Critical dynamics of the Kuramoto model on sparse random networks

Róbert Juhász, Jeffrey Kelling, G. Ódor

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the Kuramoto model on sparse random networks such as the Erdős-Rényi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition by large-scale, massively parallel numerical integration. By this method, we obtain an estimate of critical coupling strength more accurate than obtained earlier by finite-size scaling of the stationary order parameter. Our results confirm the compatibility of the correlation-size and the temporal correlation-length exponent with the mean-field universality class. However, the scaling of the order parameter exhibits corrections much stronger than those of the Kuramoto model with all-to-all coupling, making thereby an accurate estimate of the order-parameter exponent hard. We find furthermore that, as a qualitative difference to the model with all-to-all coupling, the effective critical exponents involving the order-parameter exponent, such as the effective decay exponent characterizing the critical desynchronization dynamics show a non-monotonic approach toward the asymptotic value. In the light of these results, the technique of finite-size scaling of limited size data for the Kuramoto model on sparse graphs has to be treated cautiously.

Original languageEnglish
Article number53403
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2019
Issue number5
DOIs
Publication statusPublished - May 24 2019

Keywords

  • Critical exponents and amplitudes
  • Dynamical processes
  • Networks
  • Nonlinear dynamics
  • Random graphs

ASJC Scopus subject areas

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

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