High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing

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dc.creatorGarcia-Alvarez, David
dc.creatorStefanovska, Aneta
dc.creatorMcClintock, Peter V. E.
dc.date2007-03-28
dc.date2008-11-14
dc.date.accessioned2026-07-07T10:18:06Z
dc.date.available2026-07-07T10:18:06Z
dc.descriptionWe consider a rotator whose equation of motion for the angle $θ$ consists of the zeroth and first Fourier modes. Numerical analysis based on the trailing of saddle-node bifurcations is used to locate the n:1 Arnold tongues where synchronization occurs. Several of them are wide enough for high-order synchronization to be seen in passive observations. By sweeping the system parameters within a certain range, we find that the stronger the dependence of $\dotθ$ on $θ$, the wider the regions of synchronization. Use of a synchronization index reveals a vast number of very narrow n:m Arnold tongues. A competition phenomenon among the tongues is observed, in that they "push" and "squeeze" one another: as some tongues widen, others narrow. Two mechanisms for transitions between different n:m synchronization states are considered: slow variation of the driving frequency, and the influence of low-frequency noise on the rotator.
dc.description10 pages, 7 figures, revtex. Many major changes compared to previous version. As appears in Physical Review E, except that the last editions by the publishers do not appear here
dc.identifierhttps://arxiv.org/abs/nlin/0703058
dc.identifierhttp://arxiv.org/abs/nlin/0703058
dc.identifierPhysical Review E 77, 056203 (2008)
dc.identifierdoi:10.1103/PhysRevE.77.056203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174082
dc.subjectChaotic Dynamics
dc.titleHigh-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing
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