We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK


93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > High-order synchronization, transitions, and co...
View graph of relations

« Back

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

Research output: Contribution to journalJournal article


Journal publication date05/2008
JournalPhysical Review E
Original languageEnglish


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.