论文标题
Nagumo晶格微分方程的定期固定解决方案：存在区域及其数量
Periodic stationary solutions of the Nagumo lattice differential equation: existence regions and their number
论文作者
论文摘要
Nagumo Lattice微分方程在足够小的扩散速率方面具有任意空间周期的固定溶液。从解耦系统的固定溶液（隔离节点系统）的延续来确定它们的类型。解决方案由三个字母字母的单词标记。每个固定解决方案类型都可以分配一个参数区域，可以在其中唯一地识别解决方案。方程中存在的许多对称性导致某些区域具有相同的形状。在组合枚举的帮助下，我们得出了确定定性不同存在区域数量的公式。我们还讨论了具有更通用的非线性项和/或空间结构的其他系统的可能扩展。
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.
