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

Hayato Chiba, Diego Pazó

Research output: Contribution to journalArticle

12 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 - 2009 Jun 15
Externally publishedYes

Keywords

  • Kuramoto model
  • Quasiperiodicity
  • Renormalization group method

ASJC Scopus subject areas

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

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