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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A kinetic description of the strong interaction re
gime in a FitzHug-Nagumo neural network. - Alain B
laustein (Université Paul Sabatier Toulouse III)
DTSTART;TZID=Europe/London:20220517T133000
DTEND;TZID=Europe/London:20220517T141500
UID:TALK174437AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/174437
DESCRIPTION:We consider the solution to a non-linear mean-fiel
d equation modeling a FitzHug-Nagumo neural networ
k. The non-linearity in this equation arises from
the interaction between neurons. We suppose that t
hese interactions depend on the spatial location o
f neurons and we focus on the behavior of the solu
tion in the regime where short-range interactions
are dominant. The solution then converges to a Dir
ac mass. The aim of this talk is to characterize t
he blow-up profile: we will prove that it is Gauss
ian. More precisely\, we will compare several appr
oaches: \; we will first present a weak conver
gence result\, based on a analytic coupling method
for Wasserstein distances\, then we will strength
en this result by obtaining strong convergence est
imates\, using relative entropy methods and we wil
l conclude by presenting a different approach\, in
spired from the analysis of Hamilton Jacobi equati
ons\, which enables to obtain L infinity convergen
ce estimates.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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