Title :
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
fDate :
4/1/2000 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
