The effects of diffusion on the dynamics of a Lotka-Volterra predator-prey model with a protection zone

This paper is concerned with the dynamics of a diffusive predator-prey model with a protection zone under homogeneous Neumann boundary conditions. By assuming that the diffusion rates of two species are one, Du and Shi (JDE 229:63–91, 2006) studied the impact of protection zone on the dynamics and derived significant difference of the model’s behavior from the original no-protection zone model. The main purpose of this paper is to remove this assumption and investigate the impact of different diffusion rates and protection zone on the dynamics of the model. The sufficient conditions for the existence and non-existence of positive steady states in term of the diffusion rates are established. More importantly, the limiting profiles of positive steady states (when they exist) are also derived as the diffusion rates tend to 0 or ∞. Our research here provides important information about how the diffusion rates affect the dynamics of the model.