Stability and Hopf bifurcation analysis of a predator-prey system with diffusion and two delays

In this paper, a predator-prey system with diffusion and two delays is investigated. By analyzing the characteristic equations, the local stability of positive equilibrium and local Hopf bifurcations is discussed. Moreover, some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions are obtained by using normal form theory and center manifold theory. The results we obtain can be used to provide reliable foundation for making control strategy.