High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing
| Autor: | Peter V. E. McClintock, David Garcia-Alvarez, Aneta Stefanovska |
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| Rok vydání: | 2007 |
| Předmět: |
Forcing (recursion theory)
Equations of motion FOS: Physical sciences Harmonic (mathematics) Nonlinear Sciences - Chaotic Dynamics Phase synchronization symbols.namesake Zeroth law of thermodynamics Fourier transform Classical mechanics Synchronization (computer science) symbols Chaotic Dynamics (nlin.CD) Noise (radio) Mathematics |
| Zdroj: | Physical review. E, Statistical, nonlinear, and soft matter physics. 77(5 Pt 2) |
| ISSN: | 1539-3755 |
| Popis: | 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 $\dot\theta$ on $\theta$, 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. Comment: 10 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 |
| Databáze: | OpenAIRE |
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