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math.AP2022★ 3 cited
A simplified voltage-conductance kinetic model for interacting neurons and its asymptotic limit
José A. Carrillo, Xu'an Dou, Zhennan Zhou
The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its sol…
math.AP2022
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…
math.AP2022★ 2 cited
Exponential convergence to equilibrium for a two-speed model with variant drift fields via the resolvent estimate
Xu'an Dou, Zhennan Zhou
We study a two-speed model with variant drift fields, which generalizes the Goldstein-Taylor model but the two advection fields are not necessarily in proportion. Due to the lack o…