- Turkish Journal of Mathematics
- Vol: 44 Issue: 4
- On a three-dimensional solvable system of difference equations
On a three-dimensional solvable system of difference equations
Authors : Yacıne Halim, Massaoud Berkal, Amıra Khelifa
Pages : 1263-1288
Doi:10.3906/mat-2001-40
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper we solve the following system of difference equations \begin{equation*} x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0} \end{equation*} where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.Keywords : System of difference equations, general solution, representation of solutions