High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing.
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[over ] 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.
García-Alvarez
David
D
Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom. d.garcia-alvarez@lancaster.ac.uk
Stefanovska
Aneta
A
McClintock
Peter V E
PV