Periodic stationary solutions of the Nagumo lattice differential equation: existence regions and their number

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.14232/EJQTDE.2021.1.23

V. Svígler

引用次数: 2

Abstract

The Nagumo lattice differential equation admits stationary solutions with arbitrary spatial period for sufficiently small diffusion rate. The continuation from the stationary solutions of the decoupled system (a system of isolated nodes) is used to determine their types; the solutions are labelled by words from a three-letter alphabet. Each stationary solution type can be assigned a parameter region in which the solution can be uniquely identified. Numerous symmetries present in the equation cause some of the regions to have identical or similar shape. With the help of combinatorial enumeration, we derive formulas determining the number of qualitatively different existence regions. We also discuss possible extensions to other systems with more general nonlinear terms and/or spatial structure.

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Nagumo格微分方程的周期平稳解:存在区域及其数目

当扩散速率足够小时，Nagumo晶格微分方程允许具有任意空间周期的平稳解。用解耦系统(孤立节点系统)的平稳解的延拓来确定它们的类型;答案由三个字母的字母表中的单词标记。每个固定的解决方案类型可以分配一个参数区域，其中的解决方案可以唯一地识别。方程中存在的许多对称性导致一些区域具有相同或相似的形状。利用组合枚举的方法，导出了定性不同存在区域数目的确定公式。我们还讨论了对其他具有更一般非线性项和/或空间结构的系统的可能扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.