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Bibliography

Major publications by the team in recent years
  • 1J. 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
  • 2B. Cessac.

    A discrete time neural network model with spiking neurons II. Dynamics with noise, in: J. Math. Biol., 2011, vol. 62, pp. 863-900.
  • 3P. Chossat, O. Faugeras.

    Hyperbolic planforms in relation to visual edges and textures perception, in: Plos Comput Biol, December 2009, vol. 5, no 12, e1000625.

    http://dx.doi.org/doi:10.1371/journal.pcbi.1000625
  • 4R. Cofre, B. Cessac.

    Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: Chaos, Solitons and Fractals, 2012, submitted.

    http://lanl.arxiv.org/abs/1212.3577
  • 5R. Cofre, B. Cessac.

    Exact computation of the Maximum Entropy Potential of spiking neural networks models, in: Physical Reviev E, 2014, vol. 89, no 052117, 13 p.

    https://hal.inria.fr/hal-01095599
  • 6J. Naudé, B. Cessac, H. Berry, B. Delord.

    Effects of Cellular Homeostatic Intrinsic Plasticity on Dynamical and Computational Properties of Biological Recurrent Neural Networks, in: Journal of Neuroscience, 2013, vol. 33, no 38, pp. 15032-15043. [ DOI : 10.1523/JNEUROSCI.0870-13.2013 ]

    https://hal.inria.fr/hal-00844218
  • 7E. Tlapale, G. S. Masson, P. Kornprobst.

    Modelling the dynamics of motion integration with a new luminance-gated diffusion mechanism, in: Vision Research, August 2010, vol. 50, no 17, pp. 1676–1692.

    http://dx.doi.org/10.1016/j.visres.2010.05.022
  • 8J. 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
  • 9R. 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
  • 10R. 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
  • 11R. Veltz.

    Nonlinear analysis methods in neural field models, Université Paris Est, 2011.

    ftp://ftp-sop.inria.fr/neuromathcomp/publications/phds/veltz-11.pdf
Publications of the year

Articles in International Peer-Reviewed Journals

  • 12J. Burke, M. Desroches, A. Granados, T. J. Kaper, M. Krupa, T. Vo.

    From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation, in: Journal of Nonlinear Science, April 2016, vol. 26, no 2, pp. 405-451. [ DOI : 10.1007%2Fs00332-015-9279-0 ]

    https://hal.inria.fr/hal-01242892
  • 13G. Carmantini, P. Beim Graben, M. Desroches, S. Rodrigues.

    A modular architecture for transparent computation in recurrent neural networks, in: Neural Networks, September 2016. [ DOI : 10.1016/j.neunet.2016.09.001 ]

    https://hal.inria.fr/hal-01386281
  • 14M. Desroches, O. Faugeras, M. Krupa.

    Slow-fast transitions to seizure states in the Wendling-Chauvel neural mass model, in: Opera Medica et Physiologica, November 2016.

    https://hal.inria.fr/hal-01404623
  • 15M. Desroches, S. Fernández-García, M. Krupa.

    Canards and spike-adding transitions in a minimal piecewise-linear Hindmarsh-Rose square-wave burster, in: Chaos, July 2016, vol. 26, no 7, 073111. [ DOI : 10.1063/1.4958297 ]

    https://hal.inria.fr/hal-01243302
  • 16M. 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
  • 17M. Desroches, M. Krupa, S. Rodrigues.

    Spike-adding mechanism in parabolic bursters: the role of folded-saddle canards, in: Physica D: Nonlinear Phenomena, September 2016, vol. 331, no 1, pp. 58-70. [ DOI : 10.1016/j.physd.2016.05.011 ]

    https://hal.inria.fr/hal-01136874
  • 18S. Fernández-García, M. Krupa, F. Clément.

    Mixed-Mode Oscillations in a piecewise linear system with multiple time scale coupling, in: Physica D: Nonlinear Phenomena, July 2016, vol. 332, pp. 9–22. [ DOI : 10.1016/j.physd.2016.06.002 ]

    https://hal.inria.fr/hal-01342978
  • 19A. I. Meso, J. S. Rankin, O. S. Faugeras, P. S. Kornprobst, G. S. Masson.

    The relative contribution of noise and adaptation to competition during tri-stable motion perception, in: Journal of Vision, October 2016.

    https://hal.inria.fr/hal-01383118
  • 20S. 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

Internal Reports

  • 21A. Drogoul, R. Veltz.

    Exponential stability of stationary distributions for some nonlocal transport equations: application to neural dynamic, Inria Sophia Antipolis - Méditerranée, April 2016, no RR-8899.

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

Other Publications

  • 22P. C. Bressloff, O. C. Faugeras.

    On the Hamiltonian structure of large deviations in stochastic hybrid systems, December 2016, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01414872
  • 23P. Chossat, M. Krupa, F. Lavigne.

    Latching dynamics in neural networks with synaptic depression, November 2016, working paper or preprint.

    https://hal.inria.fr/hal-01402179
  • 24A. Drogoul, R. Veltz.

    Evidence for Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics, December 2016, working paper or preprint.

    https://hal.inria.fr/hal-01412154
  • 25O. Faugeras, J. Maclaurin.

    Large Deviations of a Spatially-Stationary Network of Interacting Neurons, December 2016, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01421319
  • 26A. Granados, L. Alsedà, M. Krupa.

    The Period adding and incrementing bifurcations: from rotation theory to applications, January 2017, accepted for publication in SIAM Review on 15 July 2016.

    https://hal.inria.fr/hal-01416249
  • 27S. Visser, R. Nicks, O. Faugeras, S. Coombes.

    Standing and travelling waves in a spherical brain model: the Nunez model revisited, December 2016, working paper or preprint.

    https://hal.archives-ouvertes.fr/hal-01414902
References in notes
  • 28E. 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.
  • 29M. 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.
  • 30M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga, M. Wechselberger.

    Mixed-mode oscillations with multiple time scales, in: SIAM Review, 2012, vol. 54, no 2, pp. 211–288.
  • 31M. 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
  • 32M. 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.
  • 33E. M. Izhikevich.

    Neural excitability, spiking and bursting, in: International Journal of Bifurcation and Chaos, 2000, vol. 10, no 06, pp. 1171–1266.
  • 34M. 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.
  • 35M. Krupa, P. Szmolyan.

    Relaxation oscillation and canard explosion, in: Journal of Differential Equations, 2001, vol. 174, no 2, pp. 312–368.
  • 36E. Tlapale, P. Kornprobst, G. S. Masson, O. Faugeras.

    A Neural Field Model for Motion Estimation, in: Mathematical Image Processing, S. Verlag (editor), Springer Proceedings in Mathematics, 2011, vol. 5, pp. 159–180.

    http://dx.doi.org/10.1007/978-3-642-19604-1
  • 37J. 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.
  • 38R. 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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