Skip to main content
Springer Nature Link
Log in

Synchronization in the System of Synaptically Coupled Neural Oscillators with Frequency-Dependent Coupling

  • Published:
Radiophysics and Quantum Electronics Aims and scope

We study the influence of the frequency-dependent coupling on synchronization in a model system of the synaptically coupled neural oscillators is studied. The ranges of parameters for which the locking of the frequency of the driven (output) neural oscillator is observed are obtained. The phase characteristics of oscillations in the synchronization regime are studied. The phase mappings are numerically plotted to describe the above-mentioned characteristics and analytical estimates for these mappings are obtained for certain restrictions imposed on the frequency characteristics of the oscillators. The effect of the frequency-dependent variation in the coupling is shown to lead to a substantial change (narrowing) of the synchronization regions compared with the case of fixed synaptic coupling.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. E. M. Izhikevich and G. M. Edelman, Proc. Nat. Acad. Sci., 105, No. 9, 3593 (2008).

    Article  ADS  Google Scholar 

  2. V. B. Kazantsev, V. I. Nekorkin, D. V. Artyuhin, and M. G. Velarde, Phys. Rev. E, 63, No. 1, 1 (2000).

    Article  Google Scholar 

  3. Q. R. Quian, T. Kreuz, and P. Grassberger, Phys. Rev. E, 66, No. 4, 041904 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  4. V. I. Nekorkin, V. B. Kazantsev, and M. G. Velarde, Physica D, 151, No. 1, 1 (2001).

    Article  ADS  MATH  Google Scholar 

  5. M. Diesmann, M. O. Gewaltig, and A. Aertsen, Nature, 402, No. 6761, 529 (1999).

    Article  ADS  Google Scholar 

  6. E. M. Izhikevich, Dynamical Systems, MIT Press, Cambridge, Mass. (2007), Ch. 10, p. 443.

  7. E. Yu. Sitnikova, A. A. Koronovskii, and A. E. Khramov, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Din., 19, No. 6, 173 (2011).

  8. A. A. Koronovskii, and A. E. Khramov, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Din., 19, No. 4, 91 (2011).

    MATH  Google Scholar 

  9. A. A. Koronovskii, G. van Luijtelaar, A. A. Ovchinnikov, et al., Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Din., 19, No. 1, 86 (2011).

    MATH  Google Scholar 

  10. E. Ullner, A. Zaikin, J. García-Ojalvo, and J. Kurths, Phys. Rev. Lett., 91, No. 18, 180601 (2003).

    Article  ADS  Google Scholar 

  11. A. Neiman, A. Silchenko, V. Anishchenko, and L. Schimansky-Geier, Phys. Rev. E, 58, No. 6, 7118 (1998).

    Article  ADS  Google Scholar 

  12. T. Yanagita, T. Ichinomiya, and Y. Oyama, Phys. Rev. E, 72, No. 5, 056218 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  13. H. D. Abarbanel, M. I. Rabinovich, A. Selverston, et al., Physics—Uspekhi, 166, No. 4, 337 (1996).

    ADS  Google Scholar 

  14. E. Izhikevich, Int. J. Bifur. Chaos, 10, No. 6, 1171 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  15. M. R. Guevara, L. Glass, M. C. Mackey, and A. Shrier, IEEE Trans. Syst., Man, Cybern., 13, No. 5, 790 (1983).

    Article  MATH  Google Scholar 

  16. X. Wang, in: Proc. 1992 IEEE Int. Joint Conf. Neural Networks, 1992, Vol. 3, p. 517.

  17. M. Steriade, D. McCormick, and T. Sejnowski, Science, 262, 679 (1993).

    Article  ADS  Google Scholar 

  18. W. Klimesch, Int. J. Psychophysiol., 24, Nos. 1–2, 61 (1996).

    Article  Google Scholar 

  19. E. Rodriguez, N. George, and J. Lachaux, Nature, 397, 430 (1999).

    Article  ADS  Google Scholar 

  20. R. D. Srinivasan, P. Russell, G. M. Edelman, and G. Tononi, J. Neurosci., 19, No. 13, 5435 (1999).

    Google Scholar 

  21. P. Fries, P. R. Roelfsema, A. K. Engel, et al., Proc. Nat. Acad. Sci., 94, No. 23, 12699 (1997).

    Article  ADS  Google Scholar 

  22. P. Fries, Trends Cognitive Sci., 9, No. 10, 474 (2005).

    Article  Google Scholar 

  23. J. Fell and N. Axmacher, Nature Rev. Neurosci., 12, No. 2, 105 (2011).

    Article  Google Scholar 

  24. A. Schnitzler and J. Gross, Nature Rev. Neurosci., 6, No. 4, 285 (2005).

    Article  Google Scholar 

  25. I. S. Prokin and V. B. Kazantsev, Radiophys. Quantum Electron., 54, No. 11, 763 (2011).

    Article  ADS  Google Scholar 

  26. M. L. Lapicque, J. Physiol. Patholog. Gen., 9, 620 (1907).

    Google Scholar 

  27. M. Tsodyks, A. Uziel, and H. Markram, J. Neurosci., 20, No. 1, RC50 (2000).

    Google Scholar 

  28. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge Univ. Press, Cambridge (1996).

    Google Scholar 

  29. A. Balanov, N. Janson, D. Postnov, and O. Sosnovtseva, Synchronization: from Simple to Complex, Springer, New York (2010).

    Google Scholar 

  30. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences, Cambridge Univ. Press, Cambridge (2003).

    Google Scholar 

  31. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos, Wiley, New York (2002).

    MATH  Google Scholar 

  32. R. Mirollo and S. Strogatz, SIAM J. Appl. Math., 50, No. 6, 1645 (1990).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. N. I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    I. S. Prokin & V. B. Kazantsev

  2. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    I. S. Prokin & V. B. Kazantsev

Authors
  1. I. S. Prokin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. B. Kazantsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Kazantsev.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 57, No. 10, pp. 834–848, October 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prokin, I.S., Kazantsev, V.B. Synchronization in the System of Synaptically Coupled Neural Oscillators with Frequency-Dependent Coupling. Radiophys Quantum El 57, 745–758 (2015). https://doi.org/10.1007/s11141-015-9561-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-015-9561-x

Keywords

Search

Navigation