(Special Issue) Global behavior of solutions of a two-dimensional system of difference equations
Mehmet Gümüş,
Raafat Abo-zeid,
Kemal Türk
Abstract:In this paper, we mainly investigate the qualitative and quantitative behavior of the solutions of a discrete system of difference equations
$$x_{n+1}=\frac{x_{n-1}}{y_{n-1}},\quad y_{n+1}=\frac{x_{n-1} }{ax_{n-1}+by_{n-1}},\quad n=0,1,\ldots, $$
where $a$, $b$ and the initial values $x_{-1},x_{0},y_{-1},y_{0}$ are non-zero real numbers. For $a\in \mathbb{R}_+-\{1\}$, we show any admissible solution $\{(x_n,y_n)\}_{n=-1}^\infty$ is either entirely located in a certain quadrant of the plane or there exists… Show more
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