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Interdisciplinary Center for Dynamics of Complex Systems (University of Potsdam)
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Investigations of System's Dynamics

Tools

CRP toolbox

Commandline Recurrence Plots

K2 (Recurrence plots)

PECUZAL

Recurrence plots for MATLAB

SOWAS

pyunicorn

Examples

The dynamics of systems is usually represented by its phase space portrait. However, a phase space could not have a dimension which allows it to be pictured (two or three). Higher dimensional phase spaces can only be visualized by projection into the two or three dimensional sub-spaces. Here helps the method of recurrence plots. This method can also be applied to non-deterministic data.

Examples of recurrence plots.

Typical examples of various systems: (A) uniformly distributed noise, (B) super-positioned harmonic oscillations, (C) drift (logistic map corrupted with a linearly increasing term) and (D) non-stationarity (Brownian motion).


Recurrence plot of summer insolation.

Recurrence plot of the January insolation at Italy for the last 100000 years. From such plots we can learn about symmetry and time relations in the data.

References:

Thiel, M., Romano, M. C., Read, P. L., Kurths, J.: Estimation of dynamical invariants without embedding by recurrence plots, Chaos, 14(2), 2004, 234-243, doi:10.1063/1.1667633, Article (PDF).

Marwan, N., Kurths, J.: Cross Recurrence Plots and Their Applications, in: Mathematical Physics Research at the Cutting Edge, Hauppauge, Nova Science Publishers, 2004, 101-139.



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