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DAMOCO: Data Analysis with Models Of Coupled OscillatorsMATLAB Toolbox for multivariate time series analysisBjörn 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 |
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Auxiliary functions which checks the input data |
17.01.2011 |
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Instantaneous protophase from a scalar time series, using the Hilbert transform |
17.01.2011 |
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n:m synchronization index |
17.01.2011 |
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Maximal n:m synchronization index for a given range of n, m |
17.01.2011 |
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Directionality index from norms of the coupling functions |
17.01.2011 |
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Directionality index from partial derivatives of the coupling functions |
17.01.2011 |
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Univariate transformation |
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One-dimensional Fourier-based protophase → phase transformation |
17.01.2011 |
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Bivariate transformation |
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High-level function which performs two-dimensional protophase → phase transformation and computes the coupling functions, frequencies, directionality index. Fourier-based technique. |
17.01.2011 |
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High-level function which performs two-dimensional protophase → phase transformation and computes the coupling functions, frequencies, directionality index. Iteration technique. |
17.01.2011 |
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Given two (proto)phases, the function yields two coupling functions via fitting a Fourier series |
17.01.2011 |
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Similar to co_fexp2.m, but only one coupling function is computed |
17.01.2011 |
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Using the output of co_fexp2.m , this function computes the bivariate protophase → phase transformation function |
17.01.2011 |
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Using the output of co_fbsolv, this function performs the bivariate protophase → phase transformation |
17.01.2011 |
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Norm of the coupling function, given by the Fourier coefficients |
17.01.2011 |
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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 |
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Using the output of co_itersolv, this function performs the bivariate protophase → phase transformation |
17.01.2011 |
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Additional functions |
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Plot of the coupling function |
17.01.2011 |
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Plot of two coupling functions in the same window |
17.01.2011 |
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Plot of the Fourier coefficients of the coupling function |
17.01.2011 |
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Plot of the Fourier coefficients of two coupling functions |
17.01.2011 |
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Correlation between two coupling functions (Fourier-based) |
17.01.2011 |
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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 |
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High-level Fourier-based function |
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Fourier-based technique, step-by-step with plots of intermediate results |
same as above |
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High-level function, iteration technique |
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Iteration technique, step-by-step with plots of intermediate results |
same as above |
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.
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)