Positive steady states of reaction–diffusion–advection competition models in periodic environment

Abstract

In this paper, we consider the positive steady states for reaction–diffusion–advection competition models in the whole space with a spatially periodic structure. Under the spatially periodic setting, we establish sufficient conditions for the existence of positive steady states of this model, respectively, by investigating the sign of the principal eigenvalue for some linearized eigenvalue problems. As an application, a Lotka–Volterra reaction–diffusion–advection model for two competing species in a spatially periodic environment is considered. Finally, some numerical simulations are presented to seek dynamical behaviors.