GLOBAL STABILITY AND PERSISTENCE OF THREE SPECIESFOOD WEB INVOLVING OMNIVORY

Abstract

In this paper, the dynamics of a three species food web model consisting of
producers, primary consumers and omnivory is studied analytically as well as
numeri-cally. The existence of equilibrium points and local stability analysis
for this model is carried out together with a bifurcation analysis. The
occurrence of hopf bifurcation is also investigated. The persistence conditions
of the food web model are established by using average Lyapunov function.
The global stability analysis of the food web model is also presented with help
of Lyapunov method. Finally, in order to confirm our analytical results,
numerical simulation is carried out for suitable choices of parameters values. It
is observed that, the existence of omnivory in a food web plays a vital role in
the stability of the dynamical behavior of the system.