On the dynamics of the difference equation \(x_{n+1} = \frac{1}{B_nx_n+x_{n+1}}\) (Q961591)
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scientific article; zbMATH DE number 5688878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dynamics of the difference equation \(x_{n+1} = \frac{1}{B_nx_n+x_{n+1}}\) |
scientific article; zbMATH DE number 5688878 |
Statements
On the dynamics of the difference equation \(x_{n+1} = \frac{1}{B_nx_n+x_{n+1}}\) (English)
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31 March 2010
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The authors consider the non-autonomous equation \(x_{n+1} = 1/(B_n x_n+x_{n+1})\), for \(n \geq 0\) and positive initial conditions \(x_0\) and \(x_1\). Here \(B_n\) is a two periodic sequence. They show that the unique prime two periodic solution is globally asymptotically stable. This result continues some previous studies given by Stević, Kulenović and Ladas for \(B_n\) a constant sequence.
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difference equation
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asymptotic stability
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period-2 solution
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