Global attractivity of a kind of difference equation (Q2752563)
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scientific article; zbMATH DE number 1661200
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global attractivity of a kind of difference equation |
scientific article; zbMATH DE number 1661200 |
Statements
10 September 2002
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global attractivity
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difference equation
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positive equilibrium
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Global attractivity of a kind of difference equation (English)
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It is shown that the following difference equation has a unique positive equilibrium \(\xi\): NEWLINE\[NEWLINEx_{n+1}=\left(\frac{\alpha+\beta x_n^{2k-1}}{A+Bx_n^{2m-1}+Cx_{n-1}^{2m-1}} \right)^{\frac{1}{2k-1}},\quad n\geq 1NEWLINE\]NEWLINE where \(B\in [0,\infty),~\alpha,\beta,A,C\in (0,\infty),\) \(x_0,x_{-1}\in (0,\infty),\) and \(m,k\in N.\) Sufficient conditions for the global attractivity of the equilibrium \(\xi\) are also derived.
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