Recurrence Plot

A recurrence plot is defined as a plot of the quantity

where  is the Heaviside step function and  denotes a norm. A recurrence plot is therefore a binary plot. The figure above shows a recurrence plot for the Lorenz attractor with , , , , , , and .

Recurrence plots were initially used to graphically display nonstationarity in time series (Eckmann et al. 1987, Gao and Cai 2000), but are also useful for visualizing functions.

A so-called global recurrence plot or unthresholded recurrence plot of a function  is a plot of  (or ) in the - plane. Recurrence plots for a number of common functions are illustrated above.

REFERENCES:

Casdagli, M. C. "Recurrence Plots Revisited." Physica D 108, 12-44, 1997.

Eckmann, J. P.; Kamphorst, S. O.; and Ruelle, D. "Recurrence Plots of Dynamical Systems." Europhys. Lett. 4, 973-977, 1987.

Gao, J. and Cai, H. "On the Structures and Quantification of Recurrence Plots." Phys. Lett. A 270, 75-87, 2000.

Marwan, N. "Recurrence Plots and Cross Recurrence Plots." http://www.recurrence-plot.tk/.

Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 20, 2004. http://www.mathematicaguidebooks.org/.