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 feasible equilibria 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.

Mathematical study of a Leslie–Gower-type tritrophic population model in a polluted environment

“…Previously, some research work has been carried out on tri-trophic food-chain systems including toxicant effects on the survival or extinction of species using mathematical models Raveendra Babu 2014, 2016;Hallam and Luna 1984;Thomann et al 1974;Thomann and Connolly 1984). In Misra and Raveendra Babu (2014) the authors have studied the effects of toxicant in a three species food chain system with ''food-limited'' growth of prey population. In the model, the authors have assumed that the carrying capacity and growth rate of prey is affected by environmental toxicant which is being transferred to intermediate and top predator populations through food chain pathways.…”

The qualitative behavior of a plankton-fish interaction model with food limited growth rate and non-constant fish harvesting

“…Zhou and Shi [35] have revisited a diffusive Leslie-Gower predator-prey model and discussed the bifurcation and stability of multiple steady state solutions. In this paper Misra and Babu.A [21] have analyzed the local and global stability of the feasible equilibrium points. They have also given a comparative study with the corresponding non-toxicant system where they have observed that toxicants have very clear effects on the species if the availability of resource is limited.…”