Dynamics of a general prey–predator model with prey-stage structure and diffusive effects

In this paper, we propose and study the dynamics of a diffusive prey–predator model with general functional response and stage-structure for the prey. Firstly, we consider the asymptotical stability of equilibrium points and Hopf bifurcation for the reduced ODE system. Secondly, the existence and uniform boundedness of global solutions and stability of equilibrium points for the corresponding reaction–diffusion system are discussed. Finally, we establish the existence and the nonexistence of nonconstant positive steady states of this reaction–diffusion system, which indicates the effect of large diffusivity. Our results shows the importance of the diffusion rate of the predator species (i.e., d3d3). The large diffusion rate of the predator alone will help the generation of patterns. However, a large diffusion rate of the immature prey species or a large diffusion rate of the mature prey species can lead to the nonexistence of spatial patterns.