Related Experiment Video
Updated: Jul 3, 2026

In Vivo Evaluation of the Mechanical and Viscoelastic Properties of the Rat Tongue
Published on: July 6, 2017
High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing
David García-Alvarez1, Aneta Stefanovska, Peter V E McClintock
1Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom. d.garcia-alvarez@lancaster.ac.uk
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[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.
Related Concept Videos
Forced Oscillations
Torsional Pendulum
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
Stability of structures
Simple Harmonic Motion
Oscillations about an Equilibrium Position
Muscle Stimulation Frequency
Wave summation
At low firing rates, motor neurons induce individual twitch contractions in muscle fibers. These twitches...

