Related papers: Relaxation and self-sustained oscillations in the …
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…
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…
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…
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…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient…
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…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
We study dynamics of a reverberating neural net by means of computer simulation. The net, which is composed of 9 leaky integrate-and-fire (LIF) neurons arranged in a square lattice, is fully connected with interneuronal communication delay…
The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. Numerical and analytical calculations show that the network relaxes into a stationary state of…
We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means…
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…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman, Perthame, and Salort (2010, 2014). In the first model, the structuring variable $s$ represents the time elapsed since its last…