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

Milton Mondal, Ch. Srinivasa Rao and Tonghua Zhang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PB, 665-706

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.

Keywords: Flow-induced disturbance; Three-dimensional patch; Plankton bloom; Seasonality; Periodic solution; Global attractiveness (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pb:p:665-706

DOI: 10.1016/j.matcom.2025.10.034

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