{
  "id": "0707.3621",
  "version": "v2",
  "published": "2007-07-24T18:45:08.000Z",
  "updated": "2008-02-21T15:38:50.000Z",
  "title": "Critical Line in Random Threshold Networks with Inhomogeneous Thresholds",
  "authors": [
    "Thimo Rohlf"
  ],
  "comment": "18 figures, 17 pages revtex",
  "doi": "10.1103/PhysRevE.78.066118",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "nlin.CG",
    "q-bio.MN"
  ],
  "abstract": "We calculate analytically the critical connectivity $K_c$ of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of $K_c$ with the (average) absolute threshold $|h|$, which approaches $K_c(|h|) \\sim h^2/(2\\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than $h^2$. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity $K_d$, that has no counterpart in Boolean networks. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-21T15:38:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Da",
      "05.45.-a",
      "05.65.+b"
    ],
    "keywords": [
      "random threshold networks",
      "inhomogeneous thresholds",
      "critical line",
      "side-effect strongly modify damage propagation",
      "strongly modify damage propagation behavior"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "Dec",
      "volume": 78,
      "number": 6,
      "pages": "066118"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..78f6118R"
    }
  }
}