao Xinhong Pan Chuanjun Dai |
| author_sort | Yapei Wang |
| collection | DOAJ |
| description | We investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pair of semicontinuous systems with biological and artificial control. First, the existence of an order-1 periodic solution to the system is analyzed using a Poincaré map and a geometric method. The stability conditions of the order-1 periodic solution are obtained by a theoretical mathematical analysis. Furthermore, based on previous analysis, we investigate the bifurcation in the order-1 periodic solution and prove that the order-1 periodic solution breaks up an order-1 periodic solution at least. In addition, the transcritical bifurcation of the system is described. Finally, we provide a series of numerical results that illustrate the feasibility of the theoretical results. Based on the theoretical and numerical results, we analyzed the feasibility of biological and artificial control, which showed that biological and artificial methods can control phytoplankton blooms. These results are expected to be useful for the study of phytoplankton dynamics in aquatic ecosystems. |
| format | Article |
| id | doaj-art-5088d20247f54005893820efbb8d775c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5088d20247f54005893820efbb8d775c2025-02-03T05:46:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/914647914647Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial ControlYapei Wang0Min Zhao1Xinhong Pan2Chuanjun Dai3School 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, ChinaWe investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pair of semicontinuous systems with biological and artificial control. First, the existence of an order-1 periodic solution to the system is analyzed using a Poincaré map and a geometric method. The stability conditions of the order-1 periodic solution are obtained by a theoretical mathematical analysis. Furthermore, based on previous analysis, we investigate the bifurcation in the order-1 periodic solution and prove that the order-1 periodic solution breaks up an order-1 periodic solution at least. In addition, the transcritical bifurcation of the system is described. Finally, we provide a series of numerical results that illustrate the feasibility of the theoretical results. Based on the theoretical and numerical results, we analyzed the feasibility of biological and artificial control, which showed that biological and artificial methods can control phytoplankton blooms. These results are expected to be useful for the study of phytoplankton dynamics in aquatic ecosystems.http://dx.doi.org/10.1155/2014/914647 |
| spellingShingle | Yapei Wang Min Zhao Xinhong Pan Chuanjun Dai Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control Discrete Dynamics in Nature and Society |
| title | Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control |
| title_full | Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control |
| title_fullStr | Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control |
| title_full_unstemmed | Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control |
| title_short | Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control |
| title_sort | dynamic analysis of a phytoplankton fish model with biological and artificial control |
| url | http://dx.doi.org/10.1155/2014/914647 |
| work_keys_str_mv | AT yapeiwang dynamicanalysisofaphytoplanktonfishmodelwithbiologicalandartificialcontrol AT minzhao dynamicanalysisofaphytoplanktonfishmodelwithbiologicalandartificialcontrol AT xinhongpan dynamicanalysisofaphytoplanktonfishmodelwithbiologicalandartificialcontrol AT chuanjundai dynamicanalysisofaphytoplanktonfishmodelwithbiologicalandartificialcontrol |