To synchronize or not to synchronize, that is the question: Finite-size scaling and fluctuation effects in the Kuramoto model

Lei Han TANG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the oscillator density at the synchronizing frequency. This is the source for the unusual values assumed by the correlation size exponent ν′. Locally coupled oscillators on a d-dimensional lattice exhibit two types of frequency entrainment in the thermodynamic limit: symmetry-breaking at d > 4 and aggregation of compact synchronized domains in three and four dimensions. Various critical properties of the transition are well captured by finite-size scaling relations with simple yet unconventional exponent values.

Original languageEnglish
Article numberP01034
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2011
Issue number1
DOIs
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Dynamical heterogeneities (theory)
  • Finite-size scaling
  • Network dynamics
  • Nonlinear dynamics

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