Counting and ordering periodic stationary solutions of lattice Nagumo equations

被引：7

作者：

Hupkes, Hermen Jan ^{[1
]}

Morelli, Leonardo ^{[1
]}

Stehlik, Petr ^{[2
,3
]}

Svigler, Vladimir ^{[2
,3
]}

机构：

[1] Leiden Univ, Math Inst, POB 9512, NL-2300 RA Leiden, Netherlands

[2] Univ West Bohemia, Dept Math, Univ 8, Plzen 30100, Czech Republic

[3] Univ West Bohemia, NTIS, Univ 8, Plzen 30100, Czech Republic

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 98卷

关键词：

Reaction diffusion equation; Lattice differential equation; Graph differential equations; Periodic solutions; Travelling waves; TRAVELING-WAVES;

D O I：

10.1016/j.aml.2019.06.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs we are able to divide these periodic solutions into equivalence classes that can be partially ordered and counted. In order to accomplish this, we use combinatorial concepts such as necklaces, bracelets and Lyndon words. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：398 / 405

页数：8

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