On the behaviour of the solutions of difference equation systems. (English) Zbl 1293.39008

Yazlik, Y.; Elsayed, E. M.; Taskara, N.

J. Comput. Anal. Appl. 16, No. 5, 932-941 (2014).

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.

Reviewer: Vladimir Răsvan (Craiova)

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

Keywords:

system of rational difference equations; explicit solutions; periodicity; stability