Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay

Details Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay

2005-01-14

arxiv.org/abs/nlin/0501031v1

Physical Review E 67, 056205/1-8 (2003)

Nonlinear Sciences

Chaotic Dynamics

12 pages

Scientific paper

10.1103/PhysRevE.67.056205

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 $\delta \approx 4.669$ in one-dimensional discrete systems.

Affiliated with

Also associated with

No associations

Rating

Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytical and Numerical Investigation of the Phase-Locked Loop with Time Delay will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-88085