activity
20182023
most citedNoise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields

10 citations · 19 across the 6 of their papers we have counts for

collaborators

6 papers

math.AP2023

Well-posedness and stability of a stochastic neural field in the form of a partial differential equation

José Antonio Carrillo, Pierre Roux, Susanne Solem

A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal trav…

math.AP2022★ 10 cited

Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields

José A. Carrillo, Pierre Roux, Susanne Solem

The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential…

math.AP2021

Adaptation to DNA damage, an asymptotic approach for a cooperative non-local system

Alexis Leculier, Pierre Roux

Following previous works about integro-differential equations of parabolic type modelling the Darwinian evolution of a population, we study a two-population system in the cooperati…

math.AP2020

A hyperbolic-elliptic-parabolic PDE model describing chemotactic E. coli colonies

Danielle Hilhorst, Pierre Roux

We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three par…

math.AP2020★ 5 cited

Mathematical treatment of PDE model describing chemotactic E. coli colonies

Rafał Celiński, Danielle Hilhorst, Grzegorz Karch +2

We consider an initial-boundary value problem describing the formation of colony patterns of bacteria Escherichia coli. This model consists of reaction-diffusion equations coupled…

math.AP2018★ 4 cited

Global-in-time classical solutions and qualitative properties for the NNLIF neuron model with synaptic delay

María J. Cáceres, Pierre Roux, Delphine Salort +1

The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a s…