Stability and Hopf bifurcation for a prey-predator model with prey-stage structure and diffusion

In this paper, we first propose a prey-predator model with prey-stage structure and diffusion. Then we discuss the following three problems: (1) stability of non-negative constant steady states for the reduced ODE system and the corresponding reaction diffusion system with homogeneous Neumann boundary conditions; (2) Hopf bifurcation for the ODE system; (3) Hopf bifurcation created by diffusion.