{
  "id": "0707.1963",
  "version": "v2",
  "published": "2007-07-13T10:27:19.000Z",
  "updated": "2007-07-24T09:43:13.000Z",
  "title": "Kauffman Boolean model in undirected scale free networks",
  "authors": [
    "Piotr Fronczak",
    "Agata Fronczak",
    "Janusz A. Holyst"
  ],
  "doi": "10.1103/PhysRevE.77.036119",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)\\sim k^{-\\gamma}$. We show that in infinite scale-free networks the transition between frozen and chaotic phase occurs for $3<\\gamma < 3.5$. The observation is interesting for two reasons. First, since most of critical phenomena in scale-free networks reveal their non-trivial character for $\\gamma<3$, the position of the critical line in Kauffman model seems to be an important exception from the rule. Second, since gene regulatory networks are characterized by scale-free topology with $\\gamma<3$, the observation that in finite-size networks the mentioned transition moves towards smaller $\\gamma$ is an argument for Kauffman model as a good starting point to model real systems. We also explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-24T09:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Hc",
      "64.60.Cn",
      "05.45.-a"
    ],
    "keywords": [
      "undirected scale free networks",
      "kauffman boolean model",
      "critical line",
      "scale-free topology",
      "kauffman model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "Mar",
      "volume": 77,
      "number": 3,
      "pages": "036119"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..77c6119F"
    }
  }
}