Skip to main content
SpringerLink
Log in

Analysis of pulsed-signal transmission in a system of interacting neural oscillators with frequency-dependent connections

  • Published:
Radiophysics and Quantum Electronics Aims and scope

In this paper, we study the influence of the frequency-dependent connection on the signal transmission in a system of two interacting pulsed neural oscillators. The system is a model of two neurons with synaptic connection having the synaptic-plasticity feature, i.e., synaptic-parameter variation as a function of the frequency characteristics of the signal. It is shown that plastic connection can control the signal-transmission efficiency depending on the pulse-repetition rate and ensures stable synchronization modes of the pulse trains with different ratios between the frequencies of the output and input pulses. Analytical estimates for the parameter ranges corresponding to generation of the pulse response at the detector neuron depending on the pulse-repetition rate at the oscillator neuron were obtained.

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. A. Andronov, A.A. Vitt, and S.E.Khaikin, Theory of Oscillations [in Russian] (1959).

  2. M. I. Rabinovich and D. I.Trubetskov, Introduction into the Theory of Oscillations and Waves [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  3. N. V. Butenin, Yu. I.Neymark, and N. A. Fufayev, Introduction into the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  4. A.P. Kuznetsov, S.P. Kuznetsov, and N.M. Ryskin, Nonlinear Oscillations (Ser. Modern Theor. Oscil. Waves) [in Russian], Fizmatlit, Moscow (2006).

    Google Scholar 

  5. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization. A Universal Concept in Nonlinear Sciences, Cambridge Univ. Press, New York (2001).

    Book  MATH  Google Scholar 

  6. L. Glass and M.C. Mackey, From Clocks to Chaos. The Rythms of Life, Princeton Univ. Press, Princeton (1988).

    Google Scholar 

  7. N. Kopell and G.B. Ermentrout, Handbook of Dynamical Systems II: Toward Applications, Elsevier, Amsterdam (2002).

    Google Scholar 

  8. J. K. Lin, K. Pawelzik, U. Ernst, and T. J. Sejnowski, Network: Comput. Neural Syst., 9, 333 (1998).

    Article  MATH  Google Scholar 

  9. L. Glass and M.C. Mackey, J. Math. Biol., 7, 339 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  10. M.C. Mackey and L. Glass, Science, 197, 287 (1977).

    Article  ADS  Google Scholar 

  11. F. Zou and J. A. Nossek, IEEE Trans. Circuits Syst. I. Fundam. Theory Appl., 40, 166 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Kawato and R. Suzuki, J. Theor. Biol., 86, No. 3, 547 (1980).

    Article  MathSciNet  Google Scholar 

  13. A. Morrison, M. Diesmann, and W. Gerstner, Biol. Cybern., 98, 459 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  14. D.O. Hebb, The Organization of Behavior: a Neuropsychological Theory, Wiley, New York (1949).

    Google Scholar 

  15. M. V. Tsodyks and H. Markram, Proc. Nat. Acad. Sci. USA,bf 94, 719 (1997).

    Article  ADS  Google Scholar 

  16. H. Markram, Y. Wang, and M. Tsodyks, Proc. Nat. Acad. Sci. USA, 95, 5323 (1998).

    Article  ADS  Google Scholar 

  17. P. Dayan and L. F. Abbott, em Theoretical Neuroscience, MIT Press, Cambridge (2001).

    Google Scholar 

  18. A.P. Kuznetsov and V. I. Paksyutov, Izv. Vyssh. Uchebn. Zaved. Prikl. Nelin. Din., 11, No. 6, 48 (2003).

    Google Scholar 

  19. A.P. Kuznetsov and V. I. Paksyutov, Izv. Vyssh. Uchebn. Zaved. Prikl. Nelin. Din., 13, No. 4, 3 (2005).

    MATH  Google Scholar 

  20. A.P. Kuznetsov, V. I. Paksyutov, and Yu.P. Roman, Izv. Vyssh. Uchebn. Zaved. Prikl. Nelin. Din., 15, No. 4, 3 (2007).

    MATH  Google Scholar 

  21. M. Tsodyks, A. Uziel, and H. Markram, J. Neuroscience, 20, RC1 (2000).

    Google Scholar 

  22. M. Chiappalone, M. Bove, A. Vato, et al., Brain Res., 1093, 41 (2006).

    Article  Google Scholar 

  23. L. F. Abbott, J. A. Varela, K. Sen, and S. B. Nelson, Science, 275, 220 (1997).

    Article  Google Scholar 

  24. L. Lapicque, J. Physiol. Pathol. Gen., 9, 620 (1907).

    Google Scholar 

  25. H.C. Tuckwell, Introduction to Theoretical Neurobiology, Cambridge University Press, UK (1988).

    Book  Google Scholar 

  26. W. Gerstner and W. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity, Cambridge University Press (2002).

  27. E. M. Izhikevich, Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting, MIT Press (2007).

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 I. S. Prokin.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 54, No. 11, pp. 848–858, November 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prokin, I.S., Kazantsev, V.B. Analysis of pulsed-signal transmission in a system of interacting neural oscillators with frequency-dependent connections. Radiophys Quantum El 54, 763–772 (2012). https://doi.org/10.1007/s11141-012-9338-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-012-9338-4

Keywords

Search

Navigation