Bifurcation analysis of a food chain system incorporating time delay and the disease spreading among prey species

Abstract

In this paper, a food chain system incorporating time delay and the disease spreading among prey species is proposed. The positive of such system is given. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the corresponding characteristic equation, and the properties of Hopf bifurcation are showed by using the normal form theory and center manifold theorem. Some simulations are given to support our analytical results.