Periodicity and solutions for some systems of nonlinear rational difference equations. (English) Zbl 1351.39009
Summary: We investigate the periodic nature and the form of the solutions of nonlinear difference equations systems of order three
\[
x_{n+1} = \frac{x_{n-2}y_{n-1}}{y_n(\pm1 \pm x_{n-2}y_{n-1})}, \quad y_{n+1} = \frac{y_{n-2}x_{n-1}}{x_n(\pm1 \pm y_{n-2}x_{n-1})},
\]
with initial boundary conditions \(x_{-2},x_{-1}, x_0,y_{-2},y_{-1}\) and \(y_0\) are nonzero real numbers.
MSC:
| 39A20 | Multiplicative and other generalized difference equations |
| 39A23 | Periodic solutions of difference equations |
| 39A30 | Stability theory for difference equations |
