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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A kinetic description of the strong interaction regime in a FitzHug-Nagumo neural network.

## A kinetic description of the strong interaction regime in a FitzHug-Nagumo neural network.Add to your list(s) Download to your calendar using vCal - Alain Blaustein (Université Paul Sabatier Toulouse III)
- Tuesday 17 May 2022, 13:30-14:15
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022 We consider the solution to a non-linear mean-field equation modeling a FitzHug-Nagumo neural network. The non-linearity in this equation arises from the interaction between neurons. We suppose that these 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. The aim of this talk is to characterize the blow-up profile: we will prove that it is Gaussian. More precisely, we will compare several approaches: we will first present a weak convergence result, based on a analytic coupling method for Wasserstein distances, then we will strengthen this result by obtaining strong convergence estimates, using relative entropy methods and we will conclude by presenting a different approach, inspired from the analysis of Hamilton Jacobi equations, which enables to obtain L infinity convergence estimates. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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