@article{38186,
  keywords = {Synchronization, Kinetics, molecular-dynamics, bifurcation-analysis, differential-equations, integration, populations, equation-free, projective-methods, simulations, multiscale computation, free-energy, coupled oscillators},
  author = {Sung Joon Moon and Ioannis Kevrekidis},
  title = {An equation-free approach to coupled oscillator dynamics: The Kuramoto model example},
  abstract = { <p>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.</p> },
  year = {2006},
  journal = {International Journal of Bifurcation and Chaos},
  volume = {16},
  pages = {2043-2052},
  month = {07/2006},
  isbn = {0218-1274},
  language = {English},
}