ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kirillov S. Y., Zlobin A. А., Klinshov V. V. Collective dynamics of a neural network of excitable and inhibitory populations: oscillations, tristability, chaos. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 6, pp. 757-775. DOI: 10.18500/0869-6632-003074, EDN: WJIYFW

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Collective dynamics of a neural network of excitable and inhibitory populations: oscillations, tristability, chaos

Kirillov Sergej Yu., Institute of Applied Physics of the Russian Academy of Sciences
Zlobin Alexander Алексеевич, Institute of Applied Physics of the Russian Academy of Sciences
Klinshov Vladimir Viktorovich, Lobachevsky State University of Nizhny Novgorod

The purpose of this work is to study the collective dynamics of a neural network consisting of excitatory and inhibitory populations.

The method of reducing the network dynamics to new generation neural mass models is used, and a bifurcation analysis of the model is carried out.

As a result the conditions and mechanisms for the emergence of various modes of network collective activity are described, including collective oscillations, multistability of various types, and chaotic collective dynamics.

Conclusion. The low-dimensional reduced model is an effective tool for studying the essential patterns of collective dynamics in large-scale neural networks. At the same time, the analysis also allows us to elicit more subtle effects, such as the emergence of synchrony clusters in the network and the shifting effect for the boundaries of the existence of dynamical modes.

The work was supported by the Government assignment to the Institute of Applied Physics (Project No. FFUF-2021-0011)
  1. Deco G, Jirsa VK, Robinson PA, Breakspear M, Friston K. The dynamic brain: From spiking neurons to neural masses and cortical fields. PLoS Comput. Biol. 2008;4(8):e1000092. DOI: 10.1371/journal.pcbi.1000092.
  2. Schwalger T, Deger M, Gerstner W. Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size. PLoS Comput. Biol. 2017;13(4):e1005507. DOI: 10.1371/journal.pcbi.1005507.
  3. Coombes S, Byrne A. Next generation neural mass models. In: Corinto F, Torcini A, editors. Nonlinear Dynamics in Computational Neuroscience. PoliTO Springer Series. Cham: Springer; 2019. P. 1–16. DOI: 10.1007/978-3-319-71048-8_1.
  4. Montbrio E, Pazo D, Roxin A. Macroscopic description for networks of spiking neurons. Phys. Rev. X. 2015;5(2):021028. DOI: 10.1103/PhysRevX.5.021028.
  5. Devalle F, Roxin A, Montbrio E. Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks. PLoS Comput. Biol. 2017;13(12): e1005881. DOI: 10.1371/journal.pcbi.1005881.
  6. Bi H, Segneri M, di Volo M, Torcini A. Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons. Phys. Rev. Research. 2020;2(1):013042. DOI: 10.1103/ PhysRevResearch.2.013042.
  7. Byrne A, Brookes MJ, Coombes S. A mean field model for movement induced changes in the beta rhythm. Journal of Computational Neuroscience. 2017;43(2):143–158. DOI: 10.1007/s10827- 017-0655-7.
  8. Schmidt H, Avitabile D, Montbrio E, Roxin A. Network mechanisms underlying the role of oscillations in cognitive tasks. PLoS Comput. Biol. 2018;14(9):e1006430. DOI: 10.1371/journal.pcbi. 1006430.
  9. Byrne A, Ross J, Nicks R, Coombes S. Mean-field models for EEG/MEG: From oscillations to waves. Brain Topography. 2022;35(1):36–53. DOI: 10.1007/s10548-021-00842-4.
  10. Gerster M, Taher H, Skoch A, Hlinka J, Guye M, Bartolomei F, Jirsa V, Zakharova A, Olmi S. Patient-specific network connectivity combined with a next generation neural mass model to test clinical hypothesis of seizure propagation. Frontiers in Systems Neuroscience. 2021;15:675272. DOI: 10.3389/fnsys.2021.675272.
  11. Lavanga M, Stumme J, Yalcinkaya BH, Fousek J, Jockwitz C, Sheheitli H, Bittner B, Hashemi M, Petkoski S, Caspers S, Jirsa V. The virtual aging brain: a model-driven explanation for cognitive decline in older subjects. bioRxiv 2022.02.17.480902. DOI: 10.1101/2022.02.17.480902.
  12. Wilson HR, Cowan JD. Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal. 1972;12(1):1–24. DOI: 10.1016/S0006-3495(72)86068-5.
  13. van Vreeswijk C, Sompolinsky H. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science. 1996;274(5293):1724–1726. DOI: 10.1126/science.274.5293.1724.
  14. Brunel N. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience. 2000;8(3):183–208. DOI: 10.1023/A:1008925309027.
  15. Maslennikov OV, Kasatkin DV, Rulkov NF, Nekorkin VI. Emergence of antiphase bursting in two populations of randomly spiking elements. Phys. Rev. E. 2013;88(4):042907. DOI: 10.1103/ PhysRevE.88.042907.
  16. Maslennikov OV, Nekorkin VI. Modular networks with delayed coupling: Synchronization and frequency control. Phys. Rev. E. 2014;90(1):012901. DOI: 10.1103/PhysRevE.90.012901.
  17. di Volo M, Torcini A. Transition from asynchronous to oscillatory dynamics in balanced spiking networks with instantaneous synapses. Phys. Rev. Lett. 2018;121(12):128301. DOI: 10.1103/ PhysRevLett.121.128301.
  18. Keeley S, Byrne A, Fenton A, Rinzel J. Firing rate models for gamma oscillations. Journal of Neurophysiology. 2019;121(6):2181–2190. DOI: 10.1152/jn.00741.2018.
  19. Segneri M, Bi H, Olmi S, Torcini A. Theta-nested gamma oscillations in next generation neural mass models. Frontiers in Computational Neuroscience. 2020;14:47. DOI: 10.3389/fncom. 2020.00047.
  20. Bi H, di Volo M, Torcini A. Asynchronous and coherent dynamics in balanced excitatory-inhibitory spiking networks. Frontiers in Systems Neuroscience. 2021;15:752261. DOI: 10.3389/fnsys. 2021.752261.
  21. Ceni A, Olmi S, Torcini A, Angulo-Garcia D. Cross frequency coupling in next generation inhibitory neural mass models. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2020;30(5):053121. DOI: 10.1063/1.5125216.
  22. Pyragas K, Fedaravicius AP, Pyragiene T. Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. Phys. Rev. E. 2021;104(1):014203. DOI: 10.1103/PhysRevE.104.014203.
  23. Reyner-Parra D, Huguet G. Phase-locking patterns underlying effective communication in exact firing rate models of neural networks. PLoS Comput. Biol. 2022;18(5):e1009342. DOI: 10.1371/ journal.pcbi.1009342.
  24. Klinshov VV, Smelov PS, Kirillov SY. Constructive role of shot noise in the collective dynamics of neural networks. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2023;33(6):061101. DOI: 10.1063/5.0147409.
  25. Feigenbaum MJ. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics. 1978;19(1):25–52. DOI: 10.1007/BF01020332.
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