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Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillatorsThe theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.
Document ID
19870040076
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Golubitsky, Martin
(Houston, University TX, United States)
Stewart, Ian
(Warwick, University Coventry, United Kingdom)
Date Acquired
August 13, 2013
Publication Date
January 1, 1986
Publication Information
Publication: Contemporary Mathematics
Volume: 56
ISSN: 0271-4132
Subject Category
Numerical Analysis
Accession Number
87A27350
Funding Number(s)
CONTRACT_GRANT: SERC-GR/D/33359
CONTRACT_GRANT: NSF DMS-84-02604
CONTRACT_GRANT: NAG2-279
Distribution Limits
Public
Copyright
Other

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