Fourier methods for quasi-periodic oscillations
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In: International Journal for Numerical Methods in Engineering, Vol. 67, No. 5, 30.07.2006, p. 629–671.
Research output: Journal contributions › Journal articles › Research › peer-review
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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 -