Dynamics of an Anti-competitive Two Dimensional Rational System of Difference Equations
DOI:
https://doi.org/10.5644/SJM.07.1.05Keywords:
Difference equations, anti-competitive, map, stability, stable manifoldAbstract
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,\quad
y_{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
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