A diffusion-advection predator-prey model with a protection zone

Abstract

In this paper, we investigate a diffusion-advection predator-prey model imposed the Danckwerts boundary conditions with three different types of protection zone. Some special cases have been extensively studied, such as: diffusion-advection predator-prey model without protection zone [22,29] and diffusive predator-prey model with protection zone without advection in high dimension [5,16]. Some ideas developed in the former works do not appear to work due to the difficulty caused by diffusion, advection and protection zone. By applying the comparison principle for parabolic equations [32] and persistence theory [26,37], we obtain almost complete long-time dynamics, which describes the optimal protection zone. If the predator functional response is Holling-type I, the uniqueness of the positive steady state has been derived, which improves the method proposed by López-Gómez and Pardo [20] and developed by Nie et al. [28]. Finally, new ways of coexistence have been obtained by investigating a special three-species model.