Continuous limit and the moments system for the globally coupled phase oscillators

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16 Citations (Scopus)


The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on N-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization. In this paper, the moments systems are introduced for both of the Kuramoto model and its continuous model. It is shown that the moments systems for both systems take the same form. This fact allows one to prove that the order parameter of the N-dimensional Kuramoto model converges to that of the continuous model as N → ∞.

Original languageEnglish
Pages (from-to)1891-1903
Number of pages13
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number5
Publication statusPublished - 2013 May
Externally publishedYes


  • Continuous limit
  • Coupled oscillators
  • Kuramoto model
  • Moments system
  • Synchronization

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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