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

Garcia-Alvarez, David and Stefanovska, Aneta and McClintock, Peter VE (2008) High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing. Physical Review E, 77 (5). ISSN 1539-3755

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Abstract

We consider a rotator whose equation of motion for the angle theta 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 theta on theta, the wider the regions of synchronization. Use of a synchronization index reveals a vast number of very narrow n: in 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: in synchronization states are considered: slow variation of the driving frequency, and the influence of low-frequency noise on the rotator.

Item Type: Journal Article
Journal or Publication Title: Physical Review E
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qc
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 11263
Deposited By: Dr Aneta Stefanovska
Deposited On: 06 Aug 2008 20:01
Refereed?: Yes
Published?: Published
Last Modified: 19 Aug 2019 23:32
URI: https://eprints.lancs.ac.uk/id/eprint/11263

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