Article in Journal ART-2003-10

BibliographySchanz, Michael; Pelster, Axel: Analytical and numerical Investigations of the Phase-locked Loop with Time Delay.
In: The American Physical Society (ed.): Physical Review E. Vol. 67, 056205, 2003.
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
pp. 1-8, english.
Thomson ISI, May 14, 2003.
DOI: 10.1103/PhysRevE.67.056205.
Article in Journal.
CR-SchemaJ.2 (Physical Sciences and Engineering)
G.1.9 (Integral Functions)
Keywordslow-dimensional chaos; order parameter; bifurcation theory; normal form
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 deltaapproximate to4.669 in one-dimensional discrete systems.

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Physical Review E 67 056205 (2003) [8 pages]
CopyrightThe American Physical Society
ContactMichael.Schanz@informatik.uni-stuttgart.de
Department(s)University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
Project(s)AnT
Entry dateApril 9, 2005
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