Existence of bifurcation on a general Gause food chain model

A class of 3-dimensional Gause food chain model is considered.The stability of the equilibrium points and the existence of Hopf bifurcation are obtained via analyzing the distribution of the roots of the associated characteristic equation with the linear part of the model.Then stability and direction of the Hopf bifurcation are illustrated by using the normal form method and the center mainifold theorem.A numerical simulation is carried out to illustrate the results.