Boundedness character of a fourth-order system of difference equations

Abstract

The boundedness character of positive solutions of the following system of difference equations: xn+1=A+ynpxn−3r$x_{n+1}=A+\frac{y^{p}_{n}}{x_{n-3}^{r}}$, yn+1=A+xnpyn−3r$y_{n+1}=A+\frac {x^{p}_{n}}{y_{n-3}^{r}}$, n∈N0$n\in{\mathbb{N}}_{0}$, when min{A,r}>0$\min\{A,r\}>0$ and p≥0$p\ge0$, is studied.