Related papers: Asymptotic behaviour of neuron population models s…

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since…

We study the asymptotic stability of a two-dimensional mean-field equation, which takes the form of a nonlocal transport equation and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This…

In the context of neuroscience the elapsed-time model is an age-structured equation that describes the behavior of interconnected spiking neurons through the time since the last discharge, with many interesting dynamics depending on the…

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models, indicating how the time elapsed since the last discharge construct the probability density of…

The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the…

The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works…

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 the last discharge, i.e., the refractory period. In this extension we incorporate…

We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…

The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its solution structure has been only partially obtained in spite of…

Sensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the stimulus information contained in those responses. This information can in principle be preserved if…

We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…

Recent advances in experimental techniques have allowed the simultaneous recording of populations of hundreds of neurons, allowing more comprehensive investigation into the nature of the collective structure of population neural activity.…

In this article we present the modeling of bi-stability view problems described by the activity or firing rates of two interacting population of neurons. Starting from the study of a complex system, the sys-tem of stochastic differential…

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, without restriction on the connectivity parameter,…

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…

The time-elapsed model for neural networks is a nonlinear age structured equationwhere the renewal term describes the network activity and influences the dischargerate, possibly with a delay due to the length of connections.We solve a long…

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind…