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Dynamical behaviors of a classical Lotka–Volterra competition–diffusion–advection system
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2021-04-27 , DOI: 10.1016/j.nonrwa.2021.103344
Xiao Yan , Yanling Li , Hua Nie

This paper deals with a two-species competition model in a homogeneous advective environment, where two species are subjected to a net loss of individuals at the downstream end. Under the assumption that the advection and diffusion rates of two species are proportional, we give a basic classification on the global dynamics by employing the theory of monotone dynamical system. It turns out that bistability does not happen, but coexistence and competitive exclusion may occur. Furthermore, we present a complete classification on the global dynamics in terms of the growth rates of two species. However, once the above assumption does not hold, bistability may occur. In detail, there exists a tradeoff between growth rates of two species such that competition outcomes can shift between three possible scenarios, including competitive exclusion, bistability and coexistence. These results show that growth competence is important to determine dynamical behaviors.



中文翻译:

经典的Lotka-Volterra竞争-扩散-对流系统的动力学行为

本文研究了在同质对流环境中的两种种群竞争模型,其中两种种群在下游均遭受个体净损失。在两个物种的对流和扩散速率成比例的假设下,我们采用单调动力系统理论对整体动力学进行了基本分类。事实证明,双稳态并不会发生,但是可能会存在共存和竞争排斥。此外,我们根据两个物种的增长率提出了关于全球动态的完整分类。但是,一旦上述假设不成立,则可能会发生双稳态。详细地讲,两个物种的增长率之间存在折衷,因此竞争结果可以在三种可能的情况之间转移,包括竞争排斥,双稳态和共存。这些结果表明,增长能力对于确定动力学行为很重要。

更新日期:2021-04-28
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