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Delay terms in the slow flow
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
2016 (English)In: Journal of Applied Nonlinear Dynamics, ISSN 2164-6457, E-ISSN 2164-6473, Vol. 5, no 4, p. 471-484Article in journal (Refereed) Published
Abstract [en]

This work concerns the dynamics of nonlinear systems that are sub- jected to delayed self-feedback. Perturbation methods applied to such systems give rise to slow flows which characteristically contain delayed variables. We consider two approaches to analyzing Hopf bifurcations in such slow flows. In one approach, which we refer to as approach I, we follow many researchers in replacing the delayed variables in the slow flow with non-delayed variables, thereby reducing the DDE slow flow to an ODE. In a second approach, which we refer to as approach II, we keep the delayed variables in the slow flow. By comparing these two approaches we are able to assess the accuracy of making the simplifying assumption which replaces the DDE slow flow by an ODE. We apply this comparison to two examples, Duffing and van der Pol equations with self-feedback.

Place, publisher, year, edition, pages
L and H Scientific Publishing, LLC , 2016. Vol. 5, no 4, p. 471-484
Keywords [en]
Delay, Duffing, Hopf bifurcation, Slow flow, Van der Pol
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-216849DOI: 10.5890/JAND.2016.12.007Scopus ID: 2-s2.0-85020191597OAI: oai:DiVA.org:kth-216849DiVA, id: diva2:1160852
Note

Export Date: 24 October 2017; Article; Correspondence Address: Sah, S.M.; Nanostructure Physics, KTH Royal Institute of TechnologySweden; email: smsah@kth.se. QC 20171128

Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2017-11-28Bibliographically approved

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  • de-DE
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  • nn-NB
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