Narrow Results

A simple model of phytoplankton-zooplankton interaction with a periodic input nutrient is presented. The model is then used to study a nutrient-plankton interaction with a toxic substance that inhibits the growth rate of phytoplankton. The effects of the toxin upon the existence, magnitude, and stability of the periodic solutions are discussed.

This paper deals with a nutrient-phytoplankton-zooplankton ecosystem model consisting of dissolved limiting nutrient with nutrient uptake functions. We use a Holling type-II harvest function to model density dependent plankton population. It is assumed that phytoplankton release toxic chemical for self defense against their predators. The model system is studied analytically and the threshold conditions for the existence and stability of various steady states are worked out. It is observed that if the rate of toxin produced by phytoplankton population crosses a certain critical value, the system enters into Hopf bifurcation. We have derived the direction of Hopf-bifurcation. Our observations indicate that constant nutrient input and the maximal zooplankton conversion rate influence the nutrient-plankton ecosystem model and maintain stability around the coexistence equilibrium in the presence of toxic chemical release by phytoplankton for self defense. It is observed that harvesting rates of the plankton population play a vital role in changing the stability criteria. Computer simulations have been carried out to illustrate different analytical results.