Fourier methods for quasi-periodic oscillations

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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.

Original languageEnglish
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
Pages (from-to)629–671
Number of pages43
Publication statusPublished - 30.07.2006
Externally publishedYes

    Research areas

  • Mathematics
  • Averaging method, Fourier method, Invariant torus, Quasi-periodic oscillation, Van der Pol oscillator