12 citations · 38 across the 13 of their papers we have counts for
14 papers
Existence of solutions to the voltage-conductance kinetic equation in a general conductivity regime
C Fonte Sanchez, S Mischler, D Salort
We establish the existence of a weak solution to the Voltage-Conductance kinetic equation for any conductivity parameter and any reasonable initial datum, and in particular without…
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…
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…
Bounds and long term convergence for the voltage-conductance kinetic system arising in neuroscience
Xu'An Dou, Benoît Perthame, Delphine Salort +1
The voltage-conductance equation determines the probability distribution of a stochastic process describing a fluctuation-driven neuronal network arising in the visual cortex. Its…
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…