Mathematical Modelling of Three Species Food Web with Lotka-Volterra Interaction and Intraspecific Competition

Abstract

Food chain is the transformation of energy from autotrophs to heterotrophs in an ecological zone. Food web is a system of interconnected food chains. In this study, three species food web with intraspecific competition for limited environmental resources and Lotka-Volterra interaction of one species on the other was considered. There were five equilibrium points obtained from the assumptions of no prey exists, no predator exists, no intermediate predator exists, no top predator exists, and coexistence of the species in the environment. Taking these assumptions in to account the dynamics of the model is investigated qualitatively and the result showed that all the species settle down to their corresponding existence equilibrium points provided that in the absence of any predators, in the absence of the intermediate predator and in the absence of the top  predator. Scaling, Stability analysis and numerical simulation of the model were also considered.

Keywords: Food web, Lotka-Volterra interaction, Stability analysis, Numerical simulation.