Fourier methods for quasi-periodic oscillations

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Fourier methods for quasi-periodic oscillations. / Schilder, Frank; Vogt, Werner; Schreiber, Stephan et al.
in: International Journal for Numerical Methods in Engineering, Jahrgang 67, Nr. 5, 30.07.2006, S. 629–671.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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Schilder F, Vogt W, Schreiber S, Osinga HM. Fourier methods for quasi-periodic oscillations. International Journal for Numerical Methods in Engineering. 2006 Jul 30;67(5):629–671. doi: 10.1002/nme.1632

Bibtex

@article{cbfb9b82ce434aa1b0fe086c170984c0,
title = "Fourier methods for quasi-periodic oscillations",
abstract = "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.",
keywords = "Mathematics, Averaging method, Fourier method, Invariant torus, Quasi-periodic oscillation, Van der Pol oscillator",
author = "Frank Schilder and Werner Vogt and Stephan Schreiber and Osinga, {Hinke M.}",
year = "2006",
month = jul,
day = "30",
doi = "10.1002/nme.1632",
language = "English",
volume = "67",
pages = "629–671",
journal = "International Journal for Numerical Methods in Engineering",
issn = "1097-0207",
publisher = "John Wiley & Sons Ltd.",
number = "5",

}

RIS

TY - JOUR

T1 - Fourier methods for quasi-periodic oscillations

AU - Schilder, Frank

AU - Vogt, Werner

AU - Schreiber, Stephan

AU - Osinga, Hinke M.

PY - 2006/7/30

Y1 - 2006/7/30

N2 - 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.

AB - 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.

KW - Mathematics

KW - Averaging method

KW - Fourier method

KW - Invariant torus

KW - Quasi-periodic oscillation

KW - Van der Pol oscillator

UR - http://www.scopus.com/inward/record.url?scp=33746173012&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9ac1b3b5-8c47-3277-9534-beb0df11d4ba/

U2 - 10.1002/nme.1632

DO - 10.1002/nme.1632

M3 - Journal articles

VL - 67

SP - 629

EP - 671

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 1097-0207

IS - 5

ER -