The rule of semicycle and global asymptotic stability for a fourth-order rational difference equation (Q2485502)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The rule of semicycle and global asymptotic stability for a fourth-order rational difference equation |
scientific article |
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The rule of semicycle and global asymptotic stability for a fourth-order rational difference equation (English)
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5 August 2005
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It is proved that the positive equilibrium of the difference equation \[ x_{n+1}=\frac{x_n^bx_{n-2}+x_{n-3}^b+a}{x_n^b+x_{n-2}x_{n-3}^b+a}\, ,\; n=0,1,\dots , \] where \(a,b\geq 0\), attracts all solutions corresponding to positive initial conditions.
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rational difference equation
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semicycle
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cycle length
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global asymptotic stability
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positive equilibrium
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