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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:

39A12 Discrete version of topics in analysis
39B05 General theory of functional equations and inequalities
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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