Skip to main content
SpringerLink
Log in

Synchronization of relaxational self-oscillating systems: Synchronization in neural networks

  • Proceedings of the XVI A.P. Sukhorukov National Seminar “The Physics and Applications of Microwaves” (“Waves-2017”)
  • Published:
Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

A general problem of the synchronization and mutual synchronization of relaxational self-oscillating systems is formulated. A direct way of describing the synchronization of relaxational systems on the basis of Kronecker’s inequalities is proposed. The solution to the problem formulated by N. Wiener and A. Rosenbluth of forming a single rhythm in a system of coupled relaxational oscillators is described. Specific transient processes in the synchronization of relaxational systems are considered. Burst synchronization in neural networks and synchronization in distributed relaxational systems are also described.

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. Mazurov, M.E., Nonlinear synchronization and rhythmogenesis in electroexcitable heart systems, Doctoral (Phys.–Math.) Dissertation, Pushchino: Moscow State Univ. of Economics, Statistics, and Informatics, 2007.

    Google Scholar 

  2. Mazurov, M.E., Zh. Vychisl. Mat. Mat. Fiz., 1991, vol. 31, no. 11, p. 1619.

    MathSciNet  Google Scholar 

  3. Mazurov, M.E., Dokl. Math., 2012, vol. 85, no. 1, p. 149.

    Article  MathSciNet  Google Scholar 

  4. Mishchenko, U.F. and Rozov, N.Kh., Differentsial’nye uravneniya s malym parametrom i relaksatsionnye kolebaniya (Differential Equations with a Small Parameter and Relaxation Oscillations), Moscow: Nauka, 1975.

    MATH  Google Scholar 

  5. Pikovskii, A.A., Rozenblyum, M., and Kurts, Yu., Sinkhronizatsiya. Fundamental’noe nelineinoe yavlenie (Synchronization. A Fundamental Nonlinear Phenomenon), Moscow: Tekhnosfera, 2003.

    Google Scholar 

  6. Arnol’d, V.I., Izv. Akad. Nauk SSSR, Ser. Mat., 1961, vol. 25, no. 1, p. 21.

    MathSciNet  Google Scholar 

  7. Levitan, B.M., Pochti-periodicheskie funktsii (Almost Periodic Functions), Moscow: GITTL, 1953.

    MATH  Google Scholar 

  8. Hodgkin, A.L. and Huxley, A.F., J. Physiol., 1952, vol. 117, p. 500.

    Article  Google Scholar 

  9. Noble, D., J. Physiol., 1962, vol. 160, p. 317.

    Article  Google Scholar 

  10. Hindmarsh, J.L. and Rose, R.M., Nature, 1982, vol. 296, no. 5853, p. 162.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Plekhanov Russian University of Economics, Moscow, 117997, Russia

    M. E. Mazurov

Authors
  1. M. E. Mazurov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. E. Mazurov.

Additional information

Original Russian Text © M.E. Mazurov, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Seriya Fizicheskaya, 2018, Vol. 82, No. 1, pp. 83–87.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mazurov, M.E. Synchronization of relaxational self-oscillating systems: Synchronization in neural networks. Bull. Russ. Acad. Sci. Phys. 82, 73–77 (2018). https://doi.org/10.3103/S1062873818010161

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1062873818010161

Search

Navigation