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arXiv · 2203.14558

Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results

Alain Blaustein
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Abstract

We consider a mesoscopic model for a spatially extended FitzHugh-Nagumo neural network and prove that in the regime where short-range interactions dominate, the probability density of the potential throughout the network concentrates into a Dirac distribution whose center of mass solves the classical non-local reaction-diffusion FitzHugh-Nagumo system. In order to refine our comprehension of this regime, we focus on the blow-up profile of this concentration phenomenon. Our main purpose here consists in deriving two quantitative and strong convergence estimates proving that the profile is Gaussian: the first one in a L1 functional framework and the second in a weighted L2 functional setting. We develop original relative entropy techniques to prove the first result whereas our second result relies on propagation of regularity.

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Alain Blaustein. 2023-06-12. Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results. https://arxiv.org/abs/2203.14558

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