Rapidly and slowly oscillating periodic solutions of a delayed van der Pol oscillator
type: Item
instance of: scholarly article
title: Rapidly and slowly oscillating periodic solutions of a delayed van der Pol oscillator
zbMATH Open document ID: 1421.65016
author: Jean-Philippe Lessard
author: Gábor Kiss
published in: Journal of Dynamics and Differential Equations
publication date: 2018-01-26T00:00:00Z
review text: The authors prove the existence of several types of slowly and rapidly varying periodic solutions for the delayed Van der Pol equation. The proof combines classical analytical techniques with numerical interval arithmetic. In a first step, the problem is rewritten as fixed-point problem. Then a contraction argument is shown using numerical tools such as interval arithmetic packages. The obtained results generalize known existence theorems.
reviewed by: Johannes Schropp
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 6829879
zbMATH Keywords: delay differential equations
zbMATH Keywords: rigorous numerics
zbMATH Keywords: rapid and slow periodic solutions
zbMATH Keywords: contraction mapping theorem
zbMATH Keywords: Van der Pol equation
describes a project that uses: TRACE-DDE
describes a project that uses: INTLAB
MaRDI profile type: Publication
full work available at URL: s10884-017-9599-x
OpenAlex ID: W2740478422
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DOI: 10.1007/S10884-017-9599-X
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description: scientific article; zbMATH DE number 6829879