This mathematical model demonstrates the effect of toxicants on ecological species in a marine food chain, implying stability conditions for the system.
To explore the impact of toxicants on a marine ecological food chain system consisting of three species, this work develops and analyzes a non-linear mathematical model. The model consists of five state variables: phytoplankton, zooplankton, fish, environmental toxicant, and organismal toxicant. We have incorporated the Monod-Haldane functional response as a predation function for each species. Using the Jacobian matrix, the stability analysis was conducted, and necessary constraints were obtained for the system's local and global stability. Hopf bifurcation analysis was performed for carrying capacity (\(K\)) and the rate of decrease in the growth rate of phytoplankton due to the presence of toxicants (\(r_1\)). Also, phase portraits are presented for different parameters of the model. In addition, numerical simulations are executed using MATLAB to prove theoretical findings and explore the impact of parameter variation on ecological species behavior.
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Yadav et al. (2025) studied this question.
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