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On the system of rational difference equations xn+1 = f(yn-q, xn-s), yn+1 = g(xn-t, yn-p)

Abstract

We study the global behavior of positive solutions of the system of rational difference equations xn+1 = f(yn-q, xn-s), yn+1 = g(xn-t, yn-p), n = 0,1,2,..., where p, q, s, t {0,1,2,...} with st and pq, the initial values x-s, x-s+1,...,x0, y-p, y-p+1,...y0 (0,+∞). We give sufficient conditions under which every positive solution of this system converges to the unique positive equilibrium.

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Correspondence to 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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Sun, T., Xi, H. On the system of rational difference equations xn+1 = f(yn-q, xn-s), yn+1 = g(xn-t, yn-p). Adv Differ Equ 2006, 051520 (2006). https://doi.org/10.1155/ADE/2006/51520

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  • DOI: https://doi.org/10.1155/ADE/2006/51520

Keywords

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