Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2001-40
Keywords
System of difference equations, general solution, representation of solutions
First Page
1263
Last Page
1288
Recommended Citation
HALIM, Y, BERKAL, M, & KHELIFA, A (2020). On a three-dimensional solvable system of difference equations. Turkish Journal of Mathematics 44 (4): 1263-1288. https://doi.org/10.3906/mat-2001-40
