{
  "id": "math/0409390",
  "version": "v1",
  "published": "2004-09-21T11:04:29.000Z",
  "updated": "2004-09-21T11:04:29.000Z",
  "title": "Methods for determination and approximation of the domain of attraction",
  "authors": [
    "E. Kaslik",
    "A. M. Balint",
    "St. Balint"
  ],
  "comment": "17 pages, 2 figures accepted to be published in Nonlinear Analysis: Theory, Methods and Applications, Elsevier Science Publishers",
  "categories": [
    "math.DS",
    "math.GM"
  ],
  "abstract": "In this paper, an $\\mathbb{R}$-analytical function and the sequence of its Taylor polynomials (which are Lyapunov functions different from those of Vanelli & Vidyasagar (1985, Automatica, 21(1):6 9--80)) is presented, in order to determine and approximate the domain of attraction of the exponentially asymptotically stable zero steady state of an autonomous, $\\mathbb{R}$-analytical system of differential equations. The analytical function and the sequence of its Taylor polynomials are constructed by recurrence formulae using the coefficients of the power series expansion of $f$ at 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-21T11:04:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "attraction",
      "taylor polynomials",
      "approximation",
      "determination",
      "asymptotically stable zero steady state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9390K"
    }
  }
}