Global solvability of a networked integrate-and-fire model of McKean–Vlasov type
We here investigate the well-posedness of a networked integrate-and-fire model describing
an infinite population of neurons which interact with one another through their common …
an infinite population of neurons which interact with one another through their common …
Mean‐field limit of non‐exchangeable systems
This paper deals with the derivation of the mean‐field limit for multi‐agent systems on a
large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent …
large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent …
[HTML][HTML] Particle systems with a singular mean-field self-excitation. Application to neuronal networks
We discuss the construction and approximation of solutions to a nonlinear McKean–Vlasov
equation driven by a singular self-excitatory interaction of the mean-field type. Such an …
equation driven by a singular self-excitatory interaction of the mean-field type. Such an …
A McKean–Vlasov equation with positive feedback and blow-ups
We study a McKean–Vlasov equation arising from a mean-field model of a particle system
with positive feedback. As particles hit a barrier, they cause the other particles to jump in the …
with positive feedback. As particles hit a barrier, they cause the other particles to jump in the …
Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness
We consider the supercooled Stefan problem, which captures the freezing of a supercooled
liquid, in one space dimension. A probabilistic reformulation of the problem allows us to …
liquid, in one space dimension. A probabilistic reformulation of the problem allows us to …
Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
JA Carrillo, B Perthame, D Salort, D Smets - Nonlinearity, 2015 - iopscience.iop.org
Abstract The Noisy Integrate-and-Fire equation is a standard non-linear Fokker–Planck
equation used to describe the activity of a homogeneous neural network characterized by its …
equation used to describe the activity of a homogeneous neural network characterized by its …
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration
In this work, we are concerned with the Fokker-Planck equations associated with the
Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump …
Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump …
Asymptotic behaviour of neuron population models structured by elapsed-time
We study two population models describing the dynamics of interacting neurons, initially
proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J …
proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J …
At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov problem
We extend a model of positive feedback and contagion in large mean-field systems, by
introducing a common source of noise driven by Brownian motion. Although the driving …
introducing a common source of noise driven by Brownian motion. Although the driving …
Oscillations in a Fully Connected Network of Leaky Integrate-and-Fire Neurons with a Poisson Spiking Mechanism
G Dumont, J Henry, CO Tarniceriu - Journal of Nonlinear Science, 2024 - Springer
Understanding the mechanisms that lead to oscillatory activity in the brain is an ongoing
challenge in computational neuroscience. Here, we address this issue by considering a …
challenge in computational neuroscience. Here, we address this issue by considering a …