A two-species diffusion-advection competition model with protection zones

Abstract

In this paper, we study a two-species reaction-diffusion-advection competition model imposed the Danckwerts boundary conditions and with boundary protection zones. Some special cases have been extensively studied, which include reaction-diffusion-advection competition models without protection zones [25,29] and reaction-diffusion competition models with protection zones in non-advective environments [7]. If the product of the two competition rates in the unprotected zone is less than a given value, by establishing a prior estimate and applying the monotone dynamical system theory, we completely characterize the global dynamics, which extends some existing ones. If the product is bigger than the above mentioned value, we find that the size of the protection zone plays an important role in determining the global dynamics. We also discuss the problem of optimal protection zone setting and investigate the effect of advection on the critical size of the protection zone.