Analysis of a complex four species food-web system: A mathematical model

Abstract

This article 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 ordinary differential equations(ODE’s) has been proposed and analyzed.
Positivity, boundedness and extinction criteria of the system are studied. We have discussed the existence of different equilibrium points and stability of the system at these equilibrium points. We also analysed the system undergoes a Hopf-bifurcation around interior equilibrium point for a various parametric values which has very
significant ecological impacts in this work. Computer simulation are carried outto validate our analytical findings. The biological implications of analytical and
numerical findings are discussed critically.