Technical Physics Letters

, Volume 39, Issue 7, pp 601–605 | Cite as

A method for revealing coupling between oscillators with analytical assessment of statistical significance

  • D. A. SmirnovEmail author
  • E. V. Sidak
  • B. P. Bezruchko


A method based on calculating the coefficient of correlation between the increments of oscillation phases is proposed for revealing a coupling between two oscillatory systems according to their time series. A distribution of the estimate of this characteristic for uncoupling systems is found; it was used to obtain a criterion for judging the availability of the coupling with a specified confidence probability. The proposed method is simpler than known methods and has a wider range of application, since it also includes oscillators with fairly strong phase nonlinearity. The efficiency of this method is illustrated by examples of reference systems in a numerical experiment.


Technical Physic Letter Modulate Coupling Phase Nonlinearity Phase Increment Difference Coupling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. S. Pikovskii, M. G. Rozenblyum, and Yu. Kurts, in Synchronization. A Fundamental Nonlinear Phenomenon (Tekhnosfera, Moscow, 2003) [in Russian].Google Scholar
  2. 2.
    B. Bezruchko, V. Ponomarenko, M. G. Rosenblum, and A. S. Pikovsky, Chaos 13, 179 (2003).ADSCrossRefGoogle Scholar
  3. 3.
    Y.-C. Hung and C.-K. Hu, Phys. Rev. Lett. 101, 244 102 (2008).CrossRefGoogle Scholar
  4. 4.
    F. Mormann, K. Lehnertz, P. David, and C. E. Elger, Phys. D (Amsterdam) 144(3–4), 358 (2000).ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    A. E. Hramov, A. A. Koronovskii, V. I. Ponomarenko, and M. D. Prokhorov, Phys. Rev. E 75, 056 207 (2007).Google Scholar
  6. 6.
    A. N. Pavlov, O. V. Sosnovtseva, O. N. Pavlova, et al., Physiological Measurement 29, 945 (2008).ADSCrossRefGoogle Scholar
  7. 7.
    I. I. Mokhov and D. A. Smirnov, Izv. Akad. Nauk, Fiz. Atmos. Okeana 42, 650 (2006).Google Scholar
  8. 8.
    I. I. Blekhman, Synchronization of Dynamical Systems (Nauka, Moscow, 1971) [in Russian].Google Scholar
  9. 9.
    M. G. Rosenblum, A. S. Pikovsky, J. Kurths, et al., Neuroinformatics (eds. Moss F. and Gielen S.), Handbook of Biological Physics (Elsevier Science, New York, 2000) 4, 279.Google Scholar
  10. 10.
    B. Kralemann, L. Cimponeriu, M. Rosenblum, et al., Phys. Rev. E 77, 066 205 (2008).MathSciNetCrossRefGoogle Scholar
  11. 11.
    D. A. Smirnov, E. V. Sidak, and B. P. Bezruchko, Izv. vuzov. Prikladnaya nelineinaya dinamika 16(2), (2008).Google Scholar
  12. 12.
    B. Schelter, M. Winterhalder, J. Timmer, and M. Peifer, Phys. Lett. A 366, 382 (2007).ADSCrossRefGoogle Scholar
  13. 13.
    A. A. Borovkov, Mathematical Statistics (Fizmatlit, Moscow, 2007) [in Russian].zbMATHGoogle Scholar
  14. 14.
    G. Box and J. Jenkins, Time Series Analysis. Forecasting and Control (Freeman, San Francisco, 1970).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • D. A. Smirnov
    • 1
    Email author
  • E. V. Sidak
    • 1
  • B. P. Bezruchko
    • 1
  1. 1.Saratov Branch, Kotel’nikov Institute of Radio Engineering and ElectronicsRussian Academy of SciencesSaratovRussia

Personalised recommendations