Stability and Selective Harvesting of a Phytoplankton-Zooplankton System
Considering that some zooplankton can be harvested for food in some bodies of water, a phytoplankton-zooplankton model with continuous harvesting of zooplankton only is proposed and investigated. By using environmental carrying capacity as a parameter, possible dynamic behaviors, such as stability,...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/684790 |
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| _version_ | 1849399793765318656 |
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| author | Yong Wang Hongbin Wang |
| author_facet | Yong Wang Hongbin Wang |
| author_sort | Yong Wang |
| collection | DOAJ |
| description | Considering that some zooplankton can be harvested for food in some bodies of water, a phytoplankton-zooplankton model with continuous harvesting of zooplankton only is proposed and investigated. By using environmental carrying capacity as a parameter, possible dynamic behaviors, such as stability, global stability, Hopf bifurcation, and transcritical bifurcations, are analyzed. The optimal harvesting policy is disposed by imposing a tax per unit biomass of zooplankton. The problem of determining the optimal harvest policy is solved by using Pontryagin's maximum principle subject to the state equations and the control constraints, and the impact of tax is also discussed. Finally, some numerical simulations are performed to justify analytical findings. |
| format | Article |
| id | doaj-art-9cb01c417b9341f68230ab5b3b332fcd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9cb01c417b9341f68230ab5b3b332fcd2025-08-20T03:38:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/684790684790Stability and Selective Harvesting of a Phytoplankton-Zooplankton SystemYong Wang0Hongbin Wang1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaConsidering that some zooplankton can be harvested for food in some bodies of water, a phytoplankton-zooplankton model with continuous harvesting of zooplankton only is proposed and investigated. By using environmental carrying capacity as a parameter, possible dynamic behaviors, such as stability, global stability, Hopf bifurcation, and transcritical bifurcations, are analyzed. The optimal harvesting policy is disposed by imposing a tax per unit biomass of zooplankton. The problem of determining the optimal harvest policy is solved by using Pontryagin's maximum principle subject to the state equations and the control constraints, and the impact of tax is also discussed. Finally, some numerical simulations are performed to justify analytical findings.http://dx.doi.org/10.1155/2014/684790 |
| spellingShingle | Yong Wang Hongbin Wang Stability and Selective Harvesting of a Phytoplankton-Zooplankton System Journal of Applied Mathematics |
| title | Stability and Selective Harvesting of a Phytoplankton-Zooplankton System |
| title_full | Stability and Selective Harvesting of a Phytoplankton-Zooplankton System |
| title_fullStr | Stability and Selective Harvesting of a Phytoplankton-Zooplankton System |
| title_full_unstemmed | Stability and Selective Harvesting of a Phytoplankton-Zooplankton System |
| title_short | Stability and Selective Harvesting of a Phytoplankton-Zooplankton System |
| title_sort | stability and selective harvesting of a phytoplankton zooplankton system |
| url | http://dx.doi.org/10.1155/2014/684790 |
| work_keys_str_mv | AT yongwang stabilityandselectiveharvestingofaphytoplanktonzooplanktonsystem AT hongbinwang stabilityandselectiveharvestingofaphytoplanktonzooplanktonsystem |