A Model for the Effect of Toxicant on a Three Species Food-Chain System with "Food-Limited" Growth of Prey Population

Abstract

In this paper, a mathematical model is proposed and analyzed to study the effect of toxicant in a three species food chain system with food-limited growth of prey population. The mathematical model is formulated using the system of non-linear ordinary differential equations. In the model, there are seven state variables, viz, prey density, intermediate predator density, density of top predator, concentration of toxicant in the environment, concentration of toxicant in the prey, concentration of toxicant in the intermediate predator and concentration of toxicant in the top predator. In the model, it is assumed that the carrying capacity and growth rate of prey is affected by environmental toxicant. Toxicant is transferred to intermediate predator and top predator populations through food chain pathways.All the feasible equilibria of the system are obtained and the conditions are determined for the survival or extinction of species under the effect of toxicant. The local and global stability analysis of all the feasibleequilibria are carried out.Further, the results are compared with the case when toxicant is absent in the system. Finally, we support our analytical findings with numerical simulations. Keywords: Food chain; Toxicant; Food-Limited Growth; Stability; Lyapunov function.