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Stability and Selective Harvesting of a Phytoplankton‐Zooplankton System

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  • Yong Wang
  • Hongbin Wang

Abstract

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.

Suggested Citation

  • Yong Wang & Hongbin Wang, 2014. "Stability and Selective Harvesting of a Phytoplankton‐Zooplankton System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:684790
    DOI: 10.1155/2014/684790
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    References listed on IDEAS

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    2. Donald M. Anderson, 1997. "Turning back the harmful red tide," Nature, Nature, vol. 388(6642), pages 513-514, August.
    3. Roy, Shovonlal, 2009. "The coevolution of two phytoplankton species on a single resource: Allelopathy as a pseudo-mixotrophy," Theoretical Population Biology, Elsevier, vol. 75(1), pages 68-75.
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