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.


39A10 Additive difference equations
39A23 Periodic solutions of difference equations
Full Text: DOI Euclid


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