Frequency locking in the injection-locked frequency divider equation

Abstract

We consider a model for the injection-locked frequency divider, and study analytically the locking onto rational multiples of the driving frequency. We provide explicit formulae for the width of the plateaux appearing in the devil's staircase structure of the lockings, and in particular show that the largest plateaux correspond to even integer values for the ratio of the frequency of the driving signal to the frequency of the output signal. Our results prove the experimental and numerical results available in the literature.

arXiv comment20 figures, 2 figures

References in corpus (5)

• Twistless KAM tori
• Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review
• Summation of divergent series and Borel summability for strongly dissipative equations with periodic or quasi-periodic forcing terms
• Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
• Bifurcation curves of subharmonic solutions

Cited by in corpus (2)

• Quasi-periodic motions in dynamical systems. Review of a renormalisation group approach
• Arnold tongues for a resonant injection-locked frequency divider: analytical and numerical results