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Phys Rev Lett. 2007 Feb 2;98(5):054101. Epub 2007 Jan 31.

Kinetic theory of coupled oscillators.

Author information

1
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.

Abstract

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is analogous to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the kinetic theory of plasmas and gases. To calculate the lowest order system size effect, we truncate this hierarchy at second order and solve the resulting closed equations for the two-oscillator correlation function around the incoherent state. We use this correlation function to compute the fluctuations of the order parameter, including the effect of transients, and compare this computation with numerical simulations.

PMID:
17358861
PMCID:
PMC2561959
DOI:
10.1103/PhysRevLett.98.054101
[Indexed for MEDLINE]
Free PMC Article

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