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{{Short description|Type of plot in descriptive statistics and chaos theory}}
In descriptive [[statistics]] and [[chaos theory]], a '''recurrence plot''' ('''RP''') is a plot showing, for each moment <math>j</math> in time, the times at which the state of a [[dynamical system]] returns to the previous state at <math>i</math>,
i.e., when the [[phase space]] trajectory visits roughly the same area in the phase space as at time <math>j</math>. In other words, it is a plot of
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| bibcode=1987EL......4..973E
| s2cid=250847435
}}</ref> Often, the phase space does not have a low enough dimension (two or three) to be pictured, since higher-dimensional phase spaces can only be visualized by projection into the two or three-dimensional sub-spaces. One frequently used tool to study the behaviour of such phase space trajectories is then the [[Poincaré map]]. Another tool
At a '''recurrence''' the trajectory returns to a ___location (state) in phase space it has visited before up to a small error <math>\varepsilon</math> . The recurrence plot represents the collection of pairs of times of such recurrences, i.e., the set of <math>(i,j)</math> with <math>\vec{x}(i) \approx \vec{x}(j)</math>, with <math>i</math> and <math>j</math> discrete points of time and <math>\vec{x}(i)</math> the state of the system at time <math>i</math> (___location of the trajectory at time <math>i</math>).
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| doi=10.1016/j.physrep.2006.11.001
| pages=237
|bibcode = 2007PhR...438..237M | arxiv=2501.13933}}</ref> Therefore, the [[recurrence quantification analysis]] quantifies the distribution of these small-scale structures.<ref>{{cite journal
| author1=J. P. Zbilut | author2=C. L. Webber
| title=Embeddings and delays as derived from quantification of recurrence plots
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