Arnold tongue

In mathematics, particularly in dynamical systems theory, an Arnold tongue is a phase-locked or mode-locked region in a driven (kicked) weakly-coupled harmonic oscillator. Arnold tongues are observed in a large variety of complex vibrating systems, including the inharmonicity of musical instruments, orbital resonance and tidal locking of orbiting moons, mode-locking in fiber optics and phase-locked loops and other electronic oscillators, as well as in cardiac rhythms and heart arrhythmias. One of the simplest physical models that exhibits mode-locking consists of two rotating disks connected by a weak spring. One disk is allowed to spin freely, and the other is driven by a motor. Mode locking occurs when the freely-spinning disk turns at a frequency that is a rational number of the driven rotator.