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With the increasingly severe lack of resources , people's environmental awareness is growing, the extinction of plants and animals and ecosystems continued existence have become the focus of attention . In the ecosystem , how much the number of predators in order to make a protected wildlife continue to survive ? Fishermen to fish catches to keep to what extent , it will not affect the continued breeding fish ? So for prey - are properties of prey system dynamics , with high practical value. In the ecosystem , delays exist in varying degrees, affect the populations studied. For example, take some time from predator pups grow to adulthood, prey will take some time for their own food into the growth rate , predation and food species were arrested during pregnancy , lactation and so on. Of predator - prey model of the real world population trends have a more reasonable and more accurate forecasts. In this paper, a class of double- delay predator - prey system were studied. First, predator - prey model background and current situation are introduced. Secondly, the time delay respectively τ 1 , τ 2 as a parameter , containing pairs of Predator - Prey Model stability analysis. Specifically, the following : First, make delay τ 1 = 0, the τ 2 = τ as a parameter , according to the system near the equilibrium point linearization part of the characteristic equation roots the distribution system is obtained as well as the stability of the equilibrium point conditions for the existence of Hopf bifurcation ; Second , when lag τ 2 = τ within the stable region , it will be τ 1 as a parameter , obtained using the same method the stability of the system equilibrium conditions and the conditions for the existence of Hopf bifurcation ; Third , the use of the center manifold theory and normal form method gives a Hopf bifurcation bifurcation branch direction and stability of specific formula . Finally, numerical simulation , and further supports our earlier conclusion .
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