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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Main Authors: Yong Wang, Hongbin Wang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/684790
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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.
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institution Kabale University
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publishDate 2014-01-01
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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