2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Collection 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Organizer(s) Ditlevsen, Susanne ; Faugeras, Olivier ; Galves, Antonio ; Reynaud-Bouret, Patricia ; Salort, Delphine ; Shinomoto, Shigeru

Date(s) 31/01/2022 - 04/02/2022

linked URL https://indico.math.cnrs.fr/event/6532/

00:00:00 / 00:00:00

27 30

Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay

In neural networks, fast global oscillations was observed in [1] and are named gamma oscillation. Among other models aimed at understanding the self-sustained oscillations, the NNLIF model with synaptic delay and weakly firing inhibitory neurons was developed two decades ago [2]. Periodic solutions have been numerically observed in this model, but despite intensive study of this model in several researches, there was up-to-date no analytical result on this topic. In this talk, we propose to approximate formally these solutions by a Gaussian wave whose periodic movement is described by an associate difference-differential equation. We prove the existence of a periodic solution for the position in time of the centre of the Gaussian wave and we give a rigorous asymptotic result on these solutions when the connectivity parameter $b$ goes to $−∞$. Finally we provide heuristic and numerical evidence of the validity of our approximation.

Information about the video

Date of recording 04/02/2022
Date of publication 04/02/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.027
Cite this video Ikeda, Kota (04/02/2022). Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.027
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.027

Bibliography

1 - A. Draguhn, R. D. Traub, D. Schmitz and J.G.R. Jefferys / Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro. Nature, vol. 394 art. 6689 (1998), p.189–192.
2 - N. Brunel / Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of computational neuroscience, vol. 8 n°3 (2000), p.183–208.
K. Ikeda, P. Roux, D. Salort, and D. Smets / Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay, submitted.

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