Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix
Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix
复制标题
DOI：
10.1137/21m1455917
复制
发表时间：
2021-10
影响因子：
2
通讯作者：
S. Dodson;Bjorn Sandstede
中科院分区：
文献类型：
--
作者：
S. Dodson;Bjorn Sandstede
螺旋波出现在许多图案形成系统中，并且通常用反应扩散系统建模。一些用于模拟生物过程的系统，如离子通道模型，属于反应扩散范畴，通常有一个或多个非扩散物种，导致秩亏扩散矩阵。以往的理论研究主要集中在严格正扩散矩阵的螺旋谱。本文利用一个一般的二元反应扩散方程组，比较了严格正扩散矩阵和秩亏扩散矩阵的螺旋波的本质谱和绝对谱。我们证明了本质谱在一个分量的扩散为零的极限下是不连续的。此外，我们预测的绝对频谱的情况下，一个非扩散慢变量的位置。巴克利和Karma模型的预测证实了数字。
Spiral waves emerge in numerous pattern forming systems and are commonly modeled with reactiondiffusion systems. Some systems used to model biological processes, such as ion-channel models, fall under the reaction-diffusion category and often have one or more non-diffusing species which results in a rankdeficient diffusion matrix. Previous theoretical research focused on spiral spectra for strictly positive diffusion matrices. In this paper, we use a general two-variable reaction-diffusion system to compare the essential and absolute spectra of spiral waves for strictly positive and rank-deficient diffusion matrices. We show that the essential spectrum is not continuous in the limit of vanishing diffusion in one component. Moreover, we predict locations for the absolute spectrum in the case of a non-diffusing slow variable. Predictions are confirmed numerically for the Barkley and Karma models.