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Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity

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  • Agnihotri, Kulbhushan
  • Kaur, Harpreet

Abstract

In the present investigation, a prey–predator model consisting of phytoplankton, susceptible zooplankton, and infected zooplankton, incorporating the response function of Holling type II, has been explored. Logistic growth is assumed to be followed by the phytoplankton species. A combined effort (E) is applied to harvest all of the three populations. Environmental toxicity is considered to affect the phytoplankton species directly and the predating zooplankton indirectly. The dynamical behaviour of the model is examined for each of the possible steady states. Hopf-bifurcation analysis has been carried out with the combined harvesting effort E as the bifurcation parameter. The optimal control is characterized by using Pontryagin’s maximum principle. In the end, the analytical discoveries found so far have been established employing numerical simulations.

Suggested Citation

  • Agnihotri, Kulbhushan & Kaur, Harpreet, 2021. "Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 946-964.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:946-964
    DOI: 10.1016/j.matcom.2021.06.022
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    References listed on IDEAS

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    1. Juneja, Nishant & Agnihotri, Kulbhushan & Kaur, Harpreet, 2018. "Effect of delay on globally stable prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 146-156.
    2. Juneja, Nishant & Agnihotri, Kulbhushan, 2018. "Conservation of a predator species in SIS prey-predator system using optimal taxation policy," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 86-94.
    3. Agnihotri, Kulbhushan & Kaur, Harpreet, 2019. "The dynamics of viral infection in toxin producing phytoplankton and zooplankton system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 122-133.
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    Cited by:

    1. Liu, He & Dai, Chuanjun & Yu, Hengguo & Guo, Qing & Li, Jianbing & Hao, Aimin & Kikuchi, Jun & Zhao, Min, 2023. "Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 368-386.
    2. Zheng, Yanlin & Gong, Xiang & Gao, Huiwang, 2022. "Selective grazing of zooplankton on phytoplankton defines rapid algal succession and blooms in oceans," Ecological Modelling, Elsevier, vol. 468(C).
    3. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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