Arnol'd tongues for a resonant injection-locked frequency divider: analytical and numerical results

Michele Bartuccelli, Jonathan H.B. Deane, Guido Gentile, Frank Schilder

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    In this paper we consider a resonant injection-locked frequency divider which is of interest in electronics, and we investigate the frequency locking phenomenon when varying the amplitude and frequency of the injected signal. We study both analytically and numerically the structure of the Arnol’d tongues in the frequency–amplitude plane. In particular, we provide exact analytical formulae for the widths of the tongues, which correspond to the plateaux of the devil’s staircase picture. The results account for numerical and experimental findings presented in the literature for special driving terms and, additionally, extend the analysis to a more general setting.
    Original languageEnglish
    JournalNonlinear Analysis: Real World Applications
    Volume11
    Issue number5
    Pages (from-to)3344-3362
    ISSN1468-1218
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Nonlinear dynamics
    • Injection-locked frequency divider
    • Frequency locking
    • Bifurcation theory
    • Devil’s staircase
    • Subharmonic bifurcation
    • Periodic solutions
    • Arnol’d tongues

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