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On a system of two nonlinear difference equations. (English) Zbl 0908.39003
Concerning the system \(x_{n+1}=A+y_n/x_{n-p}\), \(y_{n+1}=A+x_n/y_{n-q}\) with \(A\geq 0\) and natural numbers \(p\), \(q\), the authors show: (i) the positive solutions are bounded, (ii) they oscillate about the equilibrium \((1+A,1+A)\), (iii) the equilibrium is globally asymptotically stable for \(A>1\).

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
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