Quasiperiodicity is the property of a
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
that displays irregular
periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is almost but not quite periodic. The term used to denote oscillations that appear to follow a regular pattern but which do not have a fixed period. The term thus used does not have a precise definition and should not be confused with more strictly defined mathematical concepts such as an
almost periodic function
In mathematics, an almost periodic function is, loosely speaking, a function of a real variable that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by ...
or a
quasiperiodic function
In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function f is quasiperiodic with quasiperiod \omega if f(z + \omega) = g(z,f(z)), where g is a "''simpler''" function than f. What it ...
.
Climatology
Climate oscillation
Climate variability includes all the variations in the climate that last longer than individual weather events, whereas the term climate change only refers to those variations that persist for a longer period of time, typically decades or more ...
s that appear to follow a regular pattern but which do not have a fixed period are called ''quasiperiodic''.
[''The meteorological glossary: 2d ed.'' 1930. ]Meteorological Office
The Met Office, until November 2000 officially the Meteorological Office, is the United Kingdom's national weather and climate service. It is an executive agency and trading fund of the Department for Science, Innovation and Technology and ...
, Great Britain. "Certain phenomena which recur more or less regularly but without the exactness of truly periodic phenomena are termed quasi-periodic."
Within a
dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...
such as the ocean-atmosphere system, oscillations may occur regularly when they are forced by a regular external forcing: for example, the familiar winter-summer cycle is forced by variations in sunlight from the (very close to perfectly) periodic motion of the Earth around the Sun. Or, like the recent
ice age
An ice age is a long period of reduction in the temperature of Earth's surface and atmosphere, resulting in the presence or expansion of continental and polar ice sheets and alpine glaciers. Earth's climate alternates between ice ages, and g ...
cycles, they may be less regular but still locked by external forcing. However, when the system contains the potential for an oscillation, but there is no strong external forcing to be
phase-locked
In mathematics, particularly in dynamical systems, Arnold tongues (named after Vladimir Arnold) Section 12 in page 78 has a figure showing Arnold tongues. are a pictorial phenomenon that occur when visualizing how the rotation number of a dynami ...
to, the "period" is likely to be irregular.
The canonical example of quasiperiodicity in climatology is
El Niño–Southern Oscillation
El Niño–Southern Oscillation (ENSO) is a global climate phenomenon that emerges from variation in winds and sea surface temperatures over the tropical Pacific Ocean. Those variations have an irregular pattern but do have some semblance of cyc ...
(ENSO).
[ ENSO is highly consequential for ]wheat
Wheat is a group of wild and crop domestication, domesticated Poaceae, grasses of the genus ''Triticum'' (). They are Agriculture, cultivated for their cereal grains, which are staple foods around the world. Well-known Taxonomy of wheat, whe ...
cultivation in Australia.[ Models to predict and thereby assist adaptation to ENSO have a large potential benefit to Australian wheat farmers.][
This review cites this study:
] In the modern era, it has a "period" somewhere between four and twelve years and a peak spectral density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into ...
around five years.
See also
*Nonlinear resonance In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. In nonlinear resonance the system behaviour – resonance frequency, resonance frequencies and normal mode, modes – depends on the amplitude of the oscillations, ...
*Quasiperiodic function
In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function f is quasiperiodic with quasiperiod \omega if f(z + \omega) = g(z,f(z)), where g is a "''simpler''" function than f. What it ...
*Quasiperiodic motion
In mathematics and theoretical physics, quasiperiodic motion is motion on a torus that never comes back to the same point. This behavior can also be called quasiperiodic evolution, dynamics, or flow. The torus may be a generalized torus so that t ...
*Quasi-periodic oscillations
In X-ray astronomy, quasi-periodic oscillation (QPO) is the manner in which the X-ray light from an astronomical object flickers about certain frequencies. In these situations, the X-rays are emitted near the inner edge of an accretion disk in w ...
*Quasiperiodic tiling
A quasiperiodic tiling is a tiling of the plane that exhibits local periodicity under some transformations: every finite subset of its tiles reappears infinitely often throughout the tiling, but there is no nontrivial way of superimposing the whole ...
*Seasonality
In time series data, seasonality refers to the trends that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consi ...
References
Systems theory
Dynamical systems
Wave mechanics
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