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.

中文翻译：

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具有弱Allee效应和大扩散的对流Lotka–Volterra模型的平稳解

本文致力于具有扩散和对流的平稳Lotka-Volterra模型的Neumann问题。在模型中，假定弱Allee效应描述了一个人口增长率。我们首先使用Leray-Schauder度理论获得一些条件，以确保存在非恒定解。然后，我们研究了一个限制系统（具有非局部约束），该系统起源于原始模型，其中一种物种的扩散和对流趋于无穷大。最后，我们对简化一维情况的非恒定解的全局分支结构进行分类。