{
  "id": "1104.4402",
  "version": "v1",
  "published": "2011-04-22T07:34:22.000Z",
  "updated": "2011-04-22T07:34:22.000Z",
  "title": "Stability and convergence of a higher order rational difference Equation",
  "authors": [
    "Hamid Gazor",
    "Saeed Parvandeh"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper the asymptotic stability of equilibria and periodic points of the following higher order rational difference Equation x_{n+1} =(alpha x_{n-k})/(1+x_{n}...x_{n-k}), k>=1, n=0,1,... is studied where the parameters ?alpha, betta, and gamma are positive real numbers, and the initial conditions x_{-k}, ..., x_{0} are given arbitrary real numbers. The forbidden set of this equation is found and then, the order reduction method is used to facilitate the analysis of its asymptotic dynamics",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-22T07:34:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher order rational difference equation",
      "convergence",
      "order reduction method",
      "arbitrary real numbers",
      "periodic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4402G"
    }
  }
}