Localized Patterns in Reaction-Diffusion Systems
Localized Patterns in Reaction-Diffusion Systems
复制标题
反应扩散系统中的局部模式
DOI：
10.1143/ptp.63.106
复制
发表时间：
1980
影响因子：
--
通讯作者：
Y. Kuramoto
中科院分区：
文献类型：
--
作者：
S. Koga;Y. Kuramoto
讨论了一种新的化学模式，即无限介质中的无传播孤立岛。对于一个简单的模型，我们证明了它的存在性和稳定性。本地化原来是一个潜在的兴奋系统中发生的抑制物质的快速扩散的结果。为了提取四氢大麻酚;利用奇异摄动方法研究了定域斑图的重要特征，得到如下结果：（1）对于单稳态或双稳态系统，都可以存在稳定的静止孤立斑图。(2)在合适的条件下，这样的图案经历Hop分叉，导致激活的液滴的“呼吸运动”。整个分析仅限于一维情况。
A new chemical pattern is discussed, which is a propagationless solitary island in an infinite medium. We demonstrate analytically its existence and stability for a certain simple model. The localization turns out to be a consequence of the rapid diffusion of an inhibiting substance occurring in a potentially excitable system. In order to extract thc; important features of the localized pattern, the method of singular perturbation is employed, with the following results: (1) A stable motionless solitary pattern can exist either for a monostablc or bistable system. (2) Under suitable conditions such a pattern undergoes the Hop£ bifurcation, leading to a "breathing motion" of the activated droplet. The analysis is restricted to the one-dimensional case throughout.