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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing. / Garcia-Alvarez, David; Stefanovska, Aneta; McClintock, Peter VE.
In: Physical Review E, Vol. 77, No. 5, 056203, 05.2008.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Garcia-Alvarez, D, Stefanovska, A & McClintock, PVE 2008, 'High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing.', Physical Review E, vol. 77, no. 5, 056203. https://doi.org/10.1103/PhysRevE.77.056203

APA

Garcia-Alvarez, D., Stefanovska, A., & McClintock, P. VE. (2008). High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing. Physical Review E, 77(5), Article 056203. https://doi.org/10.1103/PhysRevE.77.056203

Vancouver

Garcia-Alvarez D, Stefanovska A, McClintock PVE. High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing. Physical Review E. 2008 May;77(5):056203. doi: 10.1103/PhysRevE.77.056203

Author

Garcia-Alvarez, David ; Stefanovska, Aneta ; McClintock, Peter VE. / High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing. In: Physical Review E. 2008 ; Vol. 77, No. 5.

Bibtex

@article{b963b79a6e284e18b4e26f1c77b3bf05,
title = "High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing.",
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.",
keywords = "bifurcation, synchronisation",
author = "David Garcia-Alvarez and Aneta Stefanovska and McClintock, {Peter VE}",
year = "2008",
month = may,
doi = "10.1103/PhysRevE.77.056203",
language = "English",
volume = "77",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "5",

}

RIS

TY - JOUR

T1 - High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing.

AU - Garcia-Alvarez, David

AU - Stefanovska, Aneta

AU - McClintock, Peter VE

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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.

KW - bifurcation

KW - synchronisation

U2 - 10.1103/PhysRevE.77.056203

DO - 10.1103/PhysRevE.77.056203

M3 - Journal article

VL - 77

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 5

M1 - 056203

ER -