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Three ways of treating a linear delay differential equation
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
2017 (English)In: Recent Trends in Applied Nonlinear Mechanics and Physics, Springer Science+Business Media B.V., 2017, Vol. 199, p. 251-257Conference paper, Published paper (Refereed)
Abstract [en]

This work concerns the occurrence of Hopf bifurcations in delay differential equations (DDE). Such bifurcations are associated with the occurrence of pure imaginary characteristic roots in a linearized DDE. In this work we seek the exact analytical conditions for pure imaginary roots, and we compare them with the approximate conditions obtained by using the two variable expansion perturbation method. This method characteristically gives rise to a “slow flow” which contains delayed variables. In analyzing such approximate slow flows, we compare the exact treatment of the slow flow with a further approximation based on replacing the delayed variables in the slow flow with non-delayed variables, thereby reducing the DDE slow flow to an ODE. By comparing these three approaches we are able to assess the accuracy of making the various approximations. We apply this comparison to a linear harmonic oscillator with delayed self-feedback.

Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2017. Vol. 199, p. 251-257
Series
Springer Proceedings in Physics, ISSN 0930-8989 ; 199
Keywords [en]
Delay, Hopf bifurcation, Slow flow
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-224613DOI: 10.1007/978-3-319-63937-6_14Scopus ID: 2-s2.0-85043605795ISBN: 9783319639369 OAI: oai:DiVA.org:kth-224613DiVA, id: diva2:1191976
Conference
4th International Conference on Structural Nonlinear Dynamics and Diagnosis, CSNDD 2016, Marrakech, Morocco, 23 May 2016 through 25 May 2016
Note

QC 20180321

Available from: 2018-03-21 Created: 2018-03-21 Last updated: 2018-03-21Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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