Lotka-Volterra 反应扩散平流系统的动力学研究

Dynamics of Lotka-VolterraReaction-Diffusion Advection System

摘要: 我们研究两个竞争对手在不同扩散策略下的 Lotka-Volterra 反应 -扩散 -平流模型。一种是通过 扩散和向更有利自己的环境定向移动来扩散，另一种是通过扩散和向逃离更有利于竞争对手的环 境定向移动来扩散。我们表明：在适当的条件下，具有逃离更有利于竞争对手生存环境能力的物 种可能不具有竞争优势，即使它扩散得比其竞争对手要慢。我们将通过研究系统的主特征值如何 依赖于这些速率，来检验扩散速率 µ 和 d 以及有向运动速率 α 和 β 对竞争系统动力学的影响。 我们的方法是对主特征值进行扰动分析。

Abstract: We study a reaction-diffusion-advection model for two competitors under different diffusion strategies. One is by diffusion together with directed movement toward more favorable environments, the other by diffusion together with directed movement away from an environment more conducive to competitors. We show that, under the right conditions, a species with the ability to escape from an environment more conducive to its competitors may not have a competitive advantage, even if it diffusivity is more slowly than its competitors. We will examine the effects of the diffusion rates µ and d and the rate of directed movement α and β on the dynamics of the competition model by studying how the principal eigenvalues in model depend on those rates. The mathematical approach is a perturbation analysis of principal eigenvalues.