On a system of two nonlinear difference equations
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 \(A>1\).
scientific article; zbMATH DE number 1215744