|CRP Toolbox Reference|
PurposeComputes and plots the JRQA measures.
Recurrence quantification analysis of joint-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 joint 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 specify.
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=.4; a=.6; mu=.8:-0.7/N:.1;
% two mutually coupled logistic maps
% coupling is obtained by higher RR and DET values
Trulla, L. L., Giuliani, A., Zbilut, J. P., Webber Jr., C. L.: Recurrence quantification analysis of the logistic equation with transients, Phys. Lett. A, 223, 1996.
Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data, Phys. Rev. E, 66(2), 2002.
Romano, M., Thiel, M., Kurths, J., von Bloh, W.: Multivariate Recurrence Plots, Phys. Lett. A, 330, 2004.