Stationary solutions of advective Lotka-Volterra models with a weak Allee effect and large diffusion

This paper is devoted to the Neumann problem of a stationary Lotka-Volterra model with diffusion and advection. In the model it is assumed that one population growth rate is described by weak Allee effect. We first obtain some sufficient conditions ensuring the existence of nonconstant solutions by using the Leray-Schauder degree theory. And then we study a limiting system (with nonlocal constraint) which stems from the original model as diffusion and advection of one of the species tend to infinity. Finally, we classify the global bifurcation structure of nonconstant solutions of the simplified 1D case. (C) 2020 Elsevier Ltd. All rights reserved.