Stability of an [N / 2]-dimensional invariant torus in the Kuramoto model at small coupling

Hayato Chiba, Diego Pazó

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N / 2] + 1 (N is the population size). A global phase shift invariance allows us to reduce the model to N - 1 dimensions using the phase differences, and doing so the invariant torus becomes [N / 2]-dimensional. By means of perturbative calculations based on the renormalization group technique, we show that this torus is asymptotically stable at small coupling if N is odd. If N is even the torus can be stable or unstable depending on the natural frequencies, and both possibilities persist in the small coupling limit.

Original languageEnglish
Pages (from-to)1068-1081
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Volume238
Issue number13
DOIs
Publication statusPublished - Jun 15 2009

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resonant frequencies
invariance
phase shift

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Cite this

Stability of an [N / 2]-dimensional invariant torus in the Kuramoto model at small coupling. / Chiba, Hayato; Pazó, Diego.

In: Physica D: Nonlinear Phenomena, Vol. 238, No. 13, 15.06.2009, p. 1068-1081.

Research output: Contribution to journalArticle

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