Three-frequency resonances in coupled phase-locked loops

Author

Calvo, Oscar ; Cartwright, Julyan H E ; González, Diego L. ; Piro, Oreste ; Sportolari, Francesco

Author_Institution

L.E.I.C.I., Univ. Nacional de La Plata, Argentina

Volume

47

Issue

4

fYear

2000

fDate

4/1/2000 12:00:00 AM

Firstpage

491

Lastpage

497

Abstract

We construct an experimental model of a nonlinear dynamical system with three frequencies. With this analog electronic circuit made up of quasi-periodically forced coupled phase-locked loops, we investigate the structure of the scaling of three-frequency resonances or lockings in the dynamics. We hypothesize and confirm experimentally that for weak coupling the three-frequency resonance with the largest frequency-locked plateau in the space of parameters in the interval between two adjacent resonances p/q and r/s is given by the mediant (p+r)/(q+s). We expect this to be universal behavior in systems of three coupled oscillators

Keywords

circuit resonance; coupled circuits; nonlinear dynamical systems; nonlinear network analysis; phase locked loops; analog electronic circuit; coupled oscillators; frequency-locked plateau; nonlinear dynamical system; quasi-periodically forced coupled phase-locked loops; three-frequency resonances; weak coupling; Circuit testing; Coupling circuits; Electronic circuits; Frequency; Nonlinear dynamical systems; Nonlinear systems; Oscillators; Phase locked loops; Resonance; System testing;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.841851

Filename

841851