ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Smirnov D. A., Bodrov M. B., Bezruchko B. P. Estimation of coupling between oscillators from time series via phase dynamics modeling: limits of method’s applicability. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 6, pp. 79-92. DOI: 10.18500/0869-6632-2004-12-6-79-92

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
503.18
DOI: 
10.18500/0869-6632-2004-12-6-79-92

Estimation of coupling between oscillators from time series via phase dynamics modeling: limits of method’s applicability

Autors: 
Smirnov Dmitrij Alekseevich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Bodrov Maksim Borisovich, Saratov State University
Bezruchko Boris Petrovich, Saratov State University
Abstract: 

The problem of determination of the presence and directionality of coupling between oscillatory systems only from their time realizations is considered. One of the efficient «nonlinear» approaches to its solution is based on calculation of the phases of oscillations from the observed signals and construction of a model map describing the phase dynamics, whose properties allow coupling characterization. The approach was justified theoretically for weakly nonlinear and weakly coupled phase oscillators under the influence of normal white noise. In this work, we find out practical limits of applicability of the approach in numerical experiment (for different properties of noise and different values of phase nonlinearity and coupling intensity). Applicability of the employed working formulas for coupling estimators in a wide range of situations is shown.

Key words: 
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Acknowledgments: 
The work was supported by the RFBR (05-02-16305), programm ВRНЕ (REC-006), grant from the President of the Russian Federation (МК-1067.2004.2) and Foundation for the Promotion of Russian Science.
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Received: 
22.11.2004
Accepted: 
18.03.2005
Published: 
15.06.2005
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