The Analysis Of Predator And Prey System By Considering The Interference Of Top Predator In A Polluted Environment

Abstract

The modeling investigation in this research discusses the system level effects of a toxicant on a three species food chain system. The model has been studied to visual ize the dynamical behaviour of prey and predator populations under toxicant stress. All the feasible equilibria of the systems are obtained and using stability theory the conditions are derived for the survival or extinction of species. In the model, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. The stability analysis of the model is carried out and the sufficient conditions for the existence and extinction of the populations under the stress of toxicant are obtained. From the analysis of the model it is observed that the effect of toxicant on predator population increases the equilibrium density of prey population. Further, it is also found that the predation rate of the intermedi ate predator is a bifurcating parameter and Hopf-bifurcation occurs at some critical value of this parameter. Finally, numerical simulation is carried out to support the analytical results. We support our analytical findings with numerical simulations.