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Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish

Author

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  • Sk Golam Mortoja

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India)

  • Prabir Panja

    (Department of Applied Science, Haldia Institute of Technology, Haldia 721657, India)

  • Shyamal Kumar Mondal

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India)

Abstract

Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model consisting of phytoplankton, zooplankton, and fish, incorporating the cannibalistic nature of zooplankton harvesting the fish population. Due to differences in their feeding habits, zooplankton are divided into two sub-classes: herbivorous and carnivorous. The dynamic behavior of the model is examined for each of the possible steady states. The stability criteria of the model have been analyzed from both local and global perspectives. Hopf bifurcation analysis has been accomplished with the growth rate of carnivorous zooplankton using cannibalism as a bifurcation parameter. To characterize the optimal control, we have used Pontryagin’s maximum principle. Subsequently, the optimal system has been derived and solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Finally, to facilitate the interpretation of our mathematical results, we have proceeded to investigate it using numerical simulations.

Suggested Citation

  • Sk Golam Mortoja & Prabir Panja & Shyamal Kumar Mondal, 2023. "Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3011-:d:1188457
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    References listed on IDEAS

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    2. Panja, Prabir & Mondal, Shyamal Kumar & Jana, Dipak Kumar, 2017. "Effects of toxicants on Phytoplankton-Zooplankton-Fish dynamics and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 389-399.
    3. Castellani, Marco & Rosland, Rune & Urtizberea, Agurtzane & Fiksen, Øyvind, 2013. "A mass-balanced pelagic ecosystem model with size-structured behaviourally adaptive zooplankton and fish," Ecological Modelling, Elsevier, vol. 251(C), pages 54-63.
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    9. Mortoja, Sk Golam & Panja, Prabir & Paul, Ayan & Bhattacharya, Sabyasachi & Mondal, Shyamal Kumar, 2020. "Is the intermediate predator a key regulator of a tri-trophic food chain model?: An illustration through a new functional response," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
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