Globally asymptotic stability of a recurrence sequence (Q2720031)
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scientific article; zbMATH DE number 1610525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Globally asymptotic stability of a recurrence sequence |
scientific article; zbMATH DE number 1610525 |
Statements
10 September 2002
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difference equation
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rational sequence
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globally asymptotic stability
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global attractor
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positive solutions
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Globally asymptotic stability of a recurrence sequence (English)
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Sufficient conditions for the global attraction of the rational recurrence sequence NEWLINE\[NEWLINE x_{n+1}=\frac{a+bx_{n-1}}{c+x_{n}^{2}} NEWLINE\]NEWLINE (\(a,~b,~c>0\)) are obtained. Under some conditions on the constants \(a,b,c,\) the unique positive equilibrium point of the above equation is a global attractor of all positive solutions.
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