On the recursive sequence \(x_n = \frac{ax_{n-1}+bx_{n-2}}{c+dx_{n-1}x_{n-2}}\) (Q1765882)
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scientific article; zbMATH DE number 2137767
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursive sequence \(x_n = \frac{ax_{n-1}+bx_{n-2}}{c+dx_{n-1}x_{n-2}}\) |
scientific article; zbMATH DE number 2137767 |
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On the recursive sequence \(x_n = \frac{ax_{n-1}+bx_{n-2}}{c+dx_{n-1}x_{n-2}}\) (English)
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23 February 2005
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The authors study the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation \[ x_n=\frac{ax_{n-1}+bx_{n-2}}{c+x_{n-1}x_{n-2}},\quad n=1,2,\dots , \] where \(a\geq 0,b,c,d>0.\)
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recursive sequence
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equilibrium point
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global attractor
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exponential convergence
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invariant interval
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rational difference equation
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