发表机构
University of Bristol（布里斯托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出了一种基于色散关系极限分析的构造性方法，用于确定反应扩散系统中图灵不稳定性和波不稳定性的充要条件，并在疟疾模型、FitzHugh-Nagumo 类模型和 Brusselator 系统中进行了验证。
AI 中文摘要
本文给出了具有 $n$ 个分量和对角扩散矩阵的反应扩散系统中稳定平衡态的扩散驱动不稳定性的充要条件。这些不稳定性可以是图灵不稳定性或波不稳定性。文中重现了已知的充要条件，用于确定在无扩散情况下存在导致稳定均匀态发生图灵分岔的扩散速率。然而，本文的证明方法基于对波数趋于零和趋于无穷大这两个对比极限下色散关系的研究，为选择扩散常数提供了一种构造性方法。研究结果分别通过一个疟疾传播模型、一个用于研究可激发波列的 3 分量 FitzHugh-Nagumo 类模型以及两个不同的 4 分量耦合 Brusselator 系统进行了说明。
英文摘要
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with $n$ components and a diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on a study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to $\infty$, gives a constructive method for choosing diffusion constants. The results are illustrated on a model for the dispersion of malaria, a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4 components
Comments8 figures
Journal refVillar-Sepúlveda, E., Champneys, A.R. General conditions for Turing and wave instabilities in reaction-diffusion systems. J. Math. Biol. 86, 39 (2023)
DOI：10.1007/s00285-023-01884-x
