Journal Articles Discrete and Continuous Dynamical Systems - Series B Year : 2024

Concentration profiles in Fitzhugh-Nagumo neural networks: A Hopf-Cole approach

Abstract

In this paper we focus on a mean-field model for a spatially extended FitzHugh-Nagumo neural network. In the regime where strong and local interactions dominate, we quantify how the probability density of voltage concentrates into a Dirac distribution. Previous work investigating this question have provided relative bounds in integrability spaces. Using a Hopf-Cole framework, we derive precise $L^\infty$ estimates using subtle explicit sub-and super-solutions which prove, with rates of convergence, that the blow up profile is Gaussian.
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Dates and versions

hal-04407014 , version 1 (20-01-2024)

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Cite

Alain Blaustein, Emeric Bouin. Concentration profiles in Fitzhugh-Nagumo neural networks: A Hopf-Cole approach. Discrete and Continuous Dynamical Systems - Series B, In press, ⟨10.3934/dcdsb.2023165⟩. ⟨hal-04407014⟩
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