The stability and Hopf bifurcation for a predator-prey system with discrete and distributed delays

In this paper, we investigate a predator-prey model with discrete and distributed delays. By choosing the discrete delay as a bifurcation parameter, we show that Hopf bifurcation occur as delay crosses a critical value. Then using normal form theorem and central manifold argument, we obtain the property of the bifurcation periodic solution. Finally, we give an example to support our theoretical analysis.