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29 March 2024
 
  » arxiv » nlin.CD/0501031

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Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay
Michael Schanz ; Axel Pelster ;
Date 14 Dec 2004
Journal Physical Review E 67, 056205/1-8 (2003)
Subject Chaotic Dynamics | nlin.CD
AbstractWe 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 $delta approx 4.669$ in one-dimensional discrete systems.
Source arXiv, nlin.CD/0501031
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