An equation-free approach to coupled oscillator dynamics: The Kuramoto model example

Sung Joon Moon, Ioannis G. Kevrekidis

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4 Scopus citations


We present an equation-free multiscale approach to the computational study of the collective dynamics of the Kuramoto model [Kuramoto, 1984], a prototypical model for coupled oscillator populations. Our study takes place in a reduced phase space of coarse-grained "observables" of the system: the first few moments of the oscillator phase angle distribution. We circumvent the derivation of explicit dynamical equations (approximately) governing the evolution of these coarse-grained macroscopic variables; instead we use the equation-free framework [Kevrekidis et al., 2003] to computationally solve these equations without obtaining them in closed form. In this approach, the numerical tasks for the conceptually existing but unavailable coarse-grained equations are implemented through short bursts of appropriately initialized simulations of the "fine-scale", detailed coupled oscillator model. Coarse projective integration and coarse fixed point computations are illustrated.

Original languageEnglish (US)
Pages (from-to)2043-2052
Number of pages10
JournalInternational Journal of Bifurcation and Chaos
Issue number7
StatePublished - Jul 2006

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


  • Coupled oscillators
  • Equation-free
  • Multiscale computation


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