EFFECT OF DILUTION RATE ON THE PREDICTABILITY OF A REALISTIC ECOSYSTEM MODEL WITH INSTANTANEOUS NUTRIENT RECYCLING

Abstract

An analysis is made on a three dimensional mathematical model for the interaction of nutrient, phytoplankton and their predator zooplankton population in an open marine system. For a realistic representation of the open marine plankton ecosystem, we have incorporated various natural phenomena such as dissolved limiting nutrient with general nutrient uptake function, nutrient recycling, interspecies competition and grazing at a higher level. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non negative equilibria, as well as persistence are given. The model system is studied analytically and the threshold values for the existence and stability of various steady states are worked out. It is observed that if the dilution rate of nutrient crosses certain critical value, the system enters into Hopf-bifurcation. Finally, it is observed that planktonic bloom can be controlled and stability around the equilibrium of coexistence can be obtained if the dilution rate of phytoplankton population is increased. Computer simulations have been carried out to illustrate different analytical results.