phase.sync {synchrony}

Phase synchrony of quasi-periodic time series

Description

Compute the phase synchrony between two quasi-periodic time series by quantifying their phase difference at each time step

Usage

phase.sync (t1, t2,  nrands = 0, mod = 1, method = c("markov", "fft"), 
            nbreaks = 10, mins = FALSE, quiet = FALSE)

Arguments

t1

time series 1 in matrix format (n rows x 2 columns). The first column should contain the time steps and the second column should contain the values. If t1 is a column vector instead of a matrix, then it will be automatically converted to a matrix with column 1 corresponding to a time index ranging from 1 to the length of t1.

t2

time series 2 in matrix format (n rows x 2 columns). The first column should contain the time steps and the second column should contain the values. If t2 is a column vector instead of a matrix, then it will be automatically converted to matrix with column 1 corresponding to a time index ranging from 1 to the length of t2.

nrands

number of randomizations to perform (default is 0)

mod

flag to indicate whether to compute phase difference modulus 2\pi between 0 and 2\pi (mod=1) or phase difference modulus 2\pi between -\pi and \pi (mod=2). Default is mod=1.

method

method to generate surrogate time series for Monte Carlo simulations. This can be set to markov to use the Markov process described in Cazelles and Stone (2004) or fft to use the FFT approach described in Theiler et al. (1992). Default is method=markov.

nbreaks

number of bins to use to group the values in the time series. Default is 10.

quiet

Suppress progress bar when set to TRUE. Default is FALSE

mins

use local minima instead of local maxima to compute and the interpolate the phase. Default is FALSE.

Details

Two time series are phase-locked if the relationship between their phases remains constant over time. This function computes the phase of successive local maxima or minima for each time series and then uses linear interpolation to find the phase at time steps that fall between local maxima/minima. A histogram can be used to determine if the distribution of the phase difference at each time step is uniform (indicating no phase locking) or has a clear peak (indicating phase locking).

Value

Returns a list containing Q.obs, pval, rands, phases1, phases2, deltaphase, and icdf:

Q.obs

Phase synchrony ranging from 0 (no phase synchrony) to 1 (full phase synchrony)

pval

p-value of observed phase synchrony based on randomization test

rands

Monte Carlo randomizations

phases1

n x 3 matrix containing the timestep, value, and phase of the first time series

phases2

n x 3 matrix containing the timestep, value, and phase of the second time series

deltaphase

n x 4 matrix containing the timestep, raw phase difference, phase difference modulus 2\pi between 0 and 2\pi, phase difference modulus 2\pi between -\pi and \pi

icdf

Inverse cumulative distribution of Q values obtained from Monte Carlo randomizatons

Author(s)

Tarik C. Gouhier ([e-mail])

References

Cazelles, B., and L. Stone. 2003. Detection of imperfect population synchrony in an uncertain world. Journal of Animal Ecology 72:953–968.

Theiler, J., S. Eubank, A. Longtin, B. Galdrikian, and J. Doyne Farmer. 1992. Testing for nonlinearity in time series: the method of surrogate data. Physica D: Nonlinear Phenomena 58:77–94.

Examples

t1=runif(100)
t2=runif(100)
# Compute and interpolate phases using successive local minima
sync.mins=phase.sync(t1, t2, mins=TRUE)
# Compute and interpolate phases using successive local maxima
sync.maxs=phase.sync(t1, t2)
# Plot distribution of phase difference
hist(sync.mins$deltaphase$mod_phase_diff_2pi)