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In this paper we consider a resonant injection-locked frequency divider whichis of interest in electronics, and we investigate the frequency lockingphenomenon when varying the amplitude and frequency of the injected signal. Westudy both analytically and numerically the structure of the Arnold tongues inthe frequency-amplitude plane. In particular, we provide exact analyticalformulae for the widths of the tongues, which correspond to the plateaux of thedevil's staircase picture. The results account for numerical and experimentalfindings presented in the literature for special driving terms and,additionally, extend the analysis to a more general setting.

Arnold tongues for a resonant injection-locked frequency divider: analytical and numerical results