Harmonic distortion analysis based on HOPF bifurcation theorem and fast fourier transform

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

4 Scopus Citations
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  • F. I. Robbio
  • E. E. Paolini
  • J. L. Moiola
  • G. Chen

Related Research Unit(s)


Original languageEnglish
Pages (from-to)1623-1635
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number5
Publication statusPublished - May 2007


A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the results obtained from a completely different approach that measures the frequency content of a signal by using digital signal processing techniques such as the Fast Fourier Transform (FFT). The accuracy of the approximation is evaluated by computing the Floquet multipliers of the variational system based on the fact that for periodic solutions one multiplier must be +1. The separation from this theoretical value is proportional to the error of the approximation. A limitation of the frequency domain method is encountered when being used for continuing the secondary branch of limit cycle bifurcations, such as pitchfork and period-doubling bifurcations. Two examples are shown to illustrate the main results: Colpitis' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles. © World Scientific Publishing Company.

Research Area(s)

  • Chua's circuit, Colpitts' oscillator, Electronic oscillator, Harmonic balance, Harmonic distortion