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 environment, is described by its boundaries, structure and purpose and express ...
that displays irregular
periodicity
Periodicity or periodic may refer to:
Mathematics
* Bott periodicity theorem, addresses Bott periodicity: a modulo-8 recurrence relation in the homotopy groups of classical groups
* Periodic function, a function whose output contains values tha ...
. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement. It is different from the mathematical concept of an
almost periodic function
In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Haral ...
, which has increasing regularity over multiple periods. The mathematical definition of
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 ...
is a completely different concept; the two should not be confused.
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''.
Within a
dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...
such as the ocean-atmosphere 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 gre ...
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 it 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 it, 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 an irregular periodic variation in winds and sea surface temperatures over the tropical eastern Pacific Ocean, affecting the climate of much of the tropics and subtropics. The warming phase of the sea te ...
. In the modern era, it has a "period" somewhere between four and twelve years and a peak
spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies ...
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 frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is ...
*
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 in rough terms the type of motion executed by a dynamical system containing a finite number (two or more) of incommensurable frequencies.
That is, if we imagine that the phase space ...
*
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 whol ...
*
Seasonality
In time series data, seasonality is the presence of variations 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 a ...
References
Systems theory
Dynamical systems
Wave mechanics
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