Global asymptotic stability in a rational equation. (English) Zbl 1055.39014

The authors consider the rational difference equation \[ x_{n+1}=\frac{x_nx_{n-1}+a}{x_n+x_{n-1}}, \quad n=0,1,2,\dots, \] where \(a \in[0,\infty)\) and the initial value \(x_-1\), \(x_0\in(0,\infty)\). A sufficient condition for the global asymptotic stability of the above equation is obtained.


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