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On the system of rational difference equations xn+1 = f(x n ,yn-k), yn+1 = f(y n , xn-k)

Abstract

We study the global asymptotic behavior of the positive solutions of the system of rational difference equations xn+1 = f(x n ,yn-k), yn+1 = f(y n , xn-k), n = 0,1,2,..., under appropriate assumptions, where k {1,2,...} and the initial values x-k, x-k+1,...,x0, y-k, y-k+1, ..., y0 (0,+∞). We give sufficient conditions under which every positive solution of this equation converges to a positive equilibrium. The main theorem in [1] is included in our result.

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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. & Hong, L. On the system of rational difference equations xn+1 = f(x n ,yn-k), yn+1 = f(y n , xn-k). Adv Differ Equ 2006, 016949 (2006). https://doi.org/10.1155/ADE/2006/16949

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Asymptotic Behavior