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Bibliography

Major publications by the team in recent years
  • 1C. Aguilar, P. Chossat, M. Krupa, F. Lavigne.

    Latching dynamics in neural networks with synaptic depression, in: PLoS ONE, August 2017, vol. 12, no 8, e0183710 p. [ DOI : 10.1371/journal.pone.0183710 ]

    https://hal.inria.fr/hal-01402179
  • 2D. Avitabile, M. Desroches, E. Knobloch.

    Spatiotemporal canards in neural field equations, in: Physical Review E , April 2017, vol. 95, no 4, 042205 p. [ DOI : 10.1103/PhysRevE.95.042205 ]

    https://hal.inria.fr/hal-01558887
  • 3J. Baladron, D. Fasoli, O. Faugeras, J. Touboul.

    Mean-field description and propagation of chaos in networks of Hodgkin-Huxley neurons, in: The Journal of Mathematical Neuroscience, 2012, vol. 2, no 1.

    http://www.mathematical-neuroscience.com/content/2/1/10
  • 4F. Campillo, N. Champagnat, C. Fritsch.

    Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models, in: Journal of mathematical biology, 2016, vol. 73, no 6-7, pp. 1781–1821.

    https://hal.archives-ouvertes.fr/hal-01205467
  • 5F. Campillo, C. Fritsch.

    Weak convergence of a mass-structured individual-based model, in: Applied Mathematics & Optimization, 2015, vol. 72, no 1, pp. 37–73.

    https://hal.inria.fr/hal-01090727
  • 6F. Campillo, M. Joannides, I. Larramendy-Valverde.

    Analysis and approximation of a stochastic growth model with extinction, in: Methodology and Computing in Applied Probability, 2016, vol. 18, no 2, pp. 499–515.

    https://hal.archives-ouvertes.fr/hal-01817824
  • 7F. Campillo, C. Lobry.

    Effect of population size in a predator–prey model, in: Ecological Modelling, 2012, vol. 246, pp. 1–10.

    https://hal.inria.fr/hal-00723793
  • 8J. M. Cortes, M. Desroches, S. Rodrigues, R. Veltz, M. A. Munoz, T. J. Sejnowski.

    Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics, in: Proceedings of the National Academy of Sciences of the United States of America , 2013, vol. 110, no 41, pp. 16610-16615.

    https://hal.inria.fr/hal-00936308
  • 9M. Desroches, A. Guillamon, E. Ponce, R. Prohens, S. Rodrigues, A. Teruel.

    Canards, folded nodes and mixed-mode oscillations in piecewise-linear slow-fast systems, in: SIAM Review, November 2016, vol. 58, no 4, pp. 653-691, accepted for publication in SIAM Review on 13 August 2015. [ DOI : 10.1137/15M1014528 ]

    https://hal.inria.fr/hal-01243289
  • 10M. Desroches, T. J. Kaper, M. Krupa.

    Mixed-Mode Bursting Oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster, in: Chaos, October 2013, vol. 23, no 4, 046106 p. [ DOI : 10.1063/1.4827026 ]

    https://hal.inria.fr/hal-00932344
  • 11A. Drogoul, R. Veltz.

    Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics, in: Chaos, February 2017. [ DOI : 10.1063/1.4976510 ]

    https://hal.inria.fr/hal-01412154
  • 12E. Köksal Ersöz, M. Desroches, A. Guillamon, J. Tabak.

    Canard-induced complex oscillations in an excitatory network, November 2018, working paper or preprint.

    https://hal.inria.fr/hal-01939157
  • 13S. Rodrigues, M. Desroches, M. Krupa, J. M. Cortes, T. J. Sejnowski, A. B. Ali.

    Time-coded neurotransmitter release at excitatory and inhibitory synapses, in: Proceedings of the National Academy of Sciences of the United States of America , February 2016, vol. 113, no 8, pp. E1108-E1115. [ DOI : 10.1073/pnas.1525591113 ]

    https://hal.inria.fr/hal-01386149
  • 14R. Veltz, O. Faugeras.

    A center manifold result for delayed neural fields equations, in: SIAM Journal on Applied Mathematics (under revision), July 2012, RR-8020.

    http://hal.inria.fr/hal-00719794
  • 15R. Veltz, O. Faugeras.

    A Center Manifold Result for Delayed Neural Fields Equations, in: SIAM Journal on Mathematical Analysis, 2013, vol. 45, no 3, pp. 1527-1562. [ DOI : 10.1137/110856162 ]

    https://hal.inria.fr/hal-00850382
  • 16R. Veltz.

    Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations, in: SIAM Journal on Applied Dynamical Systems, 2013, vol. 12, no 3, pp. 1566-1612. [ DOI : 10.1137/120889253 ]

    https://hal.inria.fr/hal-00850391
  • 17R. Veltz.

    A new twist for the simulation of hybrid systems using the true jump method, December 2015, working paper or preprint.

    https://hal.inria.fr/hal-01243615
Publications of the year

Articles in International Peer-Reviewed Journals

  • 18H. Baldemir, D. Avitabile, K. Tsaneva-Atanasova.

    Pseudo-plateau bursting and mixed-mode oscillations in a model of developing inner hair cells, in: Communications in Nonlinear Science and Numerical Simulation, January 2020, vol. 80, 104979 p. [ DOI : 10.1016/j.cnsns.2019.104979 ]

    https://hal.archives-ouvertes.fr/hal-02334715
  • 19E. Baspinar, G. Citti.

    Uniqueness of Viscosity Mean Curvature Flow Solution in Two Sub-Riemannian Structures, in: SIAM Journal on Mathematical Analysis, May 2019, vol. 51, no 3, pp. 2633-2659, https://arxiv.org/abs/1610.06031. [ DOI : 10.1137/17M1150797 ]

    https://hal.archives-ouvertes.fr/hal-02319482
  • 20P. Beim Graben, A. Jimenez-Marin, I. Diez, J. M. Cortes, M. Desroches, S. Rodrigues.

    Metastable Resting State Brain Dynamics, in: Frontiers in Computational Neuroscience, September 2019, vol. 13. [ DOI : 10.3389/fncom.2019.00062 ]

    https://hal.inria.fr/hal-02300433
  • 21Á. Byrne, D. Avitabile, S. Coombes.

    Next-generation neural field model: The evolution of synchrony within patterns and waves, in: Physical Review E , January 2019, vol. 99, no 1. [ DOI : 10.1103/PhysRevE.99.012313 ]

    https://hal.inria.fr/hal-02341025
  • 22F. Campillo, M. Chebbi, S. Toumi.

    Stochastic modeling for biotechnologies Anaerobic model AM2b, in: Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, June 2019, vol. Volume 28 - 2017 - Mathematics for Biology and the Environment, pp. 13-23.

    https://hal.archives-ouvertes.fr/hal-01471203
  • 23A. Chizhov, F. Campillo, M. Desroches, A. Guillamon, S. Rodrigues.

    Conductance-Based Refractory Density Approach for a Population of Bursting Neurons, in: Bulletin of Mathematical Biology, July 2019. [ DOI : 10.1007/s11538-019-00643-8 ]

    https://hal.inria.fr/hal-02189808
  • 24Q. Cormier, E. Tanré, R. Veltz.

    Long time behavior of a mean-field model of interacting neurons, in: Stochastic Processes and their Applications, 2019, https://arxiv.org/abs/1810.08562. [ DOI : 10.1016/j.spa.2019.07.010 ]

    https://hal.inria.fr/hal-01903857
  • 25M. Desroches, O. Faugeras, M. Krupa, M. Mantegazza.

    Modeling cortical spreading depression induced by the hyperactivity of interneurons, in: Journal of Computational Neuroscience, October 2019. [ DOI : 10.1007/s10827-019-00730-8 ]

    https://hal.inria.fr/hal-01520200
  • 26M. Desroches, J.-P. Françoise, M. Krupa.

    Parabolic bursting, spike-adding, dips and slices in a minimal model, in: Mathematical Modelling of Natural Phenomena, May 2019, no 14. [ DOI : 10.1051/mmnp/2019018 ]

    https://hal.inria.fr/hal-01911267
  • 27N. Fournier, E. Tanré, R. Veltz.

    On a toy network of neurons interacting through their dendrites, in: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2019, https://arxiv.org/abs/1802.04118, forthcoming.

    https://hal.inria.fr/hal-01707663
  • 28E. Köksal Ersöz, M. Desroches, C. R. Mirasso, S. Rodrigues.

    Anticipation via canards in excitable systems, in: Chaos: An Interdisciplinary Journal of Nonlinear Science, January 2019, vol. 29, no 1, 013111 p. [ DOI : 10.1063/1.5050018 ]

    https://hal.inria.fr/hal-01960691
  • 29S. Olmi, S. Petkoski, M. Guye, F. Bartolomei, V. Jirsa.

    Controlling seizure propagation in large-scale brain networks, in: PLoS Computational Biology, February 2019, vol. 15, no 2, e1006805 p. [ DOI : 10.1371/journal.pcbi.1006805 ]

    https://www.hal.inserm.fr/inserm-02146511
  • 30D. Peurichard, M. Ousset, J. Paupert, B. Aymard, A. Lorsignol, L. Casteilla, P. Degond.

    Extra-cellular matrix rigidity may dictate the fate of injury outcome, in: Journal of Theoretical Biology, May 2019, vol. 469, pp. 127-136. [ DOI : 10.1016/j.jtbi.2019.02.017 ]

    https://hal.archives-ouvertes.fr/hal-02345773
  • 31A. Song, O. Faugeras, R. Veltz.

    A neural field model for color perception unifying assimilation and contrast, in: PLoS Computational Biology, 2019, vol. 15, no 6, 37 pages, 17 figures, 3 ancillary files. [ DOI : 10.1371/journal.pcbi.1007050 ]

    https://hal.inria.fr/hal-01909354
  • 32H. Taher, S. Olmi, E. Schöll.

    Enhancing power grid synchronization and stability through time delayed feedback control, in: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, December 2019, vol. 100, 062306 p, https://arxiv.org/abs/1901.05201. [ DOI : 10.1103/PhysRevE.100.062306 ]

    https://hal.inria.fr/hal-02374720
  • 33L. Tumash, S. Olmi, E. Schöll.

    Stability and control of power grids with diluted network topology, in: Chaos, An Interdisciplinary Journal of Nonlinear Science, December 2019, vol. 29, 123105 p, https://arxiv.org/abs/1905.13664 - 10 pages, 5 figures. [ DOI : 10.1063/1.5111686 ]

    https://hal.inria.fr/hal-02374725
  • 34D. Zakharov, M. Krupa, B. Gutkin.

    Modeling dopaminergic modulation of clustered gamma rhythms, in: Communications in Nonlinear Science and Numerical Simulation, March 2020, vol. 82, 105086 p. [ DOI : 10.1016/j.cnsns.2019.105086 ]

    https://hal.inria.fr/hal-02410040

Scientific Books (or Scientific Book chapters)

  • 35S. Olmi, A. Torcini.

    Chimera states in pulse coupled neural networks: the influence of dilution and noise, in: Nonlinear Dynamics in Computational Neuroscience, 2019, https://arxiv.org/abs/1606.08618 - 15 pages, 7 figure, contribution for the Workshop "Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT" held in Turin (Italy) in September 2015.

    https://hal.inria.fr/hal-02374714

Software

Other Publications

References in notes
  • 47N. Berglund, B. Gentz.

    Noise-induced phenomena in slow-fast dynamical systems: a sample-paths approach, Springer Science & Business Media, 2006.
  • 48N. Berglund, B. Gentz, C. Kuehn.

    Hunting French ducks in a noisy environment, in: Journal of Differential Equations, 2012, vol. 252, no 9, pp. 4786–4841.
  • 49E. L. Bienenstock, L. N. Cooper, P. W. Munro.

    Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex, in: The Journal of Neuroscience, 1982, vol. 2, no 1, pp. 32–48.
  • 50P. Chossat, O. Faugeras.

    Hyperbolic planforms in relation to visual edges and textures perception, in: PLoS Computational Biology, 2009, vol. 5, no 12, e1000625 p.
  • 51M. O. Cunningham, M. A. Whittington, A. Bibbig, A. Roopun, F. E. LeBeau, A. Vogt, H. Monyer, E. H. Buhl, R. D. Traub.

    A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro, in: Proceedings of the National Academy of Sciences of the United States of America, 2004, vol. 101, no 18, pp. 7152–7157.
  • 52M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga, M. Wechselberger.

    Mixed-Mode Oscillations with Multiple Time Scales, in: SIAM Review, May 2012, vol. 54, no 2, pp. 211-288. [ DOI : 10.1137/100791233 ]

    https://hal.inria.fr/hal-00765216
  • 53M. Desroches, T. J. Kaper, M. Krupa.

    Mixed-Mode Bursting Oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster, in: Chaos, October 2013, vol. 23, no 4, 046106 p. [ DOI : 10.1063/1.4827026 ]

    https://hal.inria.fr/hal-00932344
  • 54M. Desroches, B. Krauskopf, H. M. Osinga.

    The geometry of slow manifolds near a folded node, in: SIAM Journal on Applied Dynamical Systems, 2008, vol. 7, no 4, pp. 1131–1162.
  • 55J.-D. Deuschel, O. Zeitouni.

    Limiting curves for iid records, in: The Annals of Probability, 1995, pp. 852–878.
  • 56I. Diez, P. Bonifazi, I. Escudero, B. Mateos, M. A. Muñoz, S. Stramaglia, J. M. Cortes.

    A novel brain partition highlights the modular skeleton shared by structure and function, in: Scientific reports, 2015, vol. 5, 10532 p.
  • 57J.-P. Eckmann, S. Oliffson Kamphorst, D. Ruelle.

    Recurrence plots of dynamical systems, in: Europhysics Letters, 1987, vol. 4, no 9, pp. 973–977.
  • 58G. B. Ermentrout, D. H. Terman.

    Mathematical foundations of neuroscience, Springer, 2010, vol. 35.
  • 59O. Faugeras, J. MacLaurin.

    A large deviation principle and an expression of the rate function for a discrete stationary gaussian process, in: Entropy, 2014, vol. 16, no 12, pp. 6722–6738.
  • 60E. M. Izhikevich.

    Neural excitability, spiking and bursting, in: International Journal of Bifurcation and Chaos, 2000, vol. 10, no 06, pp. 1171–1266.
  • 61E. M. Izhikevich.

    Dynamical systems in neuroscience, MIT press, 2007.
  • 62M. Krupa, N. Popović, N. Kopel, H. G. Rotstein.

    Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron, in: Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008, vol. 18, no 1, 015106 p.
  • 63M. Krupa, P. Szmolyan.

    Relaxation oscillation and canard explosion, in: Journal of Differential Equations, 2001, vol. 174, no 2, pp. 312–368.
  • 64R. Mileusnic, C. L. Lancashire, S. P. Rose.

    Amyloid precursor protein: from synaptic plasticity to Alzheimer's disease, in: Annals of the New York Academy of Sciences, 2005, vol. 1048, no 1, pp. 149–165.
  • 65D. Pietrobon, M. A. Moskowitz.

    Pathophysiology of migraine, in: Annual review of physiology, 2013, vol. 75, pp. 365–391.
  • 66J. Tabak, M. J. O'Donovan, J. Rinzel.

    Differential control of active and silent phases in relaxation models of neuronal rhythms, in: Journal of computational neuroscience, 2006, vol. 21, no 3, pp. 307–328.
  • 67J. Tabak, J. Rinzel, R. Bertram.

    Quantifying the relative contributions of divisive and subtractive feedback to rhythm generation, in: PLoS computational biology, 2011, vol. 7, no 4, e1001124 p.
  • 68J. Tabak, J. Rinzel, M. J. O'Donovan.

    The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord, in: Journal of Neuroscience, 2001, vol. 21, no 22, pp. 8966–8978.
  • 69J. Tabak, W. Senn, M. J. O'Donovan, J. Rinzel.

    Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network, in: Journal of Neuroscience, 2000, vol. 20, no 8, pp. 3041–3056.
  • 70J. Touboul, O. Faugeras.

    A Markovian event-based framework for stochastic spiking neural networks, in: Journal of Computational Neuroscience, April 2011, vol. 30.
  • 71J. Touboul, F. Wendling, P. Chauvel, O. Faugeras.

    Neural Mass Activity, Bifurcations, and Epilepsy, in: Neural Computation, December 2011, vol. 23, no 12, pp. 3232–3286.
  • 72R. Veltz, O. Faugeras.

    Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations, in: SIAM Journal on Applied Dynamical Systems, August 2010, vol. 9, no 3, pp. 954–998. [ DOI : 10.1137/090773611 ]

    http://arxiv.org/abs/0910.2247
  • 73R. Veltz, O. Faugeras.

    A Center Manifold Result for Delayed Neural Fields Equations, in: SIAM Journal on Mathematical Analysis, 2013, vol. 45, no 3, pp. 1527-562.
  • 74P. beim Graben, A. Hutt.

    Detecting recurrence domains of dynamical systems by symbolic dynamics, in: Physical review letters, 2013, vol. 110, no 15, 154101 p.
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    Dynamical diseases of brain systems: different routes to epileptic seizures, in: IEEE transactions on biomedical engineering, 2003, vol. 50, no 5, pp. 540–548.


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