{
  "id": "1503.04539",
  "version": "v1",
  "published": "2015-03-16T06:52:31.000Z",
  "updated": "2015-03-16T06:52:31.000Z",
  "title": "The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics",
  "authors": [
    "Yogesh S. Virkar",
    "Juan G. Restrepo",
    "James D. Meiss"
  ],
  "comment": "14 pages, 10 figures, 1 Appendix",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD"
  ],
  "abstract": "The Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony occurs at a coupling constant $K$ inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters and use these equations to study the effect of network heterogeneity on the synchronization of the rotors. We find that for values of $K$ just beyond the transition to synchronization the degree of synchronization is highly dependent on the network's heterogeneity, but that for large values of $K$ the degree of synchronization is robust to changes in the heterogeneity of the network's degree distribution. Our results are illustrated with numerical simulations on Erd\\\"os-Renyi networks and networks with power-law degree distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-16T06:52:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian mean field model",
      "synchronization dynamics",
      "network structure",
      "adjacency matrix",
      "heterogeneity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}