Abstract: The Hopf bifurcation of predator-prey symbiotic model with double time delay was discussed  by using the normal form theory and the central manifold theorem. By analyzing the characteristic equation and taking the development time of the prey and the development time of the co-genitor as the parameters, the stability of equilibrium point, the existence of Hopf bifurcation, the stability of bifurcation direction and bifurcating periodic solution were given. The result that  time delay  affected the stability of the system was obtained. The correctness of obtained conclusions was verified through numerical simulation.

Key words: Hopf bifurcation, double time delay, predator-prey symbiotic model