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Dissolved oxygen, phytoplankton, and zooplankton populations represent the basis of the proposed mathematical model designed to investigate the impact of the depletion of dissolved oxygen in the plankton ecosystem. The dynamic analysis of the model is devoted to locating all possible equilibrium points. The analysis demonstrates that three equilibrium positions are possible. The existence of the Hopf-bifurcation for the interior equilibrium is investigated using the phytoplankton's photosynthesis-produced oxygen rate as the bifurcation parameter. Conditions for stable limit cycles are obtained. In conclusion, a numerical simulation is shown as evidence to support the analytic results.
Ali et al. (Thu,) studied this question.