Fourier methods for quasi-periodic oscillations

F Schilder, W Vogt, S Schreiber, HM Osinga

Research output: Contribution to journalArticle (Academic Journal)peer-review

59 Citations (Scopus)


Quasi-periodic oscillations and invariant tori play an important role in the study of forced or coupled oscillators. This paper presents two new numerical methods for the investigation of quasi-periodic oscillations. Both algorithms can be regarded as generalizations of the averaging and the harmonic (spectral) balance methods. The algorithms are easy to implement and require only minimal a priori knowledge of the system. Most importantly, the methods do not depend on an a priori co-ordinate transformation. The methods are applied to a number of illustrative examples from non-linear electrical engineering and the results show that the methods are efficient and reliable. In addition, these examples show that the presented algorithms can also continue through regions of sub-harmonic (phase-locked) resonance even though they are designed only for the quasi-periodic case.
Translated title of the contributionFourier methods for quasi-periodic oscillations
Original languageEnglish
Pages (from-to)629 - 671
Number of pages43
JournalInternational Journal for Numerical Methods in Engineering
Publication statusPublished - Jul 2006

Bibliographical note

Publisher: John Wiley & Sons Ltd


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  • Fourier methods for quasi-periodic oscillations

    Schilder, F., Vogt, W., Schreiber, S. & Osinga, HM., 2005, (Unpublished).

    Research output: Working paper


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