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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)

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