  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.
