- See entrainment for other types.
Entrainment has been used to refer to the process of mode locking of coupled driven oscillators, which is the process whereby two interacting oscillating systems, which have different periods when they function independently, assume a common period. The two oscillators may fall into synchrony, but other phase relationships are also possible. The system with the greater frequency slows down, and the other speeds up.
Dutch physicist Christian Huygens, the inventor of the pendulum clock, introduced the concept after he noticed, in 1666, that the pendulums of two clocks mounted on a common board had synchronized, and subsequent experiments duplicated this phenomenon. He described this effect as "odd sympathy". The two pendulum clocks synchronized with their pendulums swinging in opposite directions, 180° out of phase, but in phase states can also result. Entrainment occurs because small amounts of energy are transferred between the two systems when they are out of phase in such a way as to produce negative feedback. As they assume a more stable phase relationship, the amount of energy gradually reduces to zero. In the realm of physics, Huygens' observations are related to resonance and the resonant coupling of harmonic oscillators, which also gives rise to sympathetic vibrations.
A 2002 study of Huygens' observations show that an antiphase stable oscillation was somewhat fortuitous, and that there are other possible stable solutions, including a "death state" where a clock stops running, depending on the strength of the coupling between the clocks.
Mode locking between driven oscillators can be easily demonstrated using mechanical metronomes on a common, easily movable surface.   Such mode locking is important for many biological systems including the proper operation of pacemakers.
The use of the word entrainment in the modern Physics literature most often refers to the movement of one fluid, or collection of particulates, by another (see Entrainment (hydrodynamics)). The use of the word to refer to mode locking of non-linear coupled oscillators appears mostly after about 1980, and remains relatively rare in comparison.
A similar coupling phenomenon was characterized in hearing aids when the adaptive feedback cancellation is used. This chaotic artifact (entrainment) is observed when correlated input signals are presented to an adaptive feedback canceller.
- Entrainment (hydrodynamics)
- Injection locking
- Brainwave synchronization
- Synchronization of chaos
- odd sympathy
- M Bennett, M F Schatz, H Rockwood, andK Wiesenfeld, Proc. Roy. Soc. Lond. A 458 (2002) 563-579.
- J. Pantaleone, "Synchronization of Metronomes," American Journal of Physics, vol 70 (2002) 992-1000.
- Watch the synchronization of 32 metronomes CBS News, 2013 Sept 10
- G. B. Ermentrout and J. Rinzel, "Beyond a pacemaker's entrainment limit: phase walk-through," American Journal of Physiology - Regulatory, Integrative and Comparative Physiology, Vol 246 (1984) R102-R106.
Filter Entrainment Avoidance with a Frequency Domain Transform Algorithm 
Entrainment Avoidance with Pole Stabilization 
Entrainment Avoidance with a Transform Domain Algorithm 
Entrainment Avoidance with an Auto Regressive Filter