Role of toxin producing phytoplankton on a plankton ecosystem

In this paper, a mathematical model is proposed to study the role of toxin producing phytoplankton on a phytoplankton–zooplankton system with nutrient cycling. The model includes three state variables, viz., nutrient concentration, phytoplankton biomass and zooplankton biomass. It is assumed in the model that phytoplankton biomass is producing toxicant harmful for the zooplankton biomass. All the feasible equilibria of the system are obtained and the conditions for the existence of the interior equilibrium are determined. The local stability analysis of all the feasible equilibria are carried out and the possibility of Hopf-bifurcation of the interior equilibrium is studied. The threshold value in terms of constant input rate of nutrient is determined both analytically and numerically.