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9 papers · 1 filter
Strongly nonlinear age structured equation,time-elapsed model and large delays
Benoît Perthame, Delphine Salort, Clément Rieutord
The time-elapsed model for neural networks is a nonlinear age structured equationwhere the renewal term describes the network activity and influences the dischargerate, possibly wi…
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…
Incompressible limit of porous media equation with chemotaxis and growth
Qingyou He, Hai-Liang Li, Benoît Perthame
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living…
An infinite-times renewal equation
Xu'An Dou, Benoît Perthame, Chenjiayue Qi +2
In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the…
A multiple time renewal equation for neural assemblies with elapsed time model
Nicolás Torres, Benoît Perthame, Delphine Salort
We introduce and study an extension of the classical elapsed time equation in the context of neuron populations that are described by the elapsed time since the last discharge, i.e…
An elapsed time model for strongly coupled inhibitory and excitatory neural networks
Maria Caceres, Benoît Perthame, Delphine Salort +1
The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that desc…