Skip to main content
SpringerLink
Log in

Synchronization in Interacting Networks of Hodgkin–Huxley Neurons

  • Published:
Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

A mathematical model of a “network of networks” is developed. The model consists of a small input network and four large subnetworks that interact with one another via inhibitory couplings. This model is an attempt to model processes that occur in real neural networks in similar processing of input information. It is shown the indices of synchronization of subnetworks periodically change in time. Depending on the strength of the connection, the indices of synchronization of neurons of different subnetworks can change in both phase and antiphase.

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

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. Betzel, R.S., Gu, S., Medaglia, J.D., et al., Sci. Rep., 2016, vol. 6, 30770.

    Article  ADS  Google Scholar 

  2. Hermundstad, A.M., Bassett, D.S., Brown, K.S., et al., Proc. Natl. Acad. Sci. U. S. A., 2013, vol. 110, p. 6169.

    Article  ADS  Google Scholar 

  3. Hramov, A.E., Koronovskii, A.A., Makarov, V.A., et al., Wavelets in Neuroscience, Berlin: Springer, 2015.

    Book  Google Scholar 

  4. Atasoy, S., Donnelly, I., and Pearson, J., Nat. Commun., 2016, vol. 7, no. 1, p. 1.

    Article  Google Scholar 

  5. Thomas, J.P. and Gauthier, I., Nat. Rev. Neurosci., 2004, vol. 5, p. 291.

    Article  Google Scholar 

  6. Haenschel, C., Vernon, D.J., Dwivedi, P., et al., J. Neurosci., 2005, vol. 25.

  7. Campbell, I.G., Curr. Protoc. Neurosci., 2009, vol. 49, no. 1, p. 10.

    Article  Google Scholar 

  8. Buzsaki, G., Nat. Neurosci., 2004, vol. 7, no. 5, p. 446.

    Article  Google Scholar 

  9. Badarin, A.A., Skazkina, V.V., and Grubov, V.V., Proc. SPIE, 2020, vol. 11459, 114590D.

    Google Scholar 

  10. Buzsaki, G. and Draguhn, A., Science, 2004, vol. 304, p. 1926.

    Article  ADS  Google Scholar 

  11. Kurkin, S., et al., Eur. Phys. J. Plus, 2021, vol. 136, no. 5, p. 548.

    Article  ADS  Google Scholar 

  12. Frolov, N., Maksimenko, V., and Hramov, A., Chaos, 2020, vol. 30, no. 12, 121108.

    Article  ADS  MathSciNet  Google Scholar 

  13. Maksimenko, V.A., Frolov, N.S., Hramov, A.E., et al., Front. Behav. Neurosci., 2019, vol. 13, p. 220.

    Article  Google Scholar 

  14. Frolov, N.S., Maksimenko, V.A., Hramova, M.V., et al., Eur. Phys. J.: Spec. Top., 2019, vol. 228, no. 11, p. 2381.

  15. Valencia, M., Martinerie, J., Dupont, S., et al., Phys. Rev. E, 2008, vol. 77, no. 5, 050905.

    Article  ADS  Google Scholar 

  16. Andreev, A.V., Maksimenko, V.A., Pisarchik, A.N., et al., Chaos, Solitons Fractals, 2021, vol. 146, 110812.

    Article  Google Scholar 

  17. Klinshov, V., Shchapin, D., Yanchuk, S., and Nekorkin, V., Phys. Rev. Lett., 2015, vol. 114, no. 17, 178103.

    Article  ADS  Google Scholar 

  18. Andreev, A. and Maksimenko, V., Cybern. Phys., 2019, vol. 8, no. 4, p. 199.

    Article  Google Scholar 

  19. Klinshov, V.V., Teramae, J., Nekorkin, V.I., and Fukai, T., PloS One, 2014, vol. 9, no. 4, e94292.

    Article  ADS  Google Scholar 

  20. Ponomarenko, V.I., Kulminskiy, D.D., Andreev, A.V., and Prokhorov, M.D., Tech. Phys. Lett., 2021, vol. 47, no. 2, p. 162.

    Article  ADS  Google Scholar 

  21. Hodgkin, A.L. and Huxley, A.F., J. Physiol., 1952, vol. 117, no. 4, p. 500.

    Article  Google Scholar 

  22. Fitz, H.R., Biophys. J., 1961, vol. 1, no. 6, p. 445.

    Article  Google Scholar 

  23. Nagumo, J., Arimoto, S., and Yoshizawa, S., Proc. IRE, 1962, vol. 50, no. 10, p. 2061.

  24. Hindmarsh, J.L. and Rose, R.M., Proc. R. Soc. London, Ser. B, 1984, vol. 221, no. 1222, p. 87.

    Article  ADS  Google Scholar 

  25. Bullmore, E. and Sporns, O., Nat. Rev. Neurosci., 2009, vol. 10, no. 3, p. 186.

    Article  Google Scholar 

  26. van den Heuvel, M.P. and Pol, H.E.H., Eur. Neuropsychopharm., 2010, vol. 20, no. 8, p. 519.

    Article  Google Scholar 

  27. White, J.A., Rubinstein, J.T., and Kay, A.R., Trends Neurosci., 2000, vol. 23, no. 3, p. 131.

    Article  Google Scholar 

  28. Watts, D.J. and Strogatz, S.H., Nature, 1998, vol. 393, no. 6684, p. 440.

    Article  ADS  Google Scholar 

  29. Muldoon, S.F., Bridgeford, E.W., and Bassett, D.S., Sci. Rep., 2016, vol. 6, 22057.

    Article  ADS  Google Scholar 

  30. Bassett, D.S. and Bullmore, E., Neuroscience, 2006, vol. 12, p. 512.

    Google Scholar 

  31. Wang, Q., Perc, M., Duan, Z., and Chen, G., Phys. Rev. E, 2009, vol. 80, no. 2, 026206.

    Article  ADS  Google Scholar 

  32. Sausedo-Solorio, J.M. and Pisarchik, A.N., Eur. Phys. J.: Spec. Top., 2017, vol. 226, no. 9, p. 1911.

Download references

Funding

This work was supported by the RF Presidential Grant Council, project no. NSh-589.2022.1.2. V.V. Grubov thanks the Russian Foundation for Basic Research for their support as part of project no. 19-32-60033.

Author information

Authors and Affiliations

  1. Center for Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 236041, Kaliningrad, Russia

    A. V. Andreev, V. A. Maksimenko, A. A. Badarin, V. V. Grubov & A. E. Hramov

  2. Razumovsky State Medical University, 410012, Saratov, Russia

    V. V. Grubov

Authors
  1. A. V. Andreev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Maksimenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Badarin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. V. Grubov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. E. Hramov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Andreev.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by A. Khaitin

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Andreev, A.V., Maksimenko, V.A., Badarin, A.A. et al. Synchronization in Interacting Networks of Hodgkin–Huxley Neurons. Bull. Russ. Acad. Sci. Phys. 86, 221–225 (2022). https://doi.org/10.3103/S1062873822020058

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1062873822020058

Search

Navigation