Summary: A three stage-structured prey-predator model with two delays is considered. The characteristic equations of the equilibrium points are analyzed. By using the Nyquist criterion, estimate of the length of the delay to preserve stability is obtained. By applying the theorem of Hopf bifurcation, the conditions for the positive equilibrium to occur local Hopf bifurcation are given, and the properties (direction, stability, etc.) analyzed by normal form theorem and center manifold. The conditions for the existence of global Hopf bifurcation of the system are obtained.
Finally, numerical simulation and brief conclusion are given.