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

15 30

Spontaneous oscillations in a pure excitatory mean field networks of neurons

By Etienne Tanré

We consider a model of network of interacting neurons based on jump processes. Briefly, the membrane potential $V^i_t$ of each individual neuron evolves according to a one-dimensional ODE. Neuron i spikes at rate which only depends on its membrane potential, $f(V^i_t)$. After a spike, $V^i_t$ is reset to a fixed value $V^{rest}$. Simultaneously, the membrane potentials of any (post-synaptic) neuron $j$ connected to the neuron $i$ receives a $kick$ of value $J^{i,j}$.

We study the limit (mean-field) equation obtained where the number of neurons goes to infinity. In this talk, we describe the long time behaviour of the solution. Depending on the intensity of the interactions, we observe convergence of the distribution to a unique invariant measure (small interactions) or we characterize the occurrence of spontaneous oscillations for interactions in the neighbourhood of critical values.

The talk is based on joint works with Quentin Cormier (Princeton) and Romain Veltz (Inria)

Information about the video

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

Citation data

DOI 10.57987/IHP.2022.T1.WS2.015
Cite this video Tanré, Etienne (02/02/2022). Spontaneous oscillations in a pure excitatory mean field networks of neurons. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.015
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.015

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