{
  "id": "cond-mat/0612303",
  "version": "v1",
  "published": "2006-12-12T21:18:38.000Z",
  "updated": "2006-12-12T21:18:38.000Z",
  "title": "Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect",
  "authors": [
    "Paolo Allegrini",
    "Mauro Bologna",
    "Paolo Grigolini",
    "Bruce J. West"
  ],
  "comment": "4 pages, 1 figure",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "The dynamical emergence (and subsequent intermittent breakdown) of collective behavior in complex systems is described as a non-Poisson renewal process, characterized by a waiting-time distribution density $\\psi (\\tau)$ for the time intervals between successively recorded breakdowns. In the intermittent case $\\psi (t)\\sim t^{-\\mu}$, with complexity index $\\mu $. We show that two systems can exchange information through complexity matching and present theoretical and numerical calculations describing a system with complexity index $\\mu_{S}$ perturbed by a signal with complexity index $\\mu_{P}$. The analysis focuses on the non-ergodic (non-stationary) case $\\mu \\leq 2$ showing that for $\\mu_{S}\\geq \\mu_{P}$, the system $S$ statistically inherits the correlation function of the perturbation $P$. The condition $\\mu_{P}=\\mu_{S}$ is a resonant maximum for correlation information exchange.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-12T21:18:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complexity matching effect",
      "complex systems",
      "complex perturbations",
      "complexity index",
      "non-poisson renewal process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006cond.mat.12303A"
    }
  }
}