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

13 30

Beyond Blow-Up for Nonlinear Noisy Leaky Integrate and Fire neuronal models: numerical approach to the "plateau" state

By Alejandro Ramos Lora

The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models that describe the activity of neural networks. These models have been studied at a microscopic level, using Stochastic Differential Equations, and at a mesoscopic/macroscopic level, through the mean field limits using Fokker-Planck type equations. To advance in the understanding of the NNLIF models, we have analyzed in depth the behaviour of the classical and physical solutions of the Stochastic Differential Equations and we compare it with what is already known about the Fokker-Planck equation, using a numerical study of their particle systems. This allows us to understand what happens in the neural network when an explosion occurs in finite time, which is one of the most important open problems about this kind of models. This allows us to go beyond the mesoscopic/macroscopic description. We answer one of the most important open questions about these models [1] : what happens after all the neurons in the network fire at the same time? We find that the neural network converges towards its unique steady state, if the system is weakly connected. Otherwise, its behaviour is more complex, tending towards a stationary state or a “plateau” distribution (membrane potentials are uniformly distributed between reset and threshold values). To our knowledge, these distributions have not been described before for these nonlinear models.

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.WS2.013
Cite this video Ramos Lora, Alejandro (02/02/2022). Beyond Blow-Up for Nonlinear Noisy Leaky Integrate and Fire neuronal models: numerical approach to the "plateau" state. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.013
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.013

Bibliography

1 - Cáceres, M. J. and Ramos-Lora, A. / An understanding of the physical solutions and the blowup phenomenon for Nonlinear Noisy Leaky Integrate and Fire neuronal models. Communications in Computational Physics, vol. 30 n°3 (2021) : p. 820-850.

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