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On a system of rational difference equations. (English) Zbl 1078.39006

The authors study several qualitative properties of the system \[ x_{n+1}=(h+x_n)(a+y_n)^{-1}\;,\;y_{n+1}=y_n(b+x_n)^{-1}\;,\;n\geq 0 \] with \(a>0\), \(b>0\), \(h>0\), \(x_0\geq 0\), \(y_0\geq 0\). There are tackled stability by the first approximation, monotone maps and global behavior, global attractiveness results and rates of convergence. Connections to already known results are presented.

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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