Abstract In this paper, we mainly study a two-species competition model in a one-dimensional advective homogeneous environment, where the two species are identical except their diffusion rates. One interesting feature of the model is that the boundary condition at the downstream end represents a net loss of individuals, which is tuned by a parameter b to measure the magnitude of the loss. When the upstream end has the no-flux condition, Lou and Zhou (2015) [11] have confirmed that large diffusion rate is more favorable when 0 ≤ b 1 . Here we consider the case where the upstream end has the free-flow condition, which means that the upstream end is linked to a lake. We firstly investigate the corresponding single species model. Here we establish the existence and uniqueness of positive steady states. Then for the two-species model, we find that the parameter b can be regarded as a bifurcation parameter. Precisely, when 0 ≤ b 1 , large diffusion rate is more favorable while when b > 1 , small diffusion rate is selected (if exists). When b = 1 , the system is degenerate in the sense that there is a compact global attractor consisting of a continuum of steady states.

中文翻译：

---

对流均质环境中 Lotka-Volterra 竞争扩散系统的全局动力学

摘要 在本文中，我们主要研究了一维对流均质环境中的两个物种竞争模型，其中两个物种除扩散速率外是相同的。该模型的一个有趣特征是下游端的边界条件代表个体的净损失，通过参数 b 调整以衡量损失的大小。当上游端为无通量条件时，Lou and Zhou (2015) [11] 已经证实，当 0 ≤ b 1 时，大的扩散速率更有利。这里我们考虑上游端具有自由流动条件的情况，这意味着上游端与湖泊相连。我们首先研究相应的单一物种模型。在这里，我们建立了正稳态的存在性和唯一性。那么对于二种模型，我们发现参数 b 可以看作是一个分岔参数。确切地说，当 0 ≤ b 1 时，大的扩散速率更有利，而当 b > 1 时，选择小的扩散速率（如果存在）。当 b = 1 时，系统是退化的，因为存在一个由连续稳态组成的紧凑全局吸引子。