Stability Analysis of a Complex Four Species Food-web Model

Abstract

This paper aims to study the dynamical behaviours of a four dimensional food web system consisting of a bottom prey, two middle predators and a superpredator(top predator) with Holling-Type I and Type II functional responses. A system of four differential equations has been proposed and analyzed. Positivity, boundedness and extinction criteria of the system are studied. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. We also explore the system undergoes a Hopf-bifurcation around interior equilibrium point for a parametric values which is very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.