Universal generation of devil's staircases near Hopf bifurcations via modulated forcing of nonlinear systems

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dc.contributor.authorLingnau, Benjamin
dc.contributor.authorShortiss, Kevin
dc.contributor.authorDubois, Fabien
dc.contributor.authorPeters, Frank H.
dc.contributor.authorKelleher, Bryan
dc.contributor.funderScience Foundation Irelanden
dc.contributor.funderDeutsche Forschungsgemeinschaften
dc.date.accessioned2021-11-30T16:26:55Z
dc.date.available2021-11-30T16:26:55Z
dc.date.issued2020-09-10
dc.description.abstractThe discrete circle map is the archetypical example of a driven periodic system, showing a complex resonance structure under a change of the forcing frequency known as the devil's staircase. Adler's equation can be seen as the direct continuous equivalent of the circle map, describing locking effects in periodic systems with continuous forcing. This type of locking produces a single fundamental resonance tongue without higher-order resonances, and a devil's staircase is not observed. We show that, with harmonically modulated forcing, nonlinear oscillations close to a Hopf bifurcation generically reproduce the devil's staircase even in the continuous case. Experimental results on a semiconductor laser driven by a modulated optical signal show excellent agreement with our theoretical predictions. The locking appears as a modulation of the oscillation amplitude as well as the angular oscillation frequency. Our results show that by proper implementation of an external drive, additional regions of stable frequency locking can be introduced in systems which originally show only a single Adler-type resonance tongue. The induced resonances can be precisely controlled via the modulation parameters.en
dc.description.sponsorshipDeutsche Forschungsgemeinschaft ((DFG, German Research Foundation) under Grant No. 404943123)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.articleid030201en
dc.identifier.citationLingnau, B., Shortiss, K., Dubois, F., Peters, F. H. and Kelleher, B. (2020) 'Universal generation of devil's staircases near Hopf bifurcations via modulated forcing of nonlinear systems', Physical Review E, 102(3), 030201 (6pp). doi: 10.1103/PhysRevE.102.030201en
dc.identifier.doi10.1103/PhysRevE.102.030201en
dc.identifier.eissn2470-0053
dc.identifier.endpage6en
dc.identifier.issn2470-0045
dc.identifier.issued3en
dc.identifier.journaltitlePhysical Review Een
dc.identifier.startpage1en
dc.identifier.urihttps://hdl.handle.net/10468/12292
dc.identifier.volume102en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.projectinfo:eu-repo/grantAgreement/SFI/SFI Investigator Programme/13/IA/1960/IE/Injection locking within Photonic Integrated Circuits supporting high spectral density optical communications/en
dc.rights© 2020, American Physical Society. All rights reserved.en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectLocks (fasteners)en
dc.subjectModulationen
dc.subjectResonanceen
dc.subjectStairsen
dc.subjectAngular oscillationsen
dc.subjectComplex resonancesen
dc.subjectForcing frequenciesen
dc.subjectFundamental resonanceen
dc.subjectHigher order resonancesen
dc.subjectModulation parametersen
dc.subjectNonlinear oscillationen
dc.subjectOscillation amplitudeen
dc.subjectHopf bifurcationen
dc.titleUniversal generation of devil's staircases near Hopf bifurcations via modulated forcing of nonlinear systemsen
dc.typeArticle (peer-reviewed)en
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