Role of nutrient and toxin in occurrence and control of planktonic bloom

Abstract

A phytoplankton-zooplankton prey-predator model has been in vestigated and the role of nutrient concentrations and toxin producing phytoplankton for controlling the planktonic bloom has been discussed. It is assumed that the nutrient uptake function for toxin producing phytoplankton (TPP) is taken as Holling type-II functional responce. We also assume two different types of predational forms: simple law of mass action and Holling type-II response term. It is found that constant nutrient input and dilution rate of nutrient and toxin influence the plankton ecosystem model and maintain stability around the coexistent equilibrium. Therefore stability analysis of all the feasible equilibria are studied. Our observations indicate that if the toxin liberation rate crosses a certain critical value, the system enters into Hopf bifurcation so the existence of Hopf-bifurcation for the interior equilibrium of the system is explored. The local analysis shows that oscillatory regimes and their combinations. In this present paper it reveals the fact that nutrient as well as toxin producing phytoplankton control planktonic bloom i.e. the rate of toxin production by toxin producing phytoplankton plays an important role for controlling oscillations in the plankton system. We also notice that mortality functions of zooplankton has an important role in controlling oscillations, coexistence, survival or extinction of the zooplankton population. Due to a high rate of toxin production of phytoplankton species can change the steady-state behaviour. Computer simulations illustrate the results.