Nov 16 – 19, 2021
Polytech Lille
Europe/Paris timezone

Concentration phenomena in a Fitzhug-Nagumo spatially extended neural network with noise

Nov 18, 2021, 11:15 AM
30m
Amphithéatre Migeon (Polytech Lille)

Amphithéatre Migeon

Polytech Lille

Contributed talk

Speaker

Alain Blaustein (Institut Mathématiques de Toulouse)

Description

We consider the solution to a non-linear mean-field equation modeling a FitzHug-Nagumo neural network (see [1], [2], [3]). The non-linearity in this equation arises from the interaction between neurons. We suppose that the interactions depend on the spatial location of neurons and we focus on the behavior of the solution in the regime where short-range interactions are dominant. The solution then converges to a Dirac mass (see [4]). The aim of this talk is to characterize the blow-up profile: we will prove that it is Gaussian. Then we present interesting consequences of this result both at the macroscopic and the mesoscopic level.

[1] J. Baladron, D. Fasoli, O. Faugeras and J. Touboul. Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons The Journal of Mathematical Neuroscience, 2(10), 2012.
[2] M. Bossy, O. Faugeras and D. Talay. Clarification and complement to ”mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons”, The Journal of Mathematical Neuroscience, 5(1), 2015.
[3] S. Mischler, C. Quininao and J. Touboul. ˜ — On a kinetic FitzHugh-Nagumo model of neuronal network, Comm. Math. Phys., 342(3):1001–1042, 2015.
[4] J. Crevat, G. Faye, F. Filbet — Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system.

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