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

Research output: Contribution to journalJournal article

Published

Journal publication date05/2008
JournalPhysical Review E
Journal number5
Volume77
Pages056203
Original languageEnglish

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.