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Dynamics of a phytoplankton–zooplankton model with three-dimensional patch under the impacts of hydrodynamic conditions

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  • Mondal, Milton
  • Rao, Ch. Srinivasa
  • Zhang, Tonghua

Abstract

In this paper, we propose and study a mathematical model for phytoplankton–zooplankton interaction, considering the impact of hydrodynamic conditions. We investigate the impact of flow-induced hydrodynamic disturbance on the predation of phytoplankton by zooplankton and its consequent effect on the overall plankton dynamics through a mathematical modeling framework. In the model, we have incorporated the ability of phytoplankton to form patches and release toxins into the aquatic environment and also taken into account environmental toxin-induced plankton mortality. Moreover, to capture system dynamics more realistically, we have studied the corresponding seasonally forced model by introducing seasonality in some relevant model parameters. An in-depth mathematical analysis has been carried out for both autonomous and nonautonomous systems, with numerical simulations delving into the diverse dynamics exhibited by each system. We have established the existence of positive periodic solution in the seasonally forced system by using the continuation theorem in coincidence degree theory and also proved its global attractiveness by defining a suitable Lyapunov functional.

Suggested Citation

  • Mondal, Milton & Rao, Ch. Srinivasa & Zhang, Tonghua, 2026. "Dynamics of a phytoplankton–zooplankton model with three-dimensional patch under the impacts of hydrodynamic conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 665-706.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pb:p:665-706
    DOI: 10.1016/j.matcom.2025.10.034
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    References listed on IDEAS

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    1. Joydev Chattopadhyay & Ezio Venturino & Samrat Chatterjee, 2013. "Aggregation of toxin-producing phytoplankton acts as a defence mechanism – a model-based study," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 19(2), pages 159-174, April.
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    3. Sajan, & Kumar Choudhary, Kapil & Dubey, Balram, 2023. "A non-autonomous approach to study the impact of environmental toxins on nutrient-plankton system," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    4. 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.
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    7. Yapei Wang & Min Zhao & Chuanjun Dai & Xinhong Pan, 2014. "Nonlinear Dynamics of a Nutrient-Plankton Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, January.
    8. 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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    10. Chakraborty, Subhendu & Roy, Shovonlal & Chattopadhyay, J., 2008. "Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: A mathematical model," Ecological Modelling, Elsevier, vol. 213(2), pages 191-201.
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