×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite