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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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 ${ℝ}^4$, 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o RR-8899.
  https://hal.inria.fr/hal-01290264

Other Publications

• 24Q. Cormier, E. Tanré, R. Veltz.
  Long time behavior of a mean-field model of interacting neurons, October 2018, https://arxiv.org/abs/1810.08562 - working paper or preprint.
  https://hal.inria.fr/hal-01903857
• 25M. Desroches, J.-P. Françoise, M. Krupa.
  Parabolic bursting, spike-adding, dips and slices in a minimal model, November 2018, working paper or preprint.
  https://hal.inria.fr/hal-01911267
• 26N. Fournier, E. Tanré, R. Veltz.
  On a toy network of neurons interacting through their dendrites, February 2018, https://arxiv.org/abs/1802.04118 - working paper or preprint.
  https://hal.inria.fr/hal-01707663
• 27E. 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
• 28S. Olmi, S. Petkoski, M. Guye, F. Bartolomei, V. Jirsa.
  Controlling seizure propagation in large-scale brain networks, December 2018, https://arxiv.org/abs/1804.03588 - working paper or preprint.
  https://hal.inria.fr/hal-01964310
• 29A. Song, O. Faugeras, R. Veltz.
  A neural field model for color perception unifying assimilation and contrast, October 2018, https://arxiv.org/abs/1810.12898 - 37 pages, 17 figures, 3 ancillary files. [ DOI : 10.12898 ]
  https://hal.inria.fr/hal-01909354

References in notes

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  Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex, in: The Journal of Neuroscience, 1982, vol. 2, n^o 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, n^o 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.
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• 33A. De Masi, A. Galves, E. Löcherbach, E. Presutti.
  Hydrodynamic limit for interacting neurons, in: Journal of Statistical Physics, 2015, vol. 158, n^o 4, pp. 866–902.
• 34M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga, M. Wechselberger.
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• 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, n^o 4, 046106 p. [ DOI : 10.1063/1.4827026 ]
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• 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, n^o 4, pp. 1131–1162.
• 37J.-D. Deuschel, O. Zeitouni.
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• 39O. Faugeras, J. MacLaurin.
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• 40N. Fournier, E. Löcherbach.
  On a toy model of interacting neurons, in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2016, vol. 52, n^o 4, pp. 1844–1876.
• 41E. M. Izhikevich.
  Neural excitability, spiking and bursting, in: International Journal of Bifurcation and Chaos, 2000, vol. 10, n^o 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, n^o 1, 015106 p.
• 44M. Krupa, P. Szmolyan.
  Relaxation oscillation and canard explosion, in: Journal of Differential Equations, 2001, vol. 174, n^o 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, n^o 27, pp. 2708–2714.
• 46P. Monnier, S. K. Shevell.
  Chromatic induction from S-cone patterns, in: Vision Research, 2004, vol. 44, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 3, pp. 954–998. [ DOI : 10.1137/090773611 ]
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