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

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Smirnov D. A., Navrotskaya E. V., Bezruchko B. P. Statistical properties of phase synchronization coefficient estimator. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 2, pp. 111-121. DOI: 10.18500/0869-6632-2008-16-2-111-121

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Statistical properties of phase synchronization coefficient estimator

Smirnov Dmitrij Alekseevich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Navrotskaya Elena Vladimirovna, Saratov State University
Bezruchko Boris Petrovich, Saratov State University

A phase synchronization coefficient estimate, obtained from a time series, can take a high value even for uncoupled oscillators in the case of short signals and close basic frequencies. Since such situations are widespread in practice, it is necessary to detect them to avoid false conclusions about the presence of coupling. We investigate statistical properties of the estimator with the use of an exemplary system – uncoupled phase oscillators. Conditions leading to high probability to get big values of the estimator are determined quantitatively. Based on the performed analysis, we suggest a special technique for surrogate data generation to control statistical significance of the estimation results.

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