{
  "id": "1902.10422",
  "version": "v1",
  "published": "2019-02-27T10:01:14.000Z",
  "updated": "2019-02-27T10:01:14.000Z",
  "title": "Critical dynamics of the Kuramoto model on sparse random networks",
  "authors": [
    "R. Juhász",
    "J. Kelling",
    "G. Ódor"
  ],
  "comment": "13 pages, 8 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We consider the Kuramoto model on sparse random networks such as the Erd\\H{o}s-R\\'enyi 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-27T10:01:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sparse random networks",
      "kuramoto model",
      "critical dynamics",
      "mean-field universality class",
      "order-parameter exponent hard"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}