Damoco

DAMOCO: Data Analysis with Models Of Coupled Oscillators

MATLAB Toolbox for multivariate time series analysis

Björn Kralemann, Michael Rosenblum, Arkady Pikovsky

This toolbox is a collection of functions for bivariate data analysis, based on the coupled oscillator approach,

developed in our publications. With the help of this toolbox you can:

transform phase estimates, or protophases, of scalar signals into true phases
reconstruct models of coupled oscillators from data
compute synchronization and directionality indices

A description of the toolbox and of how to use it can be found in this manual.

Please mail us if you encounter any problem in using the toolbox! Any questions/suggestions are highly welcome.

Please cite our publications if you use this software!

You can download the whole toolbox as an archive here or as separate files from the list of functions below.

The current version 1.0 of the toolbox contains the following functions:

Function	What it does	Version
General purpose functions
co_testproto	Auxiliary functions which checks the input data	17.01.2011
co_hilbproto	Instantaneous protophase from a scalar time series, using the Hilbert transform	17.01.2011
co_sync	n:m synchronization index	17.01.2011
co_maxsync	Maximal n:m synchronization index for a given range of n, m	17.01.2011
co_dirin	Directionality index from norms of the coupling functions	17.01.2011
co_dirpar	Directionality index from partial derivatives of the coupling functions	17.01.2011
Univariate transformation
co_fbtransf1	One-dimensional Fourier-based protophase → phase transformation	17.01.2011
Bivariate transformation
co_fbtransf2	High-level function which performs two-dimensional protophase → phase transformation and computes the coupling functions, frequencies, directionality index. Fourier-based technique.	17.01.2011
co_ittransf2	High-level function which performs two-dimensional protophase → phase transformation and computes the coupling functions, frequencies, directionality index. Iteration technique.	17.01.2011
co_fexp2	Given two (proto)phases, the function yields two coupling functions via fitting a Fourier series	17.01.2011
co_fexp1	Similar to co_fexp2.m, but only one coupling function is computed	17.01.2011
co_fbsolv	Using the output of co_fexp2.m , this function computes the bivariate protophase → phase transformation function	17.01.2011
co_fbth2phi	Using the output of co_fbsolv, this function performs the bivariate protophase → phase transformation	17.01.2011
co_fbnorm	Norm of the coupling function, given by the Fourier coefficients	17.01.2011
co_itersolv	Using the output of co_fexp2.m or, this function computes the bivariate protophase → phase transformation function by iteration technique; it also returns frequencies, true coupling functions, and their norms.	17.01.2011
co_gth2phi	Using the output of co_itersolv, this function performs the bivariate protophase → phase transformation	17.01.2011
Additional functions
co_plotcplf	Plot of the coupling function	17.01.2011
co_plot2cplf	Plot of two coupling functions in the same window	17.01.2011
co_plotcoef	Plot of the Fourier coefficients of the coupling function	17.01.2011
co_plot2coef	Plot of the Fourier coefficients of two coupling functions	17.01.2011
co_fbcfcor	Correlation between two coupling functions (Fourier-based)	17.01.2011
co_gcfcor	Correlation between two coupling functions, given on a grid	17.01.2011

The toolbox is illustrated by the following examples:

Example	Function	Sample data	Output
Two coupled van der Pol oscillators
High-level Fourier-based function	co_example1.m	co_vdp2.mat	example1.pdf
Fourier-based technique, step-by-step with plots of intermediate results	co_example2.m	same as above	example2.pdf
High-level function, iteration technique	co_example3.m	co_vdp2uni.mat	example3.pdf
Iteration technique, step-by-step with plots of intermediate results	co_example4.m	same as above	example4.pdf

If you find a bug, or have any comment or suggestion, please send us e-mail.

Tell us if you want to be informed on new programs and new releases of this software!

This site is still under construction and (we hope) will be improved soon!

The toolbox is also under development. What is coming:

efficient algorithms based on kernel density estimation;
functions for analysis of three coupled oscillators.

References:

B. Kralemann, L. Cimponeriu, M.G. Rosenblum, A.S. Pikovsky, and R. Mrowka,
Phase dynamics of coupled oscillators reconstructed from data,
Physical Review E, 77, p. 066205, 2008, pdf file (2 Mb)

B. Kralemann, L. Cimponeriu, M.G. Rosenblum, A.S. Pikovsky, and R. Mrowka
Uncovering interaction of coupled oscillators from data,
Physical Review E, 76, p. 055201, 2007, pdf file (280 Kb)

M.G. Rosenblum and A.S. Pikovsky,
Detecting direction of coupling in interacting oscillators,
Physical Review E, 64, p. 045202, 2001, pdf file (218 Kb)

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