Echelon-mode formation

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter


Bifurcation mechanism of the pattern formation in O(2) ×O(2)-invariant domains is studied. Diamond and stripe patterns are produced by direct bifurcations and echelon modes are engendered by secondary bifurcations. Bifurcating patterns are investigated based on experiments of soil, numerical simulations of sand, and image simulations of kaolin and steel. Fundamentals of group representation theory in Chap. 7 and group-theoretic bifurcation theory in Chap. 8 are the foundations of this chapter.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages53
Publication statusPublished - 2019 Jan 1

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X


  • Bifurcation
  • Diamond pattern
  • Echelon mode
  • Group-theoretic bifurcation theory
  • Image simulation
  • Kaolin
  • Pattern formation
  • Recursive bifurcation
  • Sand
  • Soil
  • Steel
  • Stripe pattern
  • Symmetry

ASJC Scopus subject areas

  • Applied Mathematics


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