{
  "id": "2308.08835",
  "version": "v1",
  "published": "2023-08-17T07:52:53.000Z",
  "updated": "2023-08-17T07:52:53.000Z",
  "title": "Stability range of parameters at fixed points for a class of complex dynamics",
  "authors": [
    "Zhen-Hua Feng",
    "Hai-Bo Sang",
    "B. S. Xie"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "We study the parameters range for the fixed point of a class of complex dynamics with the rational fractional function as $R_{n,a,c}(z)=z^n+\\frac{a}{z^n}+c$, where $n=1,2,3,4$ is specified, $a$ and $c$ are two complex parameters. The relationship between two parameters, $a$ and $c$, is obtained at the fixed point. Moreover the explicit expression of the parameter $a$ and $c$ in terms of $\\lambda$ is derived, where $\\lambda$ is the derivative function at fixed point. The parameter regimes for the stability of the fixed point are presented numerically for some typical different cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-17T07:52:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed point",
      "complex dynamics",
      "stability range",
      "rational fractional function",
      "parameter regimes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}