2023 - T1B - WS2 - Networks of spiking neurons

Collection 2023 - T1B - WS2 - Networks of spiking neurons

Organizer(s) Galves, Antonio ; Löcherbach, Eva ; Pouzat, Christophe ; Vargas, Claudia D.

Date(s) 27/03/2023 - 31/03/2023

linked URL https://indico.math.cnrs.fr/event/7793/

11 20

Interacting Hawkes processes with multiplicative inhibition

By Céline Duval

We introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two features: inhibition, which acts as a multiplicative factor onto the intensity of the excitatory population and additive retroaction from the excitatory neurons onto the inhibitory ones. We give first a detailed analysis of the well-posedness of this interacting system as well as its dynamics in large population. The second aim of the paper is to give a rigorous analysis of the longtime behavior of the mean-field limit process. We provide also numerical evidence that inhibition and retroaction may be responsible for the emergence of limit cycles in such system. (j.w. with E. Luçon and C. Pouzat)

Information about the video

Date of recording 31/03/2023
Date of publication 31/03/2023
Institution IHP
Language English
Audience Researchers
Director(s) Alexandre Duplessis
Format MP4
Venue Amphitheater Hermite, IHP

Citation data

DOI 10.57987/IHP.2023.T1B.WS2.010
Cite this video Duval, Céline (31/03/2023). Interacting Hawkes processes with multiplicative inhibition. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T1B.WS2.010
URL https://dx.doi.org/10.57987/IHP.2023.T1B.WS2.010

Domain(s)

Probability

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