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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
  • 3M. Bossy, O. Faugeras, D. Talay.

    Clarification and Complement to ” Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons ”, in: Journal of Mathematical Neuroscience, 2015, vol. 5, no 1, 19 p. [ DOI : 10.1186/s13408-015-0031-8 ]

    https://hal.inria.fr/hal-01098582
  • 4J. 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
  • 5M. 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
  • 6M. 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
  • 7A. 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
  • 8O. Faugeras, J. Inglis.

    Stochastic neural field equations: A rigorous footing, in: Journal of Mathematical Biology, July 2014, 40 p.

    https://hal.inria.fr/hal-00907555
  • 9S. 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
  • 10R. Veltz, P. Chossat, O. Faugeras.

    On the effects on cortical spontaneous activity of the symmetries of the network of pinwheels in visual area V1, in: Journal of Mathematical Neuroscience, May 2015. [ DOI : 10.1186/s13408-015-0023-8 ]

    https://hal.inria.fr/hal-01079055
  • 11R. 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
  • 12R. 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
Publications of the year

Articles in International Peer-Reviewed Journals

  • 13C. 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, https://arxiv.org/abs/1611.03645. [ DOI : 10.1371/journal.pone.0183710 ]

    https://hal.inria.fr/hal-01402179
  • 14D. Avitabile, M. Desroches, E. Knobloch.

    Spatiotemporal canards in neural field equations, in: Physical Review E , April 2017, vol. 95, no 4, 042205 p, https://arxiv.org/abs/1702.00079. [ DOI : 10.1103/PhysRevE.95.042205 ]

    https://hal.inria.fr/hal-01558887
  • 15D. Avitabile, M. Desroches, E. Knobloch, M. Krupa.

    Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system, in: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, October 2017, vol. 473, no 2207, 20170018 p, https://arxiv.org/abs/1511.09057 - submitted for publication. [ DOI : 10.1098/rspa.2017.0018 ]

    https://hal.inria.fr/hal-01243304
  • 16P. C. Bressloff, O. C. Faugeras.

    On the Hamiltonian structure of large deviations in stochastic hybrid systems, in: Journal of Statistical Mechanics: Theory and Experiment, 2017, vol. 2017, 33206 p. [ DOI : 10.1088/1742-5468/aa64f3 ]

    https://hal.inria.fr/hal-01072077
  • 17P.-L. Buono, M. Krupa, I. Stewart.

    Special issue for Martin Golubitsky, in: Dynamical Systems, February 2017, vol. 32, no 1, pp. 1-3. [ DOI : 10.1080/14689367.2017.1280905 ]

    https://hal.inria.fr/hal-01654650
  • 18F. Campillo, N. Champagnat, C. Fritsch.

    On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models, in: Communications in Mathematical Sciences, 2017, vol. 15, no 7, pp. 1801-1819, https://arxiv.org/abs/1601.02516.

    https://hal.inria.fr/hal-01254053
  • 19F. Campillo, M. Chebbi, S. Toumi.

    Stochastic modeling for biotechnologies Anaerobic model AM2b, in: Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, February 2017.

    https://hal.archives-ouvertes.fr/hal-01471203
  • 20G. Carmantini, P. Beim Graben, M. Desroches, S. Rodrigues.

    A modular architecture for transparent computation in recurrent neural networks, in: Neural Networks, January 2017, vol. 85, no 1, pp. 85-105. [ DOI : 10.1016/j.neunet.2016.09.001 ]

    https://hal.inria.fr/hal-01386281
  • 21P. Chossat, M. Krupa.

    Consecutive and non-consecutive heteroclinic cycles in Hopfield networks, in: Dynamical Systems, February 2017, vol. 32, no 1, pp. 46-60.

    https://hal.inria.fr/hal-01654634
  • 22A. 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
  • 23C. Fritsch, F. Campillo, O. Ovaskainen.

    A numerical approach to determine mutant invasion fitness and evolutionary singular strategies, in: Theoretical Population Biology, 2017, vol. 115, pp. 89-99, https://arxiv.org/abs/1612.04049. [ DOI : 10.1016/j.tpb.2017.05.001 ]

    https://hal.archives-ouvertes.fr/hal-01413638
  • 24A. Granados, L. Alsedà, M. Krupa.

    The Period adding and incrementing bifurcations: from rotation theory to applications, in: SIAM Review, May 2017, vol. 59, no 2, pp. 225-292.

    https://hal.inria.fr/hal-01416249
  • 25E. Köksal Ersöz, M. Desroches, M. Krupa.

    Synchronization of weakly coupled canard oscillators, in: Physica D: Nonlinear Phenomena, June 2017, vol. 349, pp. 46-61. [ DOI : 10.1016/j.physd.2017.02.016 ]

    https://hal.inria.fr/hal-01558897
  • 26O. Podvigina, P. Chossat.

    Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in ℝ4, in: Journal of Nonlinear Science, February 2017, vol. 27, no 1, pp. 343-375, https://arxiv.org/abs/1509.07277.

    https://hal.archives-ouvertes.fr/hal-01286143
  • 27S. Visser, R. Nicks, O. Faugeras, S. Coombes.

    Standing and travelling waves in a spherical brain model: the Nunez model revisited, in: Physica D: Nonlinear Phenomena, June 2017, vol. 349, pp. 27-45.

    https://hal.archives-ouvertes.fr/hal-01414902

Scientific Books (or Scientific Book chapters)

  • 28M. Desroches, S. Fernández-García, M. Krupa, R. Prohens, A. Teruel.

    Piecewise-linear (PWL) canard dynamics : Simplifying singular perturbation theory in the canard regime using piecewise-linear systems, in: Nonlinear Systems, Mathematical Theory and Computational Methods, Springer, 2017, vol. 1, forthcoming.

    https://hal.inria.fr/hal-01651907

Internal Reports

  • 29N. V. K. Medathati, J. Rankin, A. I. Meso, P. Kornprobst, G. S. Masson.

    Recurrent network dynamics reconciles visual motion segmentation and integration, Inria Sophia Antipolis, March 2017, no RR-9041, 28 p.

    https://hal.inria.fr/hal-01482294

Other Publications

  • 30M. Desroches, O. Faugeras, M. Krupa, M. Mantegazza.

    Modeling cortical spreading depression induced by the hyperactivity of interneurons, May 2017, working paper or preprint.

    https://hal.inria.fr/hal-01520200
  • 31M. Desroches, V. Kirk.

    Spike-adding in a canonical three time scale model: superslow explosion & folded-saddle canards, August 2017, submitted for publication.

    https://hal.inria.fr/hal-01652020
  • 32P. Helson, E. Tanré, R. Veltz.

    A simple spiking neuron model based on stochastic STDP, May 2017, International Conference on Mathematical Neuroscience, Poster.

    https://hal.archives-ouvertes.fr/hal-01652036
  • 33R. Veltz, T. Gorski, M. Galtier, H. Fragnaud, B. Teleńczuk, A. Destexhe.

    Inverse correlation processing by neurons with active dendrites, December 2017, working paper or preprint. [ DOI : 10.1101/137984 ]

    https://hal.archives-ouvertes.fr/hal-01653178
  • 34R. Veltz.

    Inverse correlation processing by neurons with active dendrites, December 2017, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01653166
References in notes
  • 35J. Baladron, D. Fasoli, O. Faugeras, J. Touboul.

    Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons, in: The Journal of Mathematical Neuroscience, 2012, vol. 2, no 1, 10 p.
  • 36E. 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.
  • 37P. Chossat, O. Faugeras.

    Hyperbolic planforms in relation to visual edges and textures perception, in: PLoS Computational Biology, 2009, vol. 5, no 12, e1000625 p.
  • 38P. Chossat, M. Krupa.

    Heteroclinic cycles in Hopfield networks, in: Journal of Nonlinear Science, 2016, vol. 26, no 2, pp. 315–344.
  • 39M. 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.
  • 40A. De Masi, A. Galves, E. Löcherbach, E. Presutti.

    Hydrodynamic limit for interacting neurons, in: Journal of Statistical Physics, 2015, vol. 158, no 4, pp. 866–902.
  • 41M. 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
  • 42M. 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
  • 43M. 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.
  • 44G. B. Ermentrout, D. H. Terman.

    Mathematical foundations of neuroscience, Springer, 2010, vol. 35.
  • 45O. 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.
  • 46N. Fournier, E. Löcherbach.

    On a toy model of interacting neurons, in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2016, vol. 52, no 4, pp. 1844–1876.
  • 47E. M. Izhikevich.

    Neural excitability, spiking and bursting, in: International Journal of Bifurcation and Chaos, 2000, vol. 10, no 06, pp. 1171–1266.
  • 48E. M. Izhikevich.

    Dynamical systems in neuroscience, MIT press, 2007.
  • 49M. 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.
  • 50M. Krupa, P. Szmolyan.

    Relaxation oscillation and canard explosion, in: Journal of Differential Equations, 2001, vol. 174, no 2, pp. 312–368.
  • 51O. Podvigina, P. Chossat.

    Simple heteroclinic cycles in ℝ4, in: Nonlinearity, 2015, vol. 28, no 4, 901 p.
  • 52J. Touboul, O. Faugeras.

    A Markovian event-based framework for stochastic spiking neural networks, in: Journal of Computational Neuroscience, April 2011, vol. 30.

    http://www.springerlink.com/content/81736mn03j2221m7/fulltext.pdf
  • 53J. 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.
  • 54R. 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
  • 55R. 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.


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