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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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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 4, 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.