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- W2002187458 abstract "We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed by numerical simulations. Further detailed numerical investigations demonstrate exemplarily that this system reveals a rich dynamical behavior. With phase portraits, Fourier analysis, and Lyapunov spectra it is possible to analyze the scaling properties of the control parameter in the period-doubling scenario, both qualitatively and quantitatively. Within the numerical accuracy there is evidence that the scaling constant of the time-delayed phase-locked loop coincides with the Feigenbaum constant delta approximately 4.669 in one-dimensional discrete systems." @default.
- W2002187458 created "2016-06-24" @default.
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- W2002187458 date "2003-05-14" @default.
- W2002187458 modified "2023-09-27" @default.
- W2002187458 title "Analytical and numerical investigations of the phase-locked loop with time delay" @default.
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- W2002187458 doi "https://doi.org/10.1103/physreve.67.056205" @default.
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