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Global asymptotic stability of a family of difference equations. (English) Zbl 1172.39018
For the difference equation
\[ x_n= [(f_1f_2f_3+ f_1+ f_2+ f_3+ h)/(f_1f_2+ f_1f_3+ f_2f_3+ g+ h)](x_{n-1},\dots, x_{n-r}) \] with continuous functions \(f_1,f_2,f_3,g,h: (\mathbb{R}_+)^r\to \mathbb{R}_+\) and positive initial values, sufficient conditions are given such that 1 is a globally asymptotic stable equilibrium.

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