Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations
type: Item
instance of: scholarly article
title: Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations
zbMATH Open document ID: 1032.34067
author: Peter Dormayer
author: Bernhard Lani-Wayda
author: Anatoli F. Ivanov
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2003-05-13T00:00:00Z
review text: The authors discuss the Floquet multiplies of symmetric rapidly oscillating periodic solutions to the differential delay equation \[ \dot x(t) =\alpha f(x(t),x(t-1)) \] with the symmetries \(f(-x,y)=f(x,y) =-f(x,-y)\) in terms of zeroes of a characteristic function. A relation to the characteristic function of symmetric slowly oscillating periodic solutions is derived. Sufficient conditions are established for the existence of at least one real multiplier located outside the unit disc. As an example, a piecewise linear equation with sine-like feedback is studied detailed both analytically and numerically.
reviewed by: Rong Yuan
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K18
zbMATH DE Number: 1854208
zbMATH Keywords: Delay equations with symmetry
zbMATH Keywords: rapidly oscillating periodic solutions
zbMATH Keywords: Floquet multiplies
MaRDI profile type: Publication
OpenAlex ID: W2001099525
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DOI: 10.2748/TMJ/1113247603
description: scientific article; zbMATH DE number 1854208