|CRP Toolbox Reference|
PurposeComputes and plots the CRQA measures.
Recurrence quantification analysis of cross-recurrence with the first vector x and the second y. The results can be plotted.
The input vectors can be multi-column vectors, where each column will be used as a component of the phase-space vector. However, if the first column is monotonically increasing, it will be used as an time scale for plotting.
Dimension m, delay t, the size of neighbourhood e, the window size w and the shift value ws are the first five numbers after the data series; if w= then the whole plot will be calculated. The minimal length of diagonal and vertical structures can be specified with lmin and vmin respectively (default is 2).
As the last numeric parameter, the size of the Theiler window tw can be specified (default is 1). This window excludes the recurrence points parallel to the main diagonal from the analysis. The application of the Theiler window is useful only for recurrence plots. In cross recurrence plots, the size of the Theiler window will be set automatically to zero.
Further parameters can be used to switch between various methods of finding the neighbours of the phasespace trajectory, to suppress the normalization of the data and to suppress the GUI (useful in order to use this programme by other programmes).
Parameters not needed to be specified.
The window of length w is applied on the data and not on the RP, i.e. the RP will have smaller size than the window, thus w-(m-1)*tau. If we consider the data window at time i ... i+w, the corresponding RQA measures are assigned to time i. Therefore, if you see a beginning of a transition in the plot of the RQA measures at time i, this transition will probably happen at time i+w-(m-1)*tau.
A prototype for estimation of confidence intervals for RQA measures is available at http://www.agnld.uni-potsdam.de/~schinkel/rqaci.php. We plan to include it in the CRP toolbox in the near future.
For higher speed in output the whole matrix of the recurrence plot is in the work space - this limits the application of long data series. However, a solution for using long data series you can find under the description for crp.
The RQA measures may differ from those of the RQA programmes by Charles Webber Jr. For compatibility use a Theiler window of size one and ensure that the data are normalized before by the same distance which is used in the RQA programmes; e.g. normalize with the maximal phase space diameter, which can be estimated with the programme pss:
b=.5; for i=2:N, b(i)=a(i)*b(i-1)*(1-b(i-1));end
title('logistic map'), axis([3.4 4 0 1])
ylabel('recurrence rate'), axis([3.4 4 0 1])
Marwan, N., Romano, M. C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems, Phys. Rep., 438, 2007.
Little, M., McSharry, P., Roberts, S., Costello, D., Moroz, I.: Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection, Biomed. Eng. Online, 6, 2007.
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: Structures and dynamics, Phys. Rep., 424, 2006.
Marwan, N., Donges, J. F., Zou, Y., Donner, R. V., Kurths, J.: Complex network approach for recurrence analysis of time series, Phys. Lett. A, 373(46), 2009.