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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
  • 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
  • 8S. 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
  • 9R. 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
  • 10R. 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
  • 11R. 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
  • 12R. 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

  • 13P. Chossat, A. Lohse, O. Podvigina.

    Pseudo-simple heteroclinic cycles in ℝ4, in: Physica D: Nonlinear Phenomena, June 2018, vol. 372, pp. 1 - 21. [ DOI : 10.1016/j.physd.2018.01.008 ]

    https://hal.inria.fr/hal-01913982
  • 14M. Desroches, V. Kirk.

    Spike-adding in a canonical three time scale model: superslow explosion & folded-saddle canards, in: SIAM Journal on Applied Dynamical Systems, July 2018, vol. 17, no 3, pp. 1989-2017. [ DOI : 10.1137/17M1143411 ]

    https://hal.inria.fr/hal-01652020
  • 15A. Dolcemascolo, B. Garbin, B. Peyce, R. Veltz, S. Barland.

    Resonator neuron and triggering multipulse excitability in laser with injected signal, in: Physical Review E , December 2018. [ DOI : 10.1103/PhysRevE.98.062211 ]

    https://hal.inria.fr/hal-01950511
  • 16T. Gorski, R. Veltz, M. Galtier, H. Fragnaud, B. Teleńczuk, A. Destexhe.

    Inverse correlation processing by neurons with active dendrites, in: Journal of Computational Neuroscience, December 2018. [ DOI : 10.1007/s10827-018-0707-7 ]

    https://hal.archives-ouvertes.fr/hal-01653178
  • 17E. Köksal Ersöz, M. Desroches, C. R. Mirasso, S. Rodrigues.

    Anticipation via canards in excitable systems, in: Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018.

    https://hal.inria.fr/hal-01960691
  • 18V. Mehrmann, R. Morandin, S. Olmi, E. Schöll.

    Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form, in: Chaos, October 2018, vol. 28, no 10, 101102 p. [ DOI : 10.1063/1.5054850 ]

    https://hal.inria.fr/hal-01964307
  • 19S. Olmi, M. Gori, I. Donato, M. Pettini.

    Collective behavior of oscillating electric dipoles, in: Scientific Reports, October 2018, vol. 8, no 1. [ DOI : 10.1038/s41598-018-33990-y ]

    https://hal.inria.fr/hal-01964303
  • 20L. Tumash, S. Olmi, E. Schöll.

    Effect of disorder and noise in shaping the dynamics of power grids, in: EPL - Europhysics Letters, July 2018, vol. 123, no 2, 20001 p. [ DOI : 10.1209/0295-5075/123/20001 ]

    https://hal.inria.fr/hal-01965054
  • 21D. Zakharov, M. Krupa, B. Gutkin, A. Kuznetsov.

    High-frequency forced oscillations in neuronlike elements, in: Physical Review E , June 2018, vol. 97, no 6. [ DOI : 10.1103/PhysRevE.97.062211 ]

    https://hal.inria.fr/hal-01962910

Scientific Books (or Scientific Book chapters)

  • 22M. 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, September 2018, vol. 1. [ DOI : 10.1007/978-3-319-66766-9_3 ]

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

Internal Reports

  • 23A. Drogoul, R. Veltz.

    Exponential stability of the stationary distribution of a mean field of spiking neural network, Inria Sophia Antipolis - Méditerranée, September 2018, no RR-8899.

    https://hal.inria.fr/hal-01290264

Other Publications

References in notes
  • 30E. 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.
  • 31P. Chossat, O. Faugeras.

    Hyperbolic planforms in relation to visual edges and textures perception, in: PLoS Computational Biology, 2009, vol. 5, no 12, e1000625 p.
  • 32M. 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.
  • 33A. 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.
  • 34M. 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
  • 35M. 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
  • 36M. 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.
  • 37J.-D. Deuschel, O. Zeitouni.

    Limiting curves for iid records, in: The Annals of Probability, 1995, pp. 852–878.
  • 38G. B. Ermentrout, D. H. Terman.

    Mathematical foundations of neuroscience, Springer, 2010, vol. 35.
  • 39O. 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.
  • 40N. 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.
  • 41E. M. Izhikevich.

    Neural excitability, spiking and bursting, in: International Journal of Bifurcation and Chaos, 2000, vol. 10, no 06, pp. 1171–1266.
  • 42E. M. Izhikevich.

    Dynamical systems in neuroscience, MIT press, 2007.
  • 43M. 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.
  • 44M. Krupa, P. Szmolyan.

    Relaxation oscillation and canard explosion, in: Journal of Differential Equations, 2001, vol. 174, no 2, pp. 312–368.
  • 45P. Monnier.

    Standard definitions of chromatic induction fail to describe induction with S-cone patterned backgrounds, in: Vision research, 2008, vol. 48, no 27, pp. 2708–2714.
  • 46P. Monnier, S. K. Shevell.

    Chromatic induction from S-cone patterns, in: Vision Research, 2004, vol. 44, no 9, pp. 849–856.
  • 47J. 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.
  • 48J. 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.
  • 49J. 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.
  • 50J. 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.
  • 51J. 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
  • 52J. 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.
  • 53R. 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
  • 54R. 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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