{
  "id": "1105.4144",
  "version": "v1",
  "published": "2011-05-20T18:08:19.000Z",
  "updated": "2011-05-20T18:08:19.000Z",
  "title": "Coarse Graining the Dynamics of Heterogeneous Oscillators in Networks with Spectral Gaps",
  "authors": [
    "Karthikeyan Rajendran",
    "Ioannis G. Kevrekidis"
  ],
  "comment": "11 pages, 9 figures",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD",
    "physics.comp-ph"
  ],
  "abstract": "We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low-dimensional. Our first choice of coarse variables consists of the components of the oscillator states -their (complex) phase angles- along the leading eigenvectors of this Laplacian. We then use the equation-free framework [1], circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed point and coarse limit cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fastdeveloping correlations between oscillator state and oscillator intrinsic properties, and establishes a connection with tools developed in the context of uncertainty quantification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-20T18:08:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.10.-a",
      "05.45.Xt"
    ],
    "keywords": [
      "spectral gap",
      "heterogeneous oscillators",
      "coarse graining",
      "coarse limit cycle computations",
      "oscillator state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.84.036708",
      "journal": "Physical Review E",
      "year": 2011,
      "month": "Sep",
      "volume": 84,
      "number": 3,
      "pages": "036708"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..84c6708R"
    }
  }
}