Stability of least energy patterns of the shadow system for an activator-inhibitor model

被引：0

作者：

Wei-Ming Ni

Izumi Takagi

Eiji Yanagida

机构：

[1] University of Minnesota,School of Mathematics

[2] Tohoku University,Mathematical Institute

来源：

Japan Journal of Industrial and Applied Mathematics | 2001年 / 18卷

关键词：

reaction-diffusion system; shadow system; spike-layer; stability; Hopf bifurcation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Stability of stationary solutions to the shadow system for the activator-inhibitor system proposed by Gierer and Meinhardt is considered in higher dimensional domains. It is shown that a stationary solution with minimal “energy” is stable in a weak sense if the inhibitor reacts sufficiently fast, while it is unstable whenever the reaction of the inhibitor is slow. Moreover, the loss of stability results in a Hopf bifurcation.

引用

页码：259 / 272

页数：13

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