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Global attractivity in the recursive sequence $x_{n+1}=(\alpha-\beta x_{n})/(\gamma-x_{n-1})$. (English) Zbl 1030.39024
Following on the analysis of the rational recursive sequence $$ x_{n+1}=(\alpha-\beta x_{n})/(\gamma-x_{n-1}),\quad n=0,1,2,\ldots $$ with arbitrary $x_{0}$, $x_{-1}$, $\alpha\geq 0$, $\beta>0$, $\gamma>0$, it is shown that the positive equilibrium is an attractor and an estimate is obtained for the attraction basin.

MSC:
39A12Discrete version of topics in analysis
39B05General theory of functional equations
37D45Strange attractors, chaotic dynamics
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References:
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