Boundary functions method for nonlinear singularly perturbed time delay systems (Q2780403)
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scientific article; zbMATH DE number 1728935
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundary functions method for nonlinear singularly perturbed time delay systems |
scientific article; zbMATH DE number 1728935 |
Statements
15 April 2002
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time delay systems
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singular perturbations
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asymptotic expansions
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Boundary functions method for nonlinear singularly perturbed time delay systems (English)
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Consider the \(m\)-dimensional time-delay system NEWLINE\[NEWLINE{dx\over dt}= f(x(t), x(t- h), z(t)),\;\varepsilon{dz\over dt}= g(x(t), x(t- h), z(t)),NEWLINE\]NEWLINE with \(\varepsilon> 0\) a small parameter. Asymptotic expansions with respect to \(\varepsilon\) are constructed for the Cauchy problem. The author solves also the problem of solution jumps at \(t= kh\) using an analogue of the technique of the boundary functions introduced by \textit{A. B. Vasil'eva}, \textit{V. F. Butuzov} and \textit{L. V. Kalachev} [SIAM Studies in Applied Mathematics. 14. Philadelphia, PA: SIAM (1995; Zbl 0823.34059)].
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