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hal-00857699v1  Journal articles
Jesus Cortes, Mathieu Desroches, Serafim Rodrigues, Romain Veltz, Miguel Muñoz et al.  Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics
Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2013
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hal-02925025v2  Journal articles
Quentin Cormier, Etienne Tanré, Romain Veltz. Hopf bifurcation in a Mean-Field model of spiking neurons
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2021, 26, ⟨10.1214/21-EJP688⟩
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hal-01290264v2  Journal articles
Audric Drogoul, Romain Veltz. Exponential stability of the stationary distribution of a mean field of spiking neural network
Journal of Differential Equations, Elsevier, 2018, ⟨10.1016/j.jde.2020.08.001⟩
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hal-00331618v1  Conference papers
Romain Veltz, Olivier Faugeras. Bifurcations in neural masses
Deuxième conférence française de Neurosciences Computationnelles, "Neurocomp08", Oct 2008, Marseille, France
hal-01412154v1  Journal articles
Audric Drogoul, Romain Veltz. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics
Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2017, ⟨10.1063/1.4976510⟩
hal-02412921v1  Journal articles
Daniele Avitabile, Mathieu Desroches, Romain Veltz, Martin Wechselberger. Local theory for spatio-temporal canards and delayed bifurcations
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), pp.5703-5747. ⟨10.1137/19M1306610⟩
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hal-02071874v1  Software
Romain Veltz. PseudoArcLengthContinuation.jl
2019, ⟨swh:1:dir:9f85c8f51850028a9fbc03463c74de29a2d24c6c;origin=https://hal.archives-ouvertes.fr/hal-02071874;visit=swh:1:snp:96df3cd8f41a04650ca4e93b2610f839c02d2899;anchor=swh:1:rev:60df0a6859f42cad7170a8560c768ff239190d3a;path=/⟩
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hal-02902346v1  Software
Romain Veltz. BifurcationKit.jl
2020, ⟨swh:1:dir:257669cd4bf202bc8393a4efa22bfe5f6f517b03;origin=https://hal.archives-ouvertes.fr/hal-02902346;visit=swh:1:snp:73c1c5e9525b1b9b09b8a79ca056057fcb26b8a9;anchor=swh:1:rev:31bea805201b64435aa28e4d036e156ab189c3d5;path=/⟩
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inria-00198808v3  Reports
Olivier Faugeras, Romain Veltz, François Grimbert. Persistent neural states: stationary localized activity patterns in nonlinear continuous $n$-population, $q$-dimensional neural networks
[Research Report] RR-6393, INRIA. 2007, pp.37
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hal-03388400v1  Preprints, Working Papers, ...
Olivier Faugeras, Anna Song, Romain Veltz. Spatial and color hallucinations in a mathematical model of primary visual cortex
2021
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hal-01652036v1  Poster communications
Pascal Helson, Etienne Tanré, Romain Veltz. A simple spiking neuron model based on stochastic STDP
International Conference on Mathematical Neuroscience, May 2017, Boulder, United States
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hal-01903857v3  Journal articles
Quentin Cormier, Etienne Tanré, Romain Veltz. Long time behavior of a mean-field model of interacting neurons
Stochastic Processes and their Applications, Elsevier, 2020, 130 (5), pp.2553-2593. ⟨10.1016/j.spa.2019.07.010⟩
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hal-01909354v1  Journal articles
Anna Song, Olivier Faugeras, Romain Veltz. A neural field model for color perception unifying assimilation and contrast
PLoS Computational Biology, Public Library of Science, 2019, 15 (6), ⟨10.1371/journal.pcbi.1007050⟩
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hal-01707663v2  Journal articles
Nicolas Fournier, Etienne Tanré, Romain Veltz. On a toy network of neurons interacting through their dendrites
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2020, 56 (2), pp.1041-1071. ⟨10.1214/19-AIHP993⟩
hal-00850382v1  Journal articles
Romain Veltz, Olivier Faugeras. A Center Manifold Result for Delayed Neural Fields Equations
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2013, 45 (3), pp.1527-1562. ⟨10.1137/110856162⟩
hal-00850391v1  Journal articles
Romain Veltz. Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations
SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2013, 12 (3), pp.1566-1612. ⟨10.1137/120889253⟩
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hal-01079055v3  Journal articles
Romain Veltz, Pascal Chossat, Olivier Faugeras. On the effects on cortical spontaneous activity of the symmetries of the network of pinwheels in visual area V1.
Journal of Mathematical Neuroscience, BioMed Central, 2015, ⟨10.1186/s13408-015-0023-8⟩
hal-00845727v1  Journal articles
Romain Veltz. An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays
Comptes Rendus. Mathématique, Académie des sciences (Paris), 2011, 349 (13-14), pp.749--752. ⟨10.1016/j.crma.2011.06.014⟩
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hal-00784425v1  Journal articles
Romain Veltz, Olivier Faugeras. Stability of the stationary solutions of neural field equations with propagation delays
Journal of Mathematical Neuroscience, BioMed Central, 2011, 1 (1), pp.1-28. ⟨10.1186/2190-8567-1-1⟩
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hal-00646387v2  Reports
James Rankin, Émilien Tlapale, Romain Veltz, Olivier Faugeras, Pierre Kornprobst. Bifurcation analysis applied to a model of motion integration with a multistable stimulus
[Research Report] RR-7822, INRIA. 2011, pp.39
hal-00712201v1  Journal articles
Romain Veltz, Olivier Faugeras. Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations
SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2010, 9 (3), pp.954-998. ⟨10.1137/090773611⟩
hal-00845733v1  Conference papers
Olivier Faugeras, Romain Veltz. Constraining the design and operation of neural field models from basic principles
Workshop on Spatio-temporal evolution equations and neural fields, 2011, Marseille, France
hal-00845744v1  Conference papers
Romain Veltz, Olivier Faugeras. Interplay between constant delays and space dependent delays in neural fields models
Brainscales General Meeting, Barcelona, 2011, Barcelona, Spain
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hal-00780444v2  Reports
Romain Veltz. Interplay between synaptic delays and propagation delays in neural fields equations
[Research Report] RR-8020, INRIA. 2013, pp.53