{
  "id": "1601.02078",
  "version": "v1",
  "published": "2016-01-09T05:45:00.000Z",
  "updated": "2016-01-09T05:45:00.000Z",
  "title": "Solution Form of a Higher Order System of Difference Equation and Dynamical Behavior of Its Special Case",
  "authors": [
    "Nabila Haddad",
    "Nouressadat Touafek",
    "Julius Fergy T. Rabago"
  ],
  "comment": "A preprint of this manuscript, which is of 13 pages with 8 figures, is submitted for publication",
  "categories": [
    "math.DS"
  ],
  "abstract": "The solution form of the system of nonlinear difference equations \\begin{equation*} x_{n+1} = \\frac{x_{n-k+1}^{p}y_{n}}{a y_{n-k}^{p}+b y_{n}},\\ y_{n+1} = \\frac{y_{n-k+1}^{p}x_{n}}{\\alpha x_{n-k}^{p}+\\beta x_{n}}, \\quad n, p \\in \\mathbb{N}_{0},\\ k\\in \\mathbb{N}, \\end{equation*} where the coefficients $a, b, \\alpha, \\beta$ and the initial values $x_{-i},y_{-i},i\\in\\{0,1,\\ldots,k\\}$ are real numbers, is obtained. Furthermore, the behavior of solutions of the above system when $p=1$ is examined. Numerical examples are presented to illustrate the results exhibited in the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-09T05:45:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A10"
    ],
    "keywords": [
      "higher order system",
      "solution form",
      "special case",
      "dynamical behavior",
      "nonlinear difference equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102078H"
    }
  }
}