Global Stability and Persistence of Three Species Food Web Involving Omnivory

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.