Local behavior around simple critical points

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A general mathematical framework of bifurcation analysis that is to be employed throughout the book is presented. In particular, the Liapunov–Schmidt reduction is introduced as a tool to derive bifurcation equation. Perfect and imperfect bifurcation behaviors at simple critical points are investigated asymptotically in view of the leading terms of the power series expansion of this equation. This chapter lays a theoretical foundation of Chaps. 3 – 6 and is extended to a system with group symmetry in Chaps. 8 and 9.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages35-76
Number of pages42
DOIs
Publication statusPublished - 2019 Jan 1

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume149
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Bifurcation
  • Bifurcation equation
  • Critical point
  • Imperfection
  • Liapunov–Schmidt reduction
  • Limit point
  • Pitchfork bifurcation
  • Stability
  • Transcritical bifurcation
  • Universal unfolding

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Ikeda, K., & Murota, K. (2019). Local behavior around simple critical points. In Applied Mathematical Sciences (Switzerland) (pp. 35-76). (Applied Mathematical Sciences (Switzerland); Vol. 149). Springer. https://doi.org/10.1007/978-3-030-21473-9_2