A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system

Shunsuke Kobayashi, Takashi Okuda Sakamoto, Yasuhide Uegata, Shigetoshi Yazaki

Research output: Contribution to journalArticle

Abstract

An oscillatory hexagonal solution in a two component reaction-diffusion system with a non-local term is studied. By applying the center manifold theory, we obtain a four-dimensional dynamical system that informs us about the bifurcation structure around the trivial solution. Our results suggest that the oscillatory hexagonal solution can bifurcate from a stationary hexagonal solution via the Hopf bifurcation. This provides a reasonable explanation for the existence of the oscillatory hexagon.

Original languageEnglish
Pages (from-to)253-267
Number of pages15
JournalHiroshima Mathematical Journal
Volume50
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Hexagon
  • Hopf bifurcation
  • Pattern formation
  • Reaction-diffusion system

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