Hopf bifurcation and symmetry: Standing and travelling waves in a circular chain

Stephan A. van Gils; Theo Valkering

doi:10.1007/BF03167098

Hopf bifurcation and symmetry: Standing and travelling waves in a circular chain

Stephan A. van Gils^*
, Theo Valkering

^*Corresponding author for this work

Computational Materials Science

Research output: Contribution to journal › Article › Academic › peer-review

18 Citations (Scopus)

Abstract

We consider a circular chain of N particles with nearest neighbour interaction. Under a condition which is generically fulfilled all periodic solutions near a normal mode frequency are obtained and their symmetry properties are investigated. The genericity condition is explicitly evaluated for a three particle system.

Original language	English
Pages (from-to)	207-222
Number of pages	16
Journal	Japan Journal of Applied Mathematics
Volume	3
Issue number	2
DOIs	https://doi.org/10.1007/BF03167098
Publication status	Published - 1 Dec 1986

Keywords

Circular chain
Hopf bifurcation
Standing waves
Symmetry
Travelling waves

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title = "Hopf bifurcation and symmetry: Standing and travelling waves in a circular chain",

abstract = "We consider a circular chain of N particles with nearest neighbour interaction. Under a condition which is generically fulfilled all periodic solutions near a normal mode frequency are obtained and their symmetry properties are investigated. The genericity condition is explicitly evaluated for a three particle system.",

keywords = "Circular chain, Hopf bifurcation, Standing waves, Symmetry, Travelling waves",

author = "\{van Gils\}, \{Stephan A.\} and Theo Valkering",

year = "1986",

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T1 - Hopf bifurcation and symmetry

T2 - Standing and travelling waves in a circular chain

AU - van Gils, Stephan A.

AU - Valkering, Theo

PY - 1986/12/1

Y1 - 1986/12/1

N2 - We consider a circular chain of N particles with nearest neighbour interaction. Under a condition which is generically fulfilled all periodic solutions near a normal mode frequency are obtained and their symmetry properties are investigated. The genericity condition is explicitly evaluated for a three particle system.

AB - We consider a circular chain of N particles with nearest neighbour interaction. Under a condition which is generically fulfilled all periodic solutions near a normal mode frequency are obtained and their symmetry properties are investigated. The genericity condition is explicitly evaluated for a three particle system.

KW - Circular chain

KW - Hopf bifurcation

KW - Standing waves

KW - Symmetry

KW - Travelling waves

UR - https://www.scopus.com/pages/publications/0040663274

U2 - 10.1007/BF03167098

DO - 10.1007/BF03167098

M3 - Article

AN - SCOPUS:0040663274

SN - 0910-2043

VL - 3

SP - 207

EP - 222

JO - Japan Journal of Applied Mathematics

JF - Japan Journal of Applied Mathematics

IS - 2

ER -

Hopf bifurcation and symmetry: Standing and travelling waves in a circular chain

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Keywords

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