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math.AP2024
Noisy integrate-and-fire equation: continuation after blow-up
Xu'An Dou, Benoît Perthame, Delphine Salort +1
The integrate and fire equation is a classical model for neural assemblies which can exhibit finite time blow-up. A major open problem is to understand how to continue solutions af…
math.AP2024
Classical solutions of a mean field system for pulse-coupled oscillators: long time asymptotics versus blowup
José Antonio Carrillo, Xu'an Dou, Pierre Roux +1
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated…