phaSyn: Phase Synchronisation Analysis
In simsalabim: A collection of methods for time series analysis and signal detection.

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the phase synchronisation index between to time series.

1 2	phaSyn(x1,x2,method="MRL",M=100) phaSynMat(X,method="MRL",M=100,verbose=TRUE)

`x1, x2`	Numeric vectors of the same length, interpreted as time series.
`method`	How to determine the phase synchronisation index. `"MRL"`: mean resultant length. `"SH"`: a measure based on the Shannon - Entropy.
`M`	Number of bins in the histogram of the cyclic phase difference. This is only used if `method="SH"` and is ignored otherwise.
`X`	A matrix containing time series in its columns.
`verbose`	If `TRUE` informations about the progress of the computation are printed.

Phase synchronisation is quantified in two steps: First, the phase of both series is extracted by means of the Hilbert - transformation. Second, the distribuition of the cyclic phase difference of both series is checked for uniformity. In case of uniformity the series are not synchronous in respect to their phase.

Uniformity of the cyclic phase difference can be quantified in two ways. If method="MRL", the dispersion of the barycenter of the phase difference on the unit circle is calculated. In the case of method="SH", a histogram of the phase difference is built and its uniformity quantified by means of the Shannon - entropy.

The indices of both methods are scaled in such a manner that 1 means perfect synchronisation and 0 stands for no synchronisation.

The output of phaSyn is an object of class pSyn containing:

`rho`	Phase synchronisation index.
`phi`	Cyclic phase difference.
`call`	The call of the generating function.
`method`	The method used to quantify peakedness of dsitribution.
`name_x1`	Name of series `x1`.
`name_x2`	Name of series `x2`.

The output of phaSynMat is a symmetric matrix containing the pairwise phase synchronisation index.

Lukas Gudmundsson

Allefeld, C. & Kurths, J. Testing for phase synchronization. International Journal of Bifurcation and Chaos, 2004, 14, 405-416

Rybski, D.; Havlin, S. & Bunde, A. Phase synchronization in temperature and precipitation records. Physica A: Statistical Mechanics and its Applications, Elsevier, 2003, 320, 601-610

synBoot

# phase synchronisation
x1 <- sin(1:100)
x2 <- cos(1:100)
phaSyn(x1,x2)

# phase synchronisation matrix
xx<-matrix(seq(0,6*pi,len=100),ncol=30,nrow=100)
colnames(xx) <- 1:30
xx[,1:10] <- sin(xx[,1:10])
xx[,11:20] <- sin(xx[,11:20]*2*pi)
xx[,21:30] <- sin(xx[,21:30]*4*pi)
cxx <- phaSynMat(xx,verbose=FALSE)