DAMOCO: Data Analysis with Models Of Coupled Oscillators

MATLAB Toolbox for multivariate time series analysis

Björn Kralemann, Michael Rosenblum, Arkady Pikovsky

 

Version 2.0 (2014)

 

 

The site is under construction! Last modification 8.06.14

 

This toolbox is a collection of functions for multivariate data analysis, based on the coupled oscillator approach, developed in our publications.

With the help of this toolbox you can:

·       compute protophases (initial phase estimates) from time series by means of the Hilbert Transform

·       transform protophases into true phases

·       reconstruct phase dynamics 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.   Sorry, the manual for Version 2 is not ready yet.

 

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

Main functions are illustrated by examples.

 

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

Please cite our publications if you use this software.

 

DAMOCO Version 1.0 can be found here.


 

Brief illustration to the theory

 

o   Coupled oscillators approach: main ideas and assumptions

o   Phase dynamics of coupled oscillators

o   Protophases and phases

o   Synchronization and its quantification

o   Direction of coupling and its quantification

o   Protophase phase transformation: why do we need it?

 


 

The current version 2.0 of the toolbox contains the following functions:

 

Function

                                                               What it does

Version

Protophase computation

co_hilbproto

Protophase from a scalar time series, using the Hilbert transform

27.02.2014

co_distproto

Protophase from a scalar time series, using the length of the trajectory in the state space

10.04.2014

co_mmzproto

Protophase from a scalar time series via markers (minima, maxima, zero-crossings)

06.05.2014

co_avcyc

Protophase from a scalar time series, via the average cycle

18.05.2014

Univariate protophase phase transformation

co_fbtransf1

Protophase phase transformation plus computation of the transformation function

02.03.2014

co_fbtrT

Protophase phase transformation with optimization (recommended)

02.03.2014

Synchronization analysis

co_sync

n:m synchronization index

17.01.2011

co_maxsync

Maximal n:m synchronization index for a given range of n, m

27.02.2014

co_sync3

n:m:p triplet synchronization index

06.03.2014

co_maxsync3

Maximal n:m:p synchronization index for a given range of n, m, p

06.03.2014

Two interacting oscillators: coupling functions

co_fcplfct2

Fourier-based technique, coupling functions for both oscillators

04.03.2014

co_fcplfct1

Fourier-based technique, coupling function for one oscillator only

04.03.2014

co_kcplfct2

Kernel estimation, coupling functions for both oscillators

03.03.2014

co_kcplfct1

Kernel estimation, coupling function for one oscillator only

03.03.2014

Analysis of two-dimensional coupling functions

co_fnorm

Norm and constant term (frequency) of the coupling function, given by the Fourier coefficients

05.03.2014

co_gnorm

Norm and constant term (frequency) of the coupling function, given on the grid

04.03.2014

co_fcfcor

Correlation between two coupling functions (Fourier-based)

06.03.2014

co_fcfcormax

Maximal correlation between two coupling functions (Fourier-based)

06.03.2014

co_gcfcor

Correlation between two coupling functions, given on a grid

06.03.2014

co_gcfcormax

Maximal correlation between two coupling functions, given on a grid

06.03.2014

co_cor_diff

Correlation and difference measure for two coupling functions on a grid

02.03.2014

co_dirin

Directionality index from norms of the coupling functions

26.02.2014

co_dirpar

Directionality index from partial derivatives of the coupling functions

26.02.2014

co_prciter

Phase Response Curve via decomposition of the coupling function

28.02.2014

More than two interacting oscillators

co_fcpltri

Three coupled oscillators, coupling functions via a Fourier-based technique

06.03.2014

co_tricplfan

Coupling structure of the triplet

12.03.2014

co_nettri

Triplet analysis of a network with N>3 oscillators

12.03.2014

co_plottri

Plot of the triplet coupling structure

05.04.2014

Additional functions

co_phidot1

Derivative of the phase via the Savitzky-Golay filter

06.03.2014

co_phidot2

Derivatives of two phases via the Savitzky-Golay filter (for bivariate analysis)

06.03.2014

co_phidot3

Derivatives of three phases via the Savitzky-Golay filter (for triplet analysis)

06.03.2014

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_testproto

Auxiliary function which checks the input data

17.01.2011

 

 


 

Publications

 

 

Reference

What it is about

1

M. Rosenblum and A. Pikovsky
Detecting direction of coupling in interacting oscillators,
Physical Review E, 64, p. 045202, 2001

Notion of directionality in coupled oscillatory systems, directionality index via partial derivatives

2,3

B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, and R. Mrowka
Uncovering interaction of coupled oscillators from data,
Physical Review E, 76, p. 055201, 2007

Phase dynamics of coupled oscillators reconstructed from data,
Physical Review E, 77, p. 066205, 2008

 

Notion of protophases, phase to protophase transformation, protophaase via the length of the trajectory, recovery of autonomous frequencies

4

B. Kralemann, A. Pikovsky, and M. Rosenblum,


Reconstructing phase dynamics of oscillator networks,

Chaos, 21, p. 025104, 2011

Reconstruction of small networks, coupling functions for three coupled oscillators, directionality index via partial norms, recovery of autonomous frequencies

5

B. Kralemann, M. Frühwirth, A. Pikovsky, M. Rosenblum,
 T. Kenner,  J. Schaefer, and M. Moser

In vivo cardiac phase response curve elucidates human respiratory heart rate variability,

Nature Communications, 4, 2418, 2013

Protophase via average cycle, phase response curve from the coupling function

6

B. Kralemann, A. Pikovsky, and M. Rosenblum,

Detecting triplet locking by triplet synchronization indices,

Phys. Rev. E, 87, p. 052904, 2013.

Computation of the triplet index, quantification of the triplet locking from data

7

B. Kralemann, A. Pikovsky, and M. Rosenblum,

Reconstructing effective phase connectivity of oscillator networks from observations,

Submitted to New Journal of Physics, xx, p. xxx, 2014

Extension of the approach from Ref. [4]; here triplet analysis of the N-oscillator network  (N>3) is used instead of traditional pair-wise analysis. Improved differentiation between structurally existing and non-existing links.

 

 

 

 

The toolbox is illustrated by the following examples: new examples are coming

Example

Function

Sample data

Output

Two coupled van der Pol oscillators

High-level Fourier-based function

 

 

 

Fourier-based technique, step-by-step with plots of intermediate results

 

 

 

High-level function, iteration technique

 

 

 

Iteration technique, step-by-step with plots of intermediate results

 

 

 


 

Related links

 

 

HERMES: Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

 

G. Niso,  R. Bruña,  E. Pereda,  R. Gutiérrez,  R. Bajo,  F. Maestú,  and F. del-Pozo.  Neuroinform (2013) 11:405–434

Trentool: an open source toolbox to estimate neural directed interactions with transfer entropy

M. Wibral, R. Vicente, V. Priesemann, and M. Lindner. BMC Neuroscience, 12 (Suppl

1): P200, 2011.

A MATLAB toolbox for Granger causal connectivity analysis

L. Barnett, A.K. Seth. J. Neurosci Methods, 223:50-68, 2014

 

 

 


 

 

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