The form of solutions and periodicity for some systems of third-order rational difference equations (Q2800519)

The author discusses four types of systems of rational difference equations of third order. The following system is considered in Section 2: NEWLINE\[NEWLINEx_{n+1}=\frac{y_{n-1}y_{n-2}}{x_{n}(1+y_{n-1}y_{n-2})},\,\, y_{n+1}=\frac{x_{n-1}x_{n-2}}{y_{n}(\pm1\pm x_{n-1}x_{n-2})}.NEWLINE\]NEWLINE In each case, the explicit representation of the solution is given and their periodicity is studied. Several examples are given to illustrate these results.