Qualitative behavior of solutions of a two-dimensional rational system of difference equations

Year 2024, Volume: 6 Issue: 2, 45 - 62, 18.12.2024

Durhasan Turgut Tollu , Merve Kayhan

https://doi.org/10.54286/ikjm.1562737

Abstract

In this study, the rational system
\begin{equation*}
x_{n+1}=\frac{\alpha _{1}+\beta _{1}y_{n-1}}{a_{1}+b_{1}y_{n}}, \quad y_{n+1}=\frac{\alpha _{2}+\beta_{2}x_{n-1}}{a_{2}+b_{2}x_{n}}, \quad n\in\mathbb{N}_{0},
\end{equation*}
where $\alpha_{i}$, $\beta_{i}$, $a_{i}$, $b_{i}$, $(i=1,2)$, and $x_{-j}$, $y_{-j}$, $(j=0,1)$, are positive real numbers, is defined and its qualitative behavior is discussed. The system in question is a two-dimensional extension of an old difference equation in the literature. The results obtained generalize the results in the literature on the equation in question.

Keywords

Boundedness and persistence, equilibrium point, globally asymptotically stability, periodicity, rate of convergence, system of difference equations.

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