The calculation of the Hopf/Hopf mode interaction point in problems with Z2-symmetry

Faridon Amdjadi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

A direct method for finding the mode interaction point of a symmetry breaking Hopf bifurcation and a symmetry preserving Hopf bifurcation in problems with ℤ2-symmetry is developed. It has been shown that the mode interaction point corresponds to an isolated solution of an extended system. The existence of this solution relies on the occurrence of the mode interaction point and this is interpreted in the context of the mode interaction, using centre manifold reduction. A numerical example with the symmetry group O(2), which has a branch of ℤ2-symmetric nontrivial steady state solutions, is considered to provide clarification of the method.

Original languageEnglish
Pages (from-to)1925-1935
Number of pages11
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume12
Issue number8
DOIs
Publication statusPublished - Aug 2002

Keywords

  • Hopf bifurcation
  • mode interaction
  • ℤ2-symmetry

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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