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