{
  "id": "1503.00427",
  "version": "v1",
  "published": "2015-03-02T07:16:39.000Z",
  "updated": "2015-03-02T07:16:39.000Z",
  "title": "Effect of randomness in logistic maps",
  "authors": [
    "Abdul Khaleque",
    "Parongama Sen"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study a random logistic map $x_{t+1} = a_{t} x_{t}[1-x_{t}]$ where $a_t$ are bounded ($q_1 \\leq a_t \\leq q_2$), random variables independently drawn from a distribution. $x_t$ does not show any regular behaviour in time. We find that $x_t$ shows fully ergodic behaviour when the maximum allowed value of $a_t$ is $4$. However $< x_{t \\to \\infty}>$, averaged over different realisations reaches a fixed point. For $1\\leq a_t \\leq 4$ the system shows nonchaotic behaviour and the Lyapunov exponent is strongly dependent on the asymmetry of the distribution from which $a_t$ is drawn. Chaotic behaviour is seen to occur beyond a threshold value of $q_1$ ($q_2$) when $q_2$ ($q_1$) is varied. The most striking result is that the random map is chaotic even when $q_2$ is less than the threshold value $3.5699......$ at which chaos occurs in the non random map. We also employ a different method in which a different set of random variables are used for the evolution of two initially identical $x$ values, here the chaotic regime exists for all $q_1 \\neq q_2 $ values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-02T07:16:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "threshold value",
      "randomness",
      "random variables independently drawn",
      "random logistic map",
      "non random map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}