In this paper, a delayed diffusive predator-prey system with Holling III functional response and prey refuge subject to Neumann boundary condition is considered. By analyzing characteristic equation, stability of the positive equilibrium and existence of Hopf bifurcation are investigated. Also, explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of normal form and center manifold. Some numerical simulations are carried out.

diffusion, delay, Hopf bifurcation, Holling III functional response, predator-prey.