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On the periodic solutions of some systems of higher order difference equations. (English) Zbl 1396.39001

Summary: In this paper, we obtain the general form of the periodic solutions of some higher order difference equations system \[ x_{n+1}=\frac {\pm x_{n-k}y_{n-(2k+1)}}{y_{n-(2k+1)}\mp y_{n-k}}, \]
\[ y_{n+1}=\frac {\pm y_{n-k}x_{n-(2k+1)}}{x_{n-(2k+1)}\mp x_{n-k}}, \] \(n,k\in \mathbb {N}_{0}\), where the initial values are arbitrary real numbers such that the denominator is always nonzero. Moreover, some numerical examples are presented to verify our theoretical results.

MSC:

39A10 Additive difference equations
39A23 Periodic solutions of difference equations
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References:

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