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Global asymptotic behavior of positive solutions on the system of rational difference equations \(x_{n+1}=1+x_ n/y_{n-m}, y_ {n+1}=1+y_ n/x_{n-m}\). (English) Zbl 1064.39004
It is shown that every positive solution of the system in the title with \(m\in\mathbb{N}\) converges to an equilibrium \((x,y)\) with \(x> 1\) and \(y= x/(x- 1)\).

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
Full Text: DOI
[1] Papaschinopoulos, G; Papadopoulos, B.K, On the fuzzy difference equation \(xn+1 = A + xnxn−m\), Fuzzy sets and systems, 129, 73-81, (2002) · Zbl 1016.39015
[2] Abu-Saris, R.M; DeVault, R, Global stability of \(yn+1 = A + ynyn−k\), Appl. math. lett., 16, 2, 173-178, (2003) · Zbl 1049.39002
[3] DeVault, R; Ladas, G; Schultz, S.W, On the recursive sequence \(xn+1 = Axn + 1xn−2\), (), 3257-3261, (11) · Zbl 0904.39012
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