59 citations · 186 across the 12 of their papers we have counts for
12 papers
Spatial and color hallucinations in a mathematical model of primary visual cortex
Olivier D. Faugeras, Anna Song, Romain Veltz
We study a simplified model of the representation of colors in the primate primary cortical visual area V1. The model is described by an initial value problem related to a Hammerst…
Hopf bifurcation in a Mean-Field model of spiking neurons
Quentin Cormier, Etienne Tanré, Romain Veltz
We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons. We give…
Local theory for spatio-temporal canards and delayed bifurcations
Daniele Avitabile, Mathieu Desroches, Romain Veltz +1
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale s…
Mean-field limit of interacting 2D nonlinear stochastic spiking neurons
Benjamin Aymard, Fabien Campillo, Romain Veltz
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Mont…
Resonator neuron and triggering multipulse excitability in laser with injected signal
Axel Dolcemascolo, Bruno Garbin, Bertand Peyce +2
Semiconductor lasers with coherent forcing are expected to behave similarly to simple neuron models in response to external perturbations, as long as the physics describing them ca…
A neural field model for color perception unifying assimilation and contrast
Anna Song, Olivier Faugeras, Romain Veltz
We address the question of color-space interactions in the brain, by proposing a neural field model of color perception with spatial context for the visual area V1 of the cortex. O…
Long time behavior of a mean-field model of interacting neurons
Quentin Cormier, Etienne Tanré, Romain Veltz
We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymp…
On a toy network of neurons interacting through their dendrites
Nicolas Fournier, Etienne Tanré, Romain Veltz
Consider a large number of neurons, each being connected to approximately other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending o…
A new twist for the simulation of hybrid systems using the true jump method
Romain Veltz
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell…
Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics
Jesus M Cortes, Mathieu Desroches, Serafim Rodrigues +3
Short-Term Synaptic Plasticity (STSP) strongly affects the neural dynamics of cortical networks. The Tsodyks and Markram (TM) model for STSP accurately accounts for a wide range of…
Illusions in the Ring Model of visual orientation selectivity
Romain Veltz, Olivier Faugeras
The Ring Model of orientation tuning is a dynamical model of a hypercolumn of visual area V1 in the human neocortex that has been designed to account for the experimentally observe…
Local/global analysis of the stationary solutions of some neural field equations
Romain Veltz, Olivier Faugeras
Neural or cortical fields are continuous assemblies of mesoscopic models, also called neural masses, of neural populations that are fundamental in the modeling of macroscopic parts…