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Journal Articles by R. Veltz

O. Faugeras and R. Veltz Bifurcation theory can predict behaviours of large assemblies of neurons 2024 RIS, BibTex
R. Veltz A mean-field model of two-dimensional nonlinear integrate-and-fire neurons 2024 RIS, BibTex
S. Habiib and R. Veltz Theoretical / numerical study of modulated traveling pulses in inhibition stabilized networks 2024 RIS, BibTex
Y. E. Rodrigues, H. Marie, C. O’Donnell, and R. Veltz A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics Elife, 2023 URL, github, RIS, BibTex
R. Veltz Theoretical / numerical study of modulated traveling pulses in inhibition stabilized networks , Paris NFW 23, 2023
M. Chafaï, A. Delrocq, P. Inquimbert, L. Pidoux, K. Delanoe, M. Toft, F. Brau, E. Lingueglia, et al.
Dual contribution of ASIC1a channels in the spinal processing of pain information by deep projection neurons revealed by computational modeling PLOS Computational Biology (Publisher: Public Library of Science), 19(4), 2023 calcium channels functional electrical stimulation neuronal dendrites neurons pain potassium channels spinal cord transfection URL, DOI, RIS, BibTex
R. Veltz Theoretical / numerical study of modulated traveling pulses in inhibition stabilized networks , IHP Paris, 2023
O. Faugeras, A. Song, and R. Veltz Spatial and color hallucinations in a mathematical model of primary visual cortex CRAS, 2022 URL, DOI, arxiv, RIS, BibTex
R. Veltz Snaking of spatially localized visual hallucinations in a model of primary visual cortex 2021 RIS, BibTex
R. Veltz Invariant manifolds in singular perturbation problems for infinite dimensional dynamical systems 2021 RIS, BibTex
Q. Cormier, E. Tanré, and R. Veltz Hopf bifurcation in a Mean-Field model of spiking neurons 2020 Arxiv, RIS, BibTex
A. Drogoul and R. Veltz Exponential stability of the stationary distribution of a mean field of spiking neural network Journal of Differential Equations, 2020 URL, DOI, Hal-INRIA, RIS, BibTex
A. Dolcemascolo, A. Miazek, R. Veltz, F. Marino, and S. Barland Effective low-dimensional dynamics of a mean-field coupled network of slow-fast spiking lasers Phys. Rev. E, 101, 2020 URL, DOI, RIS, BibTex
D. Avitabile, M. Desroches, R. Veltz, and M. Wechselberger Local theory for spatio-temporal canards and delayed bifurcations SIAM Journal on Mathematical Analysis, 52(6), 2020 RIS, BibTex
Q. Cormier, E. Tanré, and R. Veltz Long time behavior of a mean-field model of interacting neurons Stochastic Processes and their Applications, 2019 mathematics - probability URL, DOI, Arxiv, RIS, BibTex
B. Aymard, F. Campillo, and R. Veltz Mean-field limit of interacting 2D nonlinear stochastic spiking neurons arXiv e-prints, 2019 mathematics - numerical analysis Arxiv, RIS, BibTex
N. Fournier, E. Tanré, and R. Veltz On a toy network of neurons interacting through their dendrites Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2019 URL, Arxiv, RIS, BibTex
A. Song, O. Faugeras, and R. Veltz A neural field model for color perception unifying assimilation and contrast PLOS Computational Biology, 2019 URL, RIS, BibTex
T. Górski, R. Veltz, M. Galtier, H. Fragnaud, J. S. Goldman, B. Teleńczuk, and A. Destexhe Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity Journal of Computational Neuroscience, 45(3), 2018 URL, DOI, RIS, BibTex
A. Dolcemascolo, B. Garbin, B. Peyce, R. Veltz, and S. Barland Resonator neuron and triggering multipulse excitability in laser with injected signal Phys. Rev. E, 98, 2018 URL, DOI, RIS, BibTex
A. Drogoul and R. Veltz Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(2), 2017 URL, DOI, RIS, BibTex
R. Veltz and T. J. Sejnowski Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling Neural Computation, 27(12), 2477-2509, 2015 oscillation gamma band theta band URL, DOI, PDF, RIS, BibTex
R. Veltz A new twist for the simulation of hybrid systems using the true jump method arXiv [math], 2015 mathematics - numerical analysis URL, RIS, BibTex
R. Veltz and O. Faugeras ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations SIAM Journal on Mathematical Analysis, 47(2), 2015 URL, DOI, RIS, BibTex
R. Veltz, P. Chossat, and O. Faugeras On the Effects on Cortical Spontaneous Activity of the Symmetries of the Network of Pinwheels in Visual Area V1 The Journal of Mathematical Neuroscience (JMN), 5(1), 2015 visual hallucinations invariant torus poincaré–hopf URL, DOI, RIS, BibTex
J. Rankin, E. Tlapale, R. Veltz, O. Faugeras, and P. Kornprobst Bifurcation analysis applied to a model of motion integration with a multistable stimulus Journal of computational neuroscience, 34(1), 2013 RIS, BibTex
R. Veltz and O. Faugeras A center manifold result for delayed neural fields equations SIAM Journal on Mathematical Analysis, 45(3), 2013 RIS, BibTex
J. M. Cortes, M. Desroches, S. Rodrigues, R. Veltz, M. A. Munoz, and T. J. Sejnowski Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics Proceedings of the National Academy of Sciences, 110(41), 2013 URL, RIS, BibTex
R. Veltz Interplay between synaptic delays and propagation delays in neural field equations SIAM Journal on Applied Dynamical Systems, 12(3), 2013 URL, RIS, BibTex
R. Veltz and O. Faugeras Stability of the stationary solutions of neural field equations with propagation delays The Journal of Mathematical Neuroscience (JMN), 1(1), 2011 URL, RIS, BibTex
R. Veltz An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays Comptes Rendus Mathematique, 349(13), 2011 URL, PDF, RIS, BibTex
R. Veltz and O. Faugeras Local/global analysis of the stationary solutions of some neural field equations SIAM Journal on Applied Dynamical Systems, 9(3), 2010 RIS, BibTex
R. Veltz and O. Faugeras Illusions in the ring model of visual orientation selectivity arXiv preprint arXiv:1007.2493, 2010 URL, RIS, BibTex
O. Faugeras, R. Veltz, and F. Grimbert Persistent neural states: stationary localized activity patterns in nonlinear continuous n-population, q-dimensional neural networks Neural computation, 21(1), 2009 URL, PDF, RIS, BibTex

Conference Papers

R. Veltz Some results concerning a mean field of a network of 2d spiking neurons , Topics on Neuroscience, Collective Migration and Parameter Estimation, Oxford, 2023
R. Veltz Study of a mean field of a network of 2d spiking neurons , One world dynamics, 2023
R. Veltz Theoritical study of a mean-field model of two-dimensional nonlinear integrate-and-fire neurons , ANR Chamane, 2023
R. Veltz Towards calculating bifurcations for networks of AdEx mean-field models with delays , Seminar A. Destexhe, 2023
R. Veltz A Showcase of the New Functionalities of BifurcationKit.jl , SIAM CSE23, Invited talk, 2023
R. Veltz Some recent results on a mean field of a network of 2d spiking neurons , Mathematical modeling and statistical analysis in neuroscience, 2022
R. Veltz Présentation de BifurcationKit , Journée Julia (CNRS), 2022
O. D. Faugeras, A. Song, and R. Veltz Spatial and color hallucinations in a mathematical model of primary visual cortex , 2021
R. Veltz BifurcationKit.jl: bifurcation analysis of large scale systems , JuliaCon21 invited talk., 2021
R. Veltz Some recent results on a mean field of a network of spiking neurons , LJAD, invited., 2021
R. Veltz Café calcul - Julia , Invited by Pierre Navaro, 2021
R. Veltz Automatic numerical bifurcation analysis using BifurcationKit , SIAM DS21, Invited talk, 2021
R. Veltz Mean field Models of noisy spiking neurons and BifurcationKit , Invited talk, University of Cologne, 2021
R. Veltz Automatic numerical bifurcation analysis with applications to neurosciences using BifurcationKit , SIAM CSE21, Invited talk, 2021
R. Veltz Mean field Models of noisy spiking neurons , Colloqium MAP5, Invited talk, 2021
R. Veltz Mean field study of stochastic spiking neural networks , CMS Winter Meeting, Invited talk, 2020
R. Veltz Analysis of a mean field of 2d spiking neurons, theory and numerics , International Meeting UK-France Programme, Royal Society, 2019
R. Veltz Models of neurons interacting through nonlinear dendritic compartments , Seminaire LJAD, 2018
R. Veltz On a toy network of neurons interacting through nonlinear dendritic compartments , jmgambaudo60, invited talk, 2018
R. Veltz On a toy network of neurons interacting through nonlinear dendritic compartments , ICMNS 2018, invited talk., 2018
R. Veltz On a toy network of neurons interacting through nonlinear dendritic compartments , Mean-field approaches to the dynamics of neuronal networks, EITN, 2018
R. Veltz Invariants manifolds in mathematical neurosciences , Winter School, Toulouse., 2017
R. Veltz On a toy network of neurons interacting through nonlinear dendritic compartments , Random Structures on the Brain, Lorentz Center in Leiden, The Netherlands, 2017
R. Veltz Hopf bifurcation in the mean field of a stochastic spiking neural networks , EITN - Paris, 2017
R. Veltz Oscillatory dynamics in a stochastic spiking neural network , BANFF: Brain Dynamics and Statistics, Alberta Canada, 2017
R. Veltz Study of a mean field model stemming from a neural network , Gdr NonLocal, Toulouse, 2017
R. Veltz Some applications of hybrid systems in neurosciences , University of Bristol, 2016
R. Veltz How somatic spikes are influenced by nonlinear active dendrites , ICMNS, plenary talk., 2015
R. Veltz On the effects of the pinwheel network symmetries on cortical response , NicePhysicsDays (Nice), 2015
R. Veltz On the effects of the pinwheel network symmetries on cortical response , Geometrical Models in Vision, IHP, PARIS, 2014
R. Veltz Dynamics induced by long-range connections in the primary visual cortex , AIMS Conference (Madrid), 2014
R. Veltz Two examples of temporal rhythms generated by neural mass/field equations , Centre for Math. Medicine and Biology, University of Nottingham, 2013
R. Veltz Invariant tori coming from the interplay between synaptic delays and propagation delays , CNS Paris, 2013
R. Veltz Interplay between synaptic delays and propagation delays in neural fields equations , Mathemacs Meeting, 2013
R. Veltz Study of a particular working regime for a simple model of V1 , GDR Vision (Marseille), 2011
M. Clerc, R. Veltz, D. Guiraud, J. L. Divoux, and others The 3d potential induced by functional electrical stimulation with multi-contact cuff electrodes: simulation and validation International Functional Electrical Stimulation Society Conference, 2008 RIS, BibTex

Theses

R. Veltz Nonlinear analysis methods in neural field models 2011 neuronal illusion hypercolumn neural fields propagation delays center manifold bifurcation champs neuronaux retard de propagation variete centrale hypercolonne illusion neuronale URL, RIS, BibTex
R. Veltz Nonlinear analysis methods in neural field models 2011 URL, PDF, RIS, BibTex
R. Veltz Nonlinear analysis methods in neural field models 2011 URL, thesis.pdf, RIS, BibTex

Software

R. Veltz BifurcationKit.jl Inria Sophia-Antipolis, 2020 pseudo-arclength-continuation periodic-orbits floquet gpu bifurcation-diagram deflation newton-krylov URL, RIS, BibTex
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