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Phase synchronization is the process by which two or more cyclic signals tend to oscillate with a repeating sequence of relative
phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
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
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
, 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 fixed relative to the phase of an input signal. Keeping the input and output phase in lockstep also implies keeping the input and ou ...
Coherence (physics)
Coherence expresses the potential for two waves to Wave interference, interfere. Two Monochromatic radiation, monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be ''partly coherent''. ...
*
Kuramoto model
The Kuramoto model (or Kuramoto–Daido model), first proposed by , is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated b ...