We prove new results on the asymptotic behavior of the nonlinear integrate-and-fire neuron
model. Among them, we give a criterion for the linearized stability or instability of equilibria …

We introduce and study an extension of the classical elapsed time equation in the context of
neuron populations that are described by the elapsed time since last discharge. In this …

There is a wide range of mathematical models that describe populations of large numbers of
neurons. In this article, we focus on nonlinear noisy leaky integrate and fire (NNLIF) models …

In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large
network is modeled as a diffusion-jump stochastic process whose jump takes place once the …

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 …

The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models
that describe the activity of neural networks. These models have been studied at a …

There is a wide range of mathematical models that describe populations of large numbers of
neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models …

Among other models aimed at understanding self-sustained oscillations in neural networks,
the NNLIF model with synaptic delay was developed almost twenty years ago to model fast …

We prove that a single-layer neural network trained with the online actor critic algorithm
converges in distribution to a random ordinary differential equation (ODE) as the number of …

The noisy leaky integrate-and-fire (NLIF) model describes the voltage configurations of
neuron networks with an interacting many-particles system at a microscopic level. When …