{{no footnotes, date=June 2017
Phase synchronization is the process by which two or more cyclic signals tend to oscillate with a repeating sequence of relative phase angles.
Phase synchronisation is usually applied to two waveforms of the same frequency with identical phase angles with each cycle. However it can be applied if there is an integer relationship of frequency, such that the cyclic signals share a repeating sequence of phase angles over consecutive cycles. These integer relationships are called Arnold tongues which follow from bifurcation of the circle map.
One example of phase synchronization of multiple oscillators can be seen in the behavior of Southeast Asian
fireflies
The Lampyridae are a family of elateroid beetles with more than 2,000 described species, many of which are light-emitting. They are soft-bodied beetles commonly called fireflies, lightning bugs, or glowworms for their conspicuous production ...
. At dusk, the flies begin to flash periodically with random phases and a gaussian distribution of native frequencies. As night falls, the flies, sensitive to one another's behavior, begin to synchronize their flashing. After some time all the fireflies within a given tree (or even larger area) will begin to flash simultaneously in a burst.
Thinking of the fireflies as biological oscillators, we can define the phase to be 0° during the flash and +-180° exactly halfway until the next flash. Thus, when they begin to flash in unison, they synchronize in phase.
One way to keep a local oscillator "phase synchronized" with a remote transmitter uses a
phase-locked loop
A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...
.
See also
*
Algebraic connectivity
The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph ''G'' is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of ''G''. This eigenvalue i ...
Kuramoto model
The Kuramoto model (or Kuramoto–Daido model), first proposed by , is a mathematical model used to describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated b ...
*
Synchronization (alternating current) In an alternating current electric power system, synchronization is the process of matching the frequency of a generator or other source to a running network. An AC generator cannot deliver power to an electrical grid unless it is running at the sam ...
References
* ''Sync'' by S. H. Strogatz (2002).
* ''Synchronization - A universal concept in nonlinear sciences'' by A. Pikovsky, M. Rosenblum, J. Kurths (2001)