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Global Dynamics of a Lotka--Volterra Competition-Diffusion System in Advective Heterogeneous Environments
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2021-07-13 , DOI: 10.1137/20m1372639
De Tang , Yuming Chen

SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 3, Page 1232-1252, January 2021.
This work is a continuation and extension of a recent one by Tang and Chen [Global dynamics of a Lotka--Volterra competition-diffusion system in advective homogeneous environments, J. Differential Equations, 269 (2020), pp. 1465--1483]. In that work, we studied a Lotka--Volterra competition-diffusion model in a one-dimensional advective homogeneous environment, where the downstream end has a net loss of individuals measured by $b$. The global dynamics is completely characterized by $b$. In this paper, we consider the case where the environment is heterogeneous and $b\ge 1$. We first provide necessary and sufficient conditions on persistence of the corresponding single species model. Then for the two-species model, after analyzing the linear stability of the semitrivial steady states (if they exist) and excluding the existence of coexistence steady states (with highly nontrivial arguments), we apply the theory of monotone dynamical systems to find that the species with slower diffusion rate (if it persists) is always selected. This is different from the situation that $b=1$ is a bifurcation value when the environment is homogeneous. We leave the challenging case where $b<1$ for future work.


中文翻译:

Lotka--Volterra竞争-扩散系统在平流异质环境中的全局动力学

SIAM Journal on Applied Dynamical Systems,第 20 卷,第 3 期,第 1232-1252 页,2021 年 1 月。
这项工作是 Tang 和 Chen 最近工作的延续和扩展 [Lotka--Volterra 竞争扩散系统在平流均匀环境中的全局动力学,J. 微分方程,269 (2020),第 1465--1483 页] . 在这项工作中,我们研究了一维平流均质环境中的 Lotka--Volterra 竞争扩散模型,其中下游端的个体净损失以 $b$ 衡量。全球动态完全以 $b$ 为特征。在本文中,我们考虑环境异构且 $b\ge 1$ 的情况。我们首先提供了相应的单一物种模型的持久性的充分必要条件。那么对于二种模型,在分析了半平凡稳态(如果它们存在)的线性稳定性并排除共存稳态的存在(具有高度非平凡的论点)之后,我们应用单调动力系统理论来发现扩散速率较慢的物种(如果存在)持续)始终被选中。这与环境同质时$b=1$为分叉值的情况不同。我们将 $b<1$ 的具有挑战性的情况留给未来的工作。
更新日期:2021-07-14
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