6 papers
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…