
   @article{article_1524180, title={A qualitative investigation of a system of third-order difference equations with multiplicative reciprocal terms}, journal={Ikonion Journal of Mathematics}, volume={6}, pages={30–44}, year={2024}, DOI={10.54286/ikjm.1524180}, author={Tollu, Durhasan Turgut and Yalçınkaya, İbrahim}, keywords={Boundedness, equilibrium point, system of difference equations.}, abstract={In this paper, we study the system of third-order difference equations \begin{equation*}
x_{n+1}=a+\frac{a_{1 }{y_{n }+\frac{a_{2 }{y_{n-1 }+\frac{a_{3 }{y_{n-2 }%
,\quad y_{n+1}=b+\frac{b_{1 }{x_{n }+\frac{b_{2 }{x_{n-1 }+\frac{b_{3 }{%
x_{n-2 },\quad n\in \mathbb{N}_{0},
\end{equation*}%
where the parameters $a$, $a_{i}$, $b$, $b_{i}$, $i=1,2,3$, and the initial
values $x_{-j}$, $y_{-j}$, $j=0,1,2$, are positive real numbers. We first
prove a general convergence theorem. By applying this convergence theorem to
the system, we show that positive equilibrium is a global attractor. We also
study the local asymptotic stability of the equilibrium and show that it is
globally asymptotically stable. Finally, we study the invariant set of
solutions.}, number={2}, publisher={Nihat AKGÜNEŞ}
