Engineering Mathematics, University of Bristol, Ada Lovelace Building, Tankard's Cl, University Walk, Bristol, Somerset, BS8 1TW, UK.
J Math Biol. 2023 Jan 28;86(3):39. doi: 10.1007/s00285-023-01870-3.
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with n components and 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 study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to [Formula: see text], gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.
给出了具有 n 个组件和对角扩散矩阵的反应扩散系统稳定平衡点的扩散驱动不稳定性的充要条件。这些可以是图灵不稳定性或波不稳定性。对于在没有扩散的情况下导致稳定均匀状态的图灵分岔的扩散率，重现了已知的充要条件。不过，这里的证明方法是基于在波数趋于零和[公式：见文本]的对比极限中研究频散关系，这为选择扩散常数提供了一种建设性方法。结果用一个拟议用于研究兴奋波的 3 分量 FitzHugh-Nagumo 模型以及两个具有 4 个分量的不同耦合 Brusselator 系统进行了说明。
