Stability and bifurcation for a kind of nonlinear delayed differential equations

In this paper, a kind of nonlinear delayed differential equations which can describe a two species predator-prey system with stage structure is discussed. The stability of the equilibria of the system and the existence of Hopf bifurcations are given. And the stability and the direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem.