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On the behaviour of the solutions of difference equation systems. (English) Zbl 1293.39008
The authors consider the systems $\displaystyle{x_{n+1} = {{y_{n-5}}\over{\pm 1+y_{n-1}x_{n-3}y_{n-5}}}\;;\;y_{n+1} = {{x_{n-5}}\over{\pm 1+x_{n-1}y_{n-3}x_{n-5}}}}$ and $\displaystyle{x_{n+1} = {{y_{n-5}}\over{\pm 1+y_{n-1}x_{n-3}y_{n-5}}}\;;\;y_{n+1} = {{x_{n-5}}\over{\mp 1+x_{n-1}y_{n-3}x_{n-5}}}}$ under all possible sign combinations for each of them. The following problems are tackled: explicit form of the solutions, equilibria and their attractiveness, periodic solutions. Numerical examples are provided.

##### MSC:
 39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type 39A23 Periodic solutions of difference equations 39A30 Stability theory for difference equations