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An illustration of the concept of recurrence plots, using the Lorenz system (a well-known 3-dimensional non-linear system - reproduced here from [68]).

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posted on 2014-12-02, 03:18 authored by Deborah Apthorp, Fintan Nagle, Stephen Palmisano

a) The Lorenz attractor: an example trajectory of the Lorenz system represented in 3-dimensional phase space. b) The recurrence plot for this trajectory. Both axes represent time. Looking along the x axis, we can follow the system's evolution. If the system's position in phase space at is closely approached at , we place a dot at coordinates . The positions at and need not be exactly the same, but they must be close to within a tolerance which we set to be very small. The recurrence plot thus shows all time points when the system returns very close to a previous state; each dot in the graph represents a revisit, and we can read the two visiting times from the x and y axes. Note that recurrence plots are symmetric. Code for reproducing these figures can be found at http://people.physik.hu-berlin.de/schinkel/timely/html/index.html.

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