Publications (38)
Large deviations for randomly connected neural networks: I. Spatially extended systems
Tanguy Cabana, Jonathan Touboul
Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
Jonathan Touboul
Spatially extended networks with singular multi-scale connectivity patterns
Jonathan Touboul
Absorption properties of stochastic equations with Hölder diffusion coefficients
Jonathan Touboul, Gilles Wainrib
Can power-law scaling and neuronal avalanches arise from stochastic dynamics?
Jonathan Touboul, Alain Destexhe
Finite-size and correlation-induced effects in Mean-field Dynamics
Jonathan Touboul, G. Bard Ermentrout
Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions
Jonathan Touboul
The heterogeneous gas with singular interaction: Generalized circular law and heterogeneous renormalized energy
Luis Carlos Garcia del Molino, Khashayar Pakdaman, Jonathan Touboul
Noise-induced behaviors in neural mean field dynamics
Jonathan Touboul, Geoffroy Hermann, Olivier Faugeras
Stochastic firing rate models
Jonathan Touboul, Bard Ermentrout, Olivier Faugeras +1
Mean Field description of and propagation of chaos in recurrent multipopulation networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
Javier Baladron, Diego Fasoli, Olivier Faugeras +1
Sensitivity to the cutoff value in the quadratic adaptive integrate-and-fire model
Jonathan Touboul
Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain
Jonathan Touboul
Complex oscillations in the delayed Fitzhugh-Nagumo equation
Maciej Krupa, Jonathan Touboul
A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs
Olivier Faugeras, Jonathan Touboul, Bruno Cessac
Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks
Tanguy Cabana, Jonathan Touboul
The real Ginibre ensemble with $k = O(n)$ real eigenvalues
Luis Carlos GarcÃa del Molino, Khashayar Pakdaman, Jonathan Touboul +1
Propagation of chaos in neural fields
Jonathan Touboul
Power-law statistics and universal scaling in the absence of criticality
Jonathan Touboul, Alain Destexhe
The hipster effect: When anticonformists all look the same
Jonathan Touboul
Large deviations for randomly connected neural networks: II. State-dependent interactions
Tanguy Cabana, Jonathan Touboul
Heterogeneous connections induce oscillations in large scale networks
Geoffroy Hermann, Jonathan Touboul
Codimension Two Bifurcations and Rythms in Neural Mass Models
Jonathan Touboul, Olivier Faugeras
Real eigenvalues of non-symmetric random matrices: Transitions and Universality
Luis Carlos GarcÃa del Molino, Khashayar Pakdaman, Jonathan Touboul
On a kinetic FitzHugh-Nagumo model of neuronal network
Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul
Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan Touboul +1
Synchronization in random balanced networks
Luis Carlos Garcidel Molino, Khashayar Pakdaman, Jonathan Touboul +1
Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales
Jonathan Touboul, Maciej Krupa, Mathieu Desroches
Topological and Dynamical Complexity of Random Neural Networks
Gilles Wainrib, Jonathan Touboul
Competition and boundary formation in heterogeneous media: Application to neuronal differentiation
Benoit Perthame, Cristobal Quiñinao, Jonathan Touboul
Macroscopic equations governing noisy spiking neuronal populations
Mathieu Galtier, Jonathan Touboul
On the Dynamic Interplay between Positive and Negative Affects
Jonathan Touboul, Alberto Romagnoni, Robert Schwartz
Limits and dynamics of randomly connected neuronal networks
Cristobal Quininao, Jonathan Touboul
Pulsatile localized dynamics in delayed neural-field equations in arbitrary dimension
Grégory Faye, Jonathan Touboul
Multi-Resolution Schauder Approach to Multidimensional Gauss-Markov Processes
Thibaud Taillefumier, Jonathan Touboul
Index Distribution of the Ginibre Ensemble
Romain Allez, Jonathan Touboul, Gilles Wainrib
On an explicit representation of the solution of linear stochastic partial differential equations with delays
Mathieu Galtier, Jonathan Touboul
A Markovian event-based framework for stochastic spiking neural networks
Jonathan Touboul, Olivier Faugeras