info:eu-repo/semantics/article
Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
Fecha
2007-12Registro en:
Robbio, Federico I.; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chen, Guanrong; Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform; World Scientific; International Journal Of Bifurcation And Chaos; 17; 05; 12-2007; 1623-1635
0218-1274
1793-6551
CONICET Digital
CONICET
Autor
Robbio, Federico I.
Paolini, Eduardo Emilio
Moiola, Jorge Luis
Chen, Guanrong
Resumen
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: Colpitts' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles.