Dynamics of an Anti-competitive Two Dimensional Rational System of Difference Equations

We investigate the global asymptotic behavior of solutions of the following anti-competitive system of rational difference equations\begin{equation*}x_{n+1}=\frac{\gamma _{1}y_{n}}{A_{1}+x_{n}}+h,\quady_{n+1}=\frac{\beta _{2}x_{n}}{A_{2}+y_{n}},\quad n=0,1,\dots,\end{equation*}where the parameters $\gamma _1,\beta _2,A_{1},A_{2}$ and $h$ are positive numbers and the initial conditions $x_{0},y_{0}$ are arbitrary nonnegative numbers. 2000 Mathematics Subject Classification. 39A10, 39A11