We study the mean-field limit of a model of biological neuron networks based on the so-
called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a …

This article presents a biological neural network model driven by inhomogeneous Poisson
processes accounting for the intrinsic randomness of synapses. The main novelty is the …

We investigate a stochastic network composed of Integrate-and-Fire spiking neurons,
focusing on its mean-field asymptotic behavior. We consider an invariant probability …

We study the mean-field limit and stationary distributions of a pulse-coupled network
modeling the dynamics of a large neuronal assemblies. Our model takes into account …

Large ensembles of stochastically evolving interacting particles describe phenomena in
diverse fields including statistical physics, neuroscience, biology, and engineering. In such …

Neural network dynamics emerge from the interaction of spiking cells. One way to formulate
the problem is through a theoretical framework inspired by ideas coming from statistical …

In neuronal systems, inhibition contributes to stabilizing dynamics and regulating pattern
formation. Through developing mean-field theories of neuronal models, using complete …

The dynamics of neural networks is often characterized by collective behavior and quasi-
synchronous events, where a large fraction of neurons fire in short time intervals, separated …

In neuronal systems, inhibition contributes to stabilizing dynamics and regulating pattern
formation. Through developing mean-field theories of neuronal models, using complete …

We consider a spatially-extended model for a network of interacting FitzHugh-Nagumo
neurons without noise, and rigorously establish its mean-field limit towards a nonlocal …