{
  "id": "1905.02256",
  "version": "v1",
  "published": "2019-05-06T20:33:34.000Z",
  "updated": "2019-05-06T20:33:34.000Z",
  "title": "On the onset of synchronization of Kuramoto oscillators in scale-free networks",
  "authors": [
    "Thomas Peron",
    "Bruno Messias",
    "Angélica S. Mata",
    "Francisco A. Rodrigues",
    "Yamir Moreno"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "nlin.AO",
    "physics.soc-ph"
  ],
  "abstract": "Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < \\gamma \\leq 3$, in line with what has been observed for other dynamical processes in such networks. For $\\gamma > 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-06T20:33:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scale-free networks",
      "kuramoto oscillators",
      "synchronization",
      "complex networks",
      "phase oscillators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}