Stability of Least Energy Patterns of the Shadow System for an Activator-Inhibitor Model

Wei Ming Ni, Izumi Takagi, Eiji Yanagida

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)259-272
Number of pages14
JournalJapan Journal of Industrial and Applied Mathematics
Volume18
Issue number2
DOIs
StatePublished - Jun 2001

Keywords

  • Hopf bifurcation
  • Reaction-diffusion system
  • Shadow system
  • Spike-layer
  • Stability

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