On the periodic solutions of some systems of higher order difference equations

Abstract

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.