Skip to main content
SpringerLink
Log in

Estimation of the time delay of coupling between oscillators from time realizations of oscillation phases for different properties of phase dynamics

  • Dynamics Chaos in Radiophysics and Electronics
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract

The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood formalism can lead to false inferences of the value of the time delay in two typical situations: 1) nonlinear low-dimensional systems whose phases are well-determined but, as a result of significant amplitude fluctuations, the phase approximation is insufficient for describing the dynamics and 2) systems whose phases are defined not quite well because of too large amplitude fluctuations. A method for empirical diagnostics of problematic situations and its modification (coarse estimation) providing a low probability of false inferences in these situation are proposed. The efficiency of the diagnostic criterion and coarse estimation suggested is demonstrated on reference systems with different dynamic properties (linear stochastic oscillators, van der Pol oscillators, and Ressler and Lorenz chaotic systems).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. N. Malakhov, Fluctuations in Self-Oscillating Systems (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  2. L. A. Vainshtein and D. E. Vakman, Frequency Separation in Oscillation and Wave Theory (Nauka, Moscow, 1983) [in Russian].

    Google Scholar 

  3. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin, 1984).

    Book  MATH  Google Scholar 

  4. P. S. Landa, Self-Oscillations in Systems with a Finite Number of Degrees of Freedom (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  5. V. V. Matrosov and V. D. Shalfeev, Dynamic Chaos in Phase Systems (Nizhegorod. Gos. Univ., Nizhnii Novgorod, 2007) [in Russian].

    MATH  Google Scholar 

  6. A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2003; Tekhnosfera, Moscow, 2003).

    MATH  Google Scholar 

  7. M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 64, 045202 (2001).

    Article  Google Scholar 

  8. D. A. Smirnov, J. Commun. Tech. Electron. 51, 534 (2006).

    Article  Google Scholar 

  9. B. P. Bezruchko, V. I. Ponomarenko, M. D. Prokhorov, et al., Usp. Fiz. Nauk 178, 323 (2008).

    Article  Google Scholar 

  10. D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 79, 046204 (2009).

    Article  MathSciNet  Google Scholar 

  11. B. Kralemann, M. Rosenblum, and A. Pikovsky, Chaos 21, 025104 (2011).

    Article  MathSciNet  Google Scholar 

  12. B. Bezruchko, V. Ponomarenko, M. G. Rosenblum, and A. S. Pikovsky, Chaos 13, 179 (2003).

    Article  Google Scholar 

  13. I. I. Mokhov and D. A. Smirnov, Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana 42, 650 (2006).

    Google Scholar 

  14. J. Brea, D. F. Russell, and A. B. Neiman, Chaos 16, 026111 (2006).

    Article  Google Scholar 

  15. A. S. Karavaev, M. D. Prokhorov, V. I. Ponomarenko, et al., Chaos 19, 033112 (2009).

    Article  Google Scholar 

  16. P. Tass, D. Smirnov, A. Karavaev, et al., J. Neural Eng. 7, 016009 (2010).

    Article  Google Scholar 

  17. Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, Phys. Rev. Lett. 111, 024101 (2013).

    Article  Google Scholar 

  18. L. Cimponeriu, M. Rosenblum, and A. Pikovsky, Phys. Rev. E 70, 046213 (2004).

    Article  MathSciNet  Google Scholar 

  19. D. A. Smirnov, E. V. Sidak, and B. P. Bezruchko, Tech. Phys. Lett. 37, 30 (2011).

    Article  Google Scholar 

  20. E. V. Sidak, D. A. Smirnov, and B. P. Bezruchko, Tech. Phys. Lett. 40, 934 (2014).

    Article  Google Scholar 

  21. E. V. Sidak, D. A. Smirnov, and B. P. Bezruchko, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 58, 587 (2015).

    Google Scholar 

  22. A. Pikovsky, M. Rosenblum, and J. Kurths, Int. J. Bifurcation and Chaos 10, 2291 (2000).

    Google Scholar 

  23. V. S. Anishchenko, T. E. Vadivasova, G. A. Okrokvertskhov, and G. I. Strelkova, Usp. Fiz. Nauk 175, 163 (2005).

    Article  Google Scholar 

  24. D. A. Smirnov, E. V. Sidak, and B. P. Bezruchko, Eur. Phys. J. Spec. Top. 222, 2441 (2013).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kotel’nikov Institute of Radio Engineering and Electronics (Saratov Branch), Russian Academy of Sciences, Saratov, 410019, Russia

    E. V. Sidak, D. A. Smirnov & B. P. Bezruchko

  2. Chernyshevskii State University, Saratov, 410012, Russia

    E. V. Sidak, D. A. Smirnov & B. P. Bezruchko

Authors
  1. E. V. Sidak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Smirnov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. P. Bezruchko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. V. Sidak.

Additional information

Original Russian Text © E.V. Sidak, D.A. Smirnov, B.P. Bezruchko, 2017, published in Radiotekhnika i Elektronika, 2017, Vol. 62, No. 3, pp. 248–258.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sidak, E.V., Smirnov, D.A. & Bezruchko, B.P. Estimation of the time delay of coupling between oscillators from time realizations of oscillation phases for different properties of phase dynamics. J. Commun. Technol. Electron. 62, 241–250 (2017). https://doi.org/10.1134/S1064226917030196

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226917030196

Search

Navigation