CRP Toolbox Reference



Indicator of phase synchronisation by means of recurrences.




cpr=phasesynchro(x,y [,param1,param2,...]) calculates the index of phase synchronisation based on recurrences.

cpr=phasesynchro(x,y,m,t,e,w) uses the dimension m, delay t, the size of neighbourhood e and the range w of past and future time steps.

If x and y are multi-column vectors then they will be considered as phase space vectors (taucrp can be used for real phase space vectors without embedding).

The call of phasesynchro without output arguments plots the tau-recurrence rate and the CPR value in the current figure.


Dimension M, delay T, the size of neighbourhood E and the range W are the first four numbers after the data series; further parameters can be used to switch between various methods of finding the neighbours of the phasespace trajectory and to suppress the normalization of the data.

Methods of finding the neighbours/ of plot.
    'maxnorm' Maximum norm.
    'euclidean' - Euclidean norm.
    'minnorm' Minimum norm.
    'rr' Maximum norm, fixed recurrence rate.
    'fan' - Fixed amount of nearest neighbours.

Normalization of the data series.
    'normalize' - Normalization of the data.
    'nonormalize' - No normalization of the data.

Suppressing the plot.
    'silent' - Suppresses the plot of the results.

Parameters not needed to specify.


    a = sin((1:1000) * 2 * pi/67);
    b = sin((1:1000) * 2 * pi/67) + randn(1,1000);

See Also

crp, crqad


Marwan, N., Romano, M. C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5-6), 2007.

Romano, M. C., Thiel, M., Kurths, J., Kiss, I. Z., Hudson, J.: Detection of synchronization for non-phase-coherent and non-stationary data, Europhysics Letters, 71(3), 2005.

phasespace pss