{
  "id": "cond-mat/0607100",
  "version": "v1",
  "published": "2006-07-05T05:30:16.000Z",
  "updated": "2006-07-05T05:30:16.000Z",
  "title": "Phase Synchronization of non-Abelian Oscillators on Small-World Networks",
  "authors": [
    "Zhi-Ming Gu",
    "Ming Zhao",
    "Tao Zhou",
    "Chen-Ping Zhu",
    "Bing-Hong Wang"
  ],
  "comment": "5 pages, and 3 figures",
  "journal": "Phys. Lett. A 362, 115(2007)",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems on Watts-Strogatz networks are given, including the $n$-dimensional torus, the identity component of 3-dimensional general linear group, the special unitary group, and the special orthogonal group. In all cases, the greater disorder of networks will predict better synchronizability, and the small-world effect ensures the global synchronization for sufficiently large coupling strength. The collective synchronized behaviors of many dynamical systems, such as the integrable systems, the two-state quantum systems and the top systems, can be described by the present phase synchronization frame. In addition, it is intuitive that the low-dimensional systems are more easily to synchronize, however, to our surprise, we found that the high-dimensional systems display obviously synchronized behaviors in regular networks, while these phenomena can not be observed in low-dimensional systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-05T05:30:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase synchronization",
      "small-world networks",
      "non-abelian oscillators",
      "display obviously synchronized behaviors",
      "systems display"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}