Elsayed M. Elsayed : On the solutions and periodicity of some rational systems of difference equations p. 159-171

Abstract:

In this paper we deal with the form of the solutions and the periodicity nature of the following systems of nonlinear difference equations

$$x_{n+1}=\dfrac{x_{n-3}y_{n-2}}{y_{n}(\pm 1\pm x_{n-1}y_{n-2}x_... ...}=\dfrac{x_{n-2}y_{n-3}}{x_{n}(\pm 1\pm y_{n-1}x_{n-2}y_{n-3})},$$

where the initial conditions $x_{-3},\ x_{-2},\ x_{-1},\,x_{0},\ y_{-3},\ y_{-2},\ y_{-1},$ and $y_{0}$ are nonzero real numbers.

Key Words: difference equations, periodic solutions, system of difference equations.

2010 Mathematics Subject Classification: 39A10.