Authors: Michele V. Bartuccelli, Jonathan H.B. Deane, and Guido Gentile
Title:
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.
Keywords: Nonlinear dynamics; Bifurcation theory; Subharmonic bifurcation; Periodic solutions; Arnold tongues; Frequency locking; Devil's staircase; Injection-locked frequency divider.
Michele Bartuccelli
Department of Mathematics and Statistics
University of Surrey
Guildford, GU2 7HX, UK
e-mail: m.bartuccelli@surrey.ac.uk
Jonathan Deane
Department of Mathematics and Statistics
University of Surrey
Guildford, GU2 7HX, UK
e-mail: j.deane@surrey.ac.uk
Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it