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On the positive solutions of the system of rational difference equations \(x_{n+1}=1/y_{n - k}, y_{n+1}=y_{n}/x_{n - m}y_{n - m - k}\). (English) Zbl 1115.39012
The periodicity of solutions of the system of rational difference equations of the form \(x_{n+1}=1/y_{n-k,} y_{n+1}=y_{n}/x_{n-m}y_{n-m-k}, n=0,1,\dots,\) is investigated.

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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[1] A.Y. Özban, On the positive solutions of the system of difference equations \(x_{n + 1} = 1 / y_n\), \(y_{n + 1} = y_n / x_{n - m} y_{n - m}\), submitted for publication · Zbl 1115.39012
[2] Yang, X., On the system of rational difference equations \(x_n = A + y_{n - 1} / x_{n - p} y_{n - q}\), \(y_n = A + x_{n - 1} / x_{n - r} y_{n - s}\), J. math. anal. appl., 307, 305-311, (2005) · Zbl 1072.39011
[3] Clark, D.; Kulenovic, M.R., A coupled system of rational difference equations, Comput. math. appl., 43, 849-867, (2002) · Zbl 1001.39017
[4] Papaschinopoulos, G.C.; Schinas, C.J., On a system of two nonlinear difference equations, J. math. anal. appl., 219, 415-426, (1998) · Zbl 0908.39003
[5] Camouzis, E.; Papaschinopoulos, G.C., Global asymptotic behavior of positive solutions on the system of rational difference equations \(x_{n + 1} = 1 + x_n / y_{n - m}\), \(y_{n + 1} = 1 + y_n / x_{n - m}\), Appl. math. lett., 17, 733-737, (2004) · Zbl 1064.39004
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