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Global behavior of a higher-order rational difference equation

Advances in Difference Equations volume 2006, Article number: 027637 (2006) Cite this article

Abstract

We investigate in this paper the global behavior of the following difference equation: , n = 0,1,..., under appropriate assumptions, where b ∈ [0, ∞), k ≥ 1, i0, i1,...,i2k ∈ {0,1,...} with i0 <i1 < ... <i2k, the initial conditions . We prove that unique equilibrium of that equation is globally asymptotically stable.

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Authors and Affiliations

  1. Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi, 530004, China

    Hongjian Xi & Taixiang Sun

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  1. Hongjian Xi
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  2. Taixiang Sun
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Correspondence to Hongjian Xi or Taixiang Sun.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Xi, H., Sun, T. Global behavior of a higher-order rational difference equation. Adv Differ Equ 2006, 027637 (2006). https://doi.org/10.1155/ADE/2006/27637

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  • DOI: https://doi.org/10.1155/ADE/2006/27637

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation