Hopf bifurcation analysis of a delayed diffusive predator-prey system with nonconstant death rate

In this paper, a delayed diffusive predator-prey model with nonconstant death rate and Holling III functional response subject to Neumann boundary condition is considered. Stability of the positive equilibrium and existence of Hopf bifurcation are investigated. And an explicit formula for determining bifurcation direction and stability of bifurcating periodic solution is derived by the theory of normal form and center manifold. Some numerical simulations are carried out.