Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Ezhov D. M., Ponomarenko V. I., Prokhorov M. D. Collective dynamics of ensembles of radio engineering models of FitzHugh–Nagumo oscillators coupled via a hub. Izvestiya of Saratov University. Physics , 2024, vol. 24, iss. 4, pp. 429-441. DOI: 10.18500/1817-3020-2024-24-4-429-441, EDN: NKTOCD

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.12.2024
Full text:
download
(downloads: 23)
Language: 
Russian
Heading: 
Radiophysics, electronics, acoustics
Article type: 
Article
UDC: 
537.86
DOI: 
10.18500/1817-3020-2024-24-4-429-441
EDN: 
NKTOCD

Collective dynamics of ensembles of radio engineering models of FitzHugh–Nagumo oscillators coupled via a hub

Autors: 
Ezhov Dmitry M., Saratov State University
Ponomarenko Vladimir Ivanovich, Saratov State University
Prokhorov Mikhail Dmitrievich, Saratov State University
Abstract: 

Background and Objectives: Since the neural networks of the brain have a multilayer structure, multilayer networks of interconnected model neurons are used to simulate and study their complex dynamics. A central role in establishing and maintaining effective communication between brain regions is played by so-called hubs, which are network nodes connected to many other network nodes. The object of study in this work is a network of model neurons coupled via a hub. We used FitzHugh–Nagumo neurooscillators as node elements of the network. Materials and Methods: The spiking activity of a network consisting of interconnected excitable FitzHugh–Nagumo analog generators was experimentally studied. The collective behavior of elements is considered first in a ring of FitzHugh–Nagumo generators connected by repulsive diffusive couplings, and then in a three-layer network consisting of two such rings connected via a common hub, which is also a FitzHugh–Nagumo generator. Since in a real experimental setup it is impossible to achieve complete identity of analog electronic generators, we numerically studied the effect of weak non-identity of FitzHugh–Nagumo oscillators ontheir collective dynamics and compared the results obtained with experimental ones. The synchronization of analog generators in a three-layer network was studied when the coupling coefficient between the generators of one of the rings and the coupling coefficient between the hub and generators in both rings were varied. Results: Diagrams of the average frequency of spiking activity of generators in each layer of the network have been constructed when the coupling coefficients between the generators of the second ring and between the hub and generators in both rings are varied. It has been shown that in a ring of FitzHugh–Nagumo generators in a radio physical experiment, various oscillatory regimes are observed at fixed values of the parameters of the excitable generators. These regimes differ in the frequency of spikes and the phase shift between the oscillations of various generators in the ring. The existence of switchings between these oscillatory regimes has been revealed. It has been shown that with repulsive couplings of FitzHugh–Nagumo generators inside the rings and repulsive interlayer couplings (connections with the hub), frequency synchronization of all network generators occurs. Conclusion: The obtained results can be used when solving problems of synchronization control in spiking neural networks.

Key words: 
FitzHugh–Nagumo oscillator
spiking neural network
hub
radio physical experiment
Acknowledgments: 
This study was supported by the Russian Science Foundation (project No. 23-12-00103, https://rscf.ru/en/project/23-12-00103/).
Reference: 
  1. Boccaletti S., Latora V., Moreno Y., Chavez M., Hwang D. Complex networks: Structure and dynamics. Phys. Rep., 2006, vol. 424, pp. 175–308. https://doi.org/10.1016/j.physrep.2005.10.009
  2. Osipov G. V., Kurths J., Zhou C. Synchronization in Oscillatory Networks. Berlin, Springer, 2007. 370 p.
  3. Maslennikov O. V., Nekorkin V. I. Adaptive dynamical networks. Phys.-Usp., 2017, vol. 60, pp. 694–704. https://doi.org/10.3367/UFNe.2016.10.037902
  4. Albert R., Barabási A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys., 2002, vol. 74, article no. 47. https://doi.org/10.1103/RevModPhys.74.47
  5. van den Heuvel M. P., Sporns O. Network hubs in the human brain. Trends in Cognitive Sciences, 2013, vol. 17, pp. 683–696. https://doi.org/10.1016/j.tics.2013.09.012
  6. Mears D., Pollard H. B. Network science and the human brain: Using graph theory to understand the brain and one of its hubs, the amygdala, in health and disease. J. Neurosci. Res., 2016, vol. 94, pp. 590–605. https://doi.org/10.1002/jnr.23705
  7. Hramov A. E., Frolov N. S., Maksimenko V. A., Kurkin S. A., Kazantsev V. B., Pisarchik A. N. Functional networks of the brain: From connectivity restoration to dynamic integration. Phys.-Usp., 2021, vol. 64, pp. 584–616. https://doi.org/10.3367/UFNe.2020.06.038807
  8. Shepherd G. M. The Synaptic Organization of the Brain. Oxford, Oxford University Press, 2004. 719 p.
  9. Muldoon S. F., Bassett D. S. Network and multilayer network approaches to understanding human brain dynamics. Philosophy of Science, 2016, vol. 83, pp. 710–720. https://doi.org/10.1086/687857
  10. De Domenico M. Multilayer modeling and analysis of human brain networks. Giga Science, 2017, vol. 6, iss. 5, article no. gix004. https://doi.org/10.1093/gigascience/gix004
  11. Vaiana M., Muldoon S. F. Multilayer brain networks. J. Nonlinear Sci., 2020, vol. 30, pp. 2147–2169. https://doi.org/10.1007/s00332-017-9436-8
  12. Majhi S., Perc M., Ghosh D. Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos, 2017, vol. 27, article no. 073109. https://doi.org/10.1063/1.4993836
  13. Bukh A. V., Strelkova G. I., Anishchenko V. S. Synchronization of chimera states in coupled networks of nonlinear chaotic oscillators. Russ. J. Nonlinear Dyn., 2018, vol. 14, no. 4, pp. 419–433. https://doi.org/10.20537/nd180401
  14. Sawicki J., Omelchenko I., Zakharova A., Schöll E. Synchronization scenarios of chimeras in multiplex networks. Eur. Phys. J. Spec. Top., 2018, vol. 227, pp. 1161–1171. https://doi.org/10.1140/epjst/e2018-800039-y
  15. Rybalova E. V., Bogatenko T. R., Bukh A. V., Vadivasova T. E. The role of coupling, noise and harmonic impact in oscillatory activity of an excitable FitzHugh–Nagumo oscillator network. Izvestiya of Saratov University. Physics, 2023, vol. 23, iss. 4, рр. 294–306 (in Russian). https://doi.org/10.18500/1817-3020-2023-23-4-294-306
  16. Rabinovich M. I., Varona P., Selverston A. I., Abarbanel H. D. I. Dynamical principles in neuroscience. Rev. Mod. Phys., 2006, vol. 78, article no. 1213. https://doi.org/10.1103/RevModPhys.78.1213
  17. Dmitrichev A. S., Кasatkin D. V., Klinshov V. V., Kirillov S. Yu., Maslennikov O. V., Shchapin D. S., Nekorkin V. I. Nonlinear dynamical models of neurons : A review. Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, no. 4, pp. 5–58. https://doi.org/10.18500/0869-6632-2018-26-4-5-58
  18. Quiroga R. Q., Panzeri S. Principles of Neural Coding. Boca Raton, CRC Press, 2013. 664 p.
  19. Lobov S. A., Chernyshov A. V., Krilova N. P., Shamshin M. O., Kazantsev V. B. Competitive learning in a spiking neural network: Towards an intelligent pattern classifier. Sensors, 2020, vol. 20, iss. 2, article no. 500. https://doi.org/10.3390/s20020500
  20. Yamazaki K., Vo-Ho V.-K., Bulsara D., Le N. Spiking neural networks and their applications: A review. Brain Sciences, 2022, vol. 12, iss. 7, article no. 863. https://doi.org/10.3390/brainsci12070863
  21. Dahlem M. A., Hiller G., Panchuk A., Schöll E. Dynamics of delay-coupled excitable neural systems. Int. J. Bifurcat. Chaos, 2009, vol. 19, pp. 745–753. https://doi.org/10.1142/S0218127409023111
  22. Shepelev I. A., Vadivasova T. E., Bukh A. V., Strelkova G. I., Anishchenko V. S. New type of chimera structures in a ring of bistable FitzHugh–Nagumo oscillators with nonlocal interaction. Phys. Lett. A, 2017, vol. 381, pp. 1398–1404. https://doi.org/10.1016/j.physleta.2017.02.034
  23. Shepelev I. A., Shamshin D. V., Strelkova G. I., Vadivasova T. E. Bifurcations of spatiotemporal structures in a medium of FitzHugh–Nagumo neurons with diffusive coupling. Chaos, Solitons and Fractals, 2017, vol. 104, pp. 153–160. https://doi.org/10.1016/j.chaos.2017.08.009
  24. Kulminskiy D. D., Ponomarenko V. I., Prokhorov M. D., Hramov A. E. Synchronization in ensembles of delaycoupled nonidentical neuronlike oscillators. Nonlinear Dyn., 2019, vol. 98, pp. 735–748. https://doi.org/10.1007/s11071-019-05224-x
  25. Plotnikov S. A., Fradkov A. L. On synchronization in heterogeneous FitzHugh–Nagumo networks. Chaos, Solitons and Fractals, 2019, vol. 121, pp. 85–91. https://doi.org/10.1016/j.chaos.2019.02.006
  26. Korneev I. A., Semenov V. V., Slepnev A. V., Vadivasova T. E. The impact of memristive coupling initial states on travelling waves in an ensemble of the FitzHugh–Nagumo oscillators. Chaos, Solitons and Fractals, 2021, vol. 147, article no. 110923. https://doi.org/10.1016/j.chaos.2021.110923
  27. Navrotskaya E. V., Kurbako A. V., Ponomarenko V. I., Prokhorov M. D. Synchronization of the ensemble of nonidentical FitzHugh–Nagumo oscillators with memristive couplings. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, no. 1, pp. 96–110. https://doi.org/10.18500/0869-6632-003085
  28. Kulminskiy D. D., Ponomarenko V. I., Sysoev I. V., Prokhorov M. D. New approach to the experimental study of large ensembles of radioengineering oscillators with complex couplings. Tech. Phys. Lett., 2020, vol. 46, no. 2, pp. 175–178. https://doi.org/10.1134/S1063785020020236
  29. Navrotskaya E. V., Kulminskiy D. D., Ponomarenko V. I., Prokhorov M. D. Estimation of impulse action parameters using a network of neuronlike oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, no. 4, pp. 495–512. https://doi.org/10.18500/0869-6632-2022-30-4-495-512
Received: 
25.06.2024
Accepted: 
20.09.2024
Published: 
25.12.2024
  • 77 reads