zbMATH — the first resource for mathematics

Asymptotic behavior of a system of linear fractional difference equations. (English) Zbl 1086.39008
The authors consider the system of difference equations \[ \begin{aligned} & x_{n+1}=(a+x_n)/(b+y_n),\\ & y_{n+1}=(d+y_n)/(e+x_n),\end{aligned}\qquad n=0,1,\dots,\tag{S} \] where \(a,b,d,e\) are positive parameters and \(x_0,y_0\) are nonnegative initial conditions. The global asymptotic behavior of solutions of (S) is studied. In particular, it is shown that the parameters \(a,d\) can have a stabilizing effect for the global behavior of the solutions of the system (S) with \(a=d=0\) in the sense that the unique positive equilibrium of (S) can become the global attractor of all positive solutions of (S) for certain values of \(a\) and \(d\).
Reviewer: Pavel Rehak (Brno)

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
Full Text: DOI EuDML