On the eigenvalue spectrum for time-delayed Floquet problems
type: Item
instance of: scholarly article
title: On the eigenvalue spectrum for time-delayed Floquet problems
zbMATH Open document ID: 0964.34070
DOI: 10.1016/S0167-2789(00)00051-8
author: Wolfram Just
published in: Physica D
publication date: 2001-07-01T00:00:00Z
review text: The author investigates linear homogeneous scalar differential-difference equations with harmonic time dependence of the type \[ dx(t)/dt = cx(t) + B(t)x(t - r) \] where the coefficient \(B(t)\) is periodic in time: \(B (t) = B (t + T)\) and \(c\) is a constant. The associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation. In addition, the dependence of the largest eigenvalue on the system parameters is discussed in detail. The result suggests features to improve control of chaos by feedback schemes with time-dependent control amplitudes.
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 49K25
zbMATH DE Number: 1474685
zbMATH Keywords: stability analysis
zbMATH Keywords: differential-difference equation
zbMATH Keywords: chaos control
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
cites work: High-dimensional chaotic behavior in systems with time-delayed feedback
cites work: Oscillation and Chaos in Physiological Control Systems
cites work: Q3842163
cites work: Introduction to functional differential equations
cites work: On analytical properties of delayed feedback control of chaos.
cites work: Differential-difference equations
cites work: Zur Theorie des Balancierens
cites work: The Fokker-Planck equation. Methods of solutions and applications.
cites work: Q4482959
cites work: Recycling of strange sets: I. Cycle expansions
cites work: Q4856607
description: scientific article; zbMATH DE number 1474685