MMN-5135
On a multidimensional close-to-cyclic system of difference equations
Yacine Halim; Asma Allam; Ibraheem M. Alsulami;Abstract
In this paper we present a new aspects on the solvability of a multidimensional close-to-cyclic system of nonlinear difference equations
\begin{equation*}
y_{n+1}^{\left(i\right)}=\frac{a_{i}y_{n}^{\left(i+1\right)}\left(y_{n-k}^{\left(i+1\right)}\right)^{p_{i+1}}+b_{i}}{\left(y_{n-k+1}^{\left(i\right)}\right)^{p_{i}}};\quad
n\in \mathbb{N}_{_{0}},
\end{equation*}
where $y_{n}^{\left(i+k\right)}=y_{n}^{\left(i\right)},
p_{i+k}=p_{i}, a_{i+k}=a_{i}, b_{i+k}=b_{i}; i=\overline{1,k}$, the
initial values $y_{-k}^{\left(i\right)}$,
$y_{-k+1}^{\left(i\right)}$, $\ldots, y_{0}^{\left(i\right)}$ and
$a_{i}$ and $b_{i}$, $i=\overline{1,k},$ are positive
real numbers and $p_{i}$, $i=\overline{1,k},$ are real numbers.
Vol. 26 (2025), No. 1, pp. 275-290