Asymptotic stability of the complex dynamic equation \(u^\Delta-z\cdot u+w\cdot u^\sigma=0\) (Q401416)
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scientific article; zbMATH DE number 6334571
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic stability of the complex dynamic equation \(u^\Delta-z\cdot u+w\cdot u^\sigma=0\) |
scientific article; zbMATH DE number 6334571 |
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Asymptotic stability of the complex dynamic equation \(u^\Delta-z\cdot u+w\cdot u^\sigma=0\) (English)
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26 August 2014
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time scales
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exponential function
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asymptotic behavior
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The author considers the exponential function \(u = e_{z \ominus w}(\cdotp,s)\) as the solution to the linear complex dynamic initial value problem NEWLINE\[NEWLINE u^\Delta - z \cdot u + w \cdot u^\sigma = 0 , \quad u(s) = 1 NEWLINE\]NEWLINE on a time scale that is unbounded with bounded graininess. After an introduction of the basic concepts from time scales calculus and the associated structures in the complex plane the main result provides a sufficient condition for the asymptotic stability of the exponential function.NEWLINENEWLINEA final example illustrates the intricate role of the graininess function in that respect.
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