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In this paper we focus on a spatially extended FitzHugh-Nagumo model withinteractions. In the regime where strong and local interactions dominate, wequantify how the probability density of neurons concentrates into a Diracdistribution. Previous work investigating this question have provided relativebounds in integrability spaces. Using a Hopf-Cole framework, we derive precise$L^\infty$ estimates using subtle explicit sub- and super- solutions whichprove, with rates of convergence, that the blow up profile is Gaussian.

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