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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.

39A12Discrete version of topics in analysis
39B05General theory of functional equations
37D45Strange attractors, chaotic dynamics
Full Text: DOI
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