Skip to Main content
Number of documents

51

Mathieu Desroches - Publications


Journal articles38 documents

  • Mathieu Desroches, Piotr Kowalczyk, Serafim Rodrigues. Spike-adding and reset-induced canard cycles in adaptive integrate and fire models. Nonlinear Dynamics, Springer Verlag, In press, ⟨10.1007/s11071-021-06441-z⟩. ⟨hal-03129713⟩
  • Elif Köksal Ersöz, Mathieu Desroches, Antoni Guillamon, John Rinzel, Joel Tabak. Canard-induced complex oscillations in an excitatory network. Journal of Mathematical Biology, Springer Verlag (Germany), 2020, 80 (7), pp.2075-2107. ⟨10.1007/s00285-020-01490-1⟩. ⟨hal-01939157v2⟩
  • Jone Uria Albizuri, Mathieu Desroches, Martin Krupa, Serafim Rodrigues. Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model. Journal of Nonlinear Science, Springer Verlag, 2020, 30 (6), pp.3265-3291. ⟨10.1007/s00332-020-09650-9⟩. ⟨hal-02977302⟩
  • Daniele Avitabile, Mathieu Desroches, Romain Veltz, Martin Wechselberger. Local theory for spatio-temporal canards and delayed bifurcations. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), pp.5703-5747. ⟨10.1137/19M1306610⟩. ⟨hal-02412921⟩
  • Mathieu Desroches, Jean-Pierre Françoise, Martin Krupa. Parabolic bursting, spike-adding, dips and slices in a minimal model. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2019, Mathematical Modelling of Natural Phenomena (MMNP), ⟨10.1051/mmnp/2019018⟩. ⟨hal-01911267⟩
  • Mathieu Desroches, Olivier Faugeras, Martin Krupa, Massimo Mantegazza. Modeling cortical spreading depression induced by the hyperactivity of interneurons. Journal of Computational Neuroscience, Springer Verlag, 2019, ⟨10.1007/s10827-019-00730-8⟩. ⟨hal-01520200⟩
  • Anton Chizhov, Fabien Campillo, Mathieu Desroches, Anton Guillamon, Serafim Rodrigues. Conductance-Based Refractory Density Approach for a Population of Bursting Neurons. Bulletin of Mathematical Biology, Springer Verlag, 2019, ⟨10.1007/s11538-019-00643-8⟩. ⟨hal-02189808⟩
  • Elif Köksal Ersöz, Mathieu Desroches, Claudio Mirasso, Serafim Rodrigues. Anticipation via canards in excitable systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2019, 29 (1), pp.013111. ⟨10.1063/1.5050018⟩. ⟨hal-01960691⟩
  • Peter Beim Graben, Antonio Jimenez-Marin, Ibai Diez, Jesus Cortes, Mathieu Desroches, et al.. Metastable Resting State Brain Dynamics. Frontiers in Computational Neuroscience, Frontiers, 2019, 13, ⟨10.3389/fncom.2019.00062⟩. ⟨hal-02300433⟩
  • Mathieu Desroches, Vivien Kirk. Spike-adding in a canonical three time scale model: superslow explosion & folded-saddle canards. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2018, 17 (3), pp.1989-2017. ⟨10.1137/17M1143411⟩. ⟨hal-01652020⟩
  • Daniele Avitabile, Mathieu Desroches, Edgar Knobloch. Spatiotemporal canards in neural field equations. Physical Review E , American Physical Society (APS), 2017, 95 (4), pp.042205. ⟨10.1103/PhysRevE.95.042205⟩. ⟨hal-01558887⟩
  • Giovanni Carmantini, Peter Beim Graben, Mathieu Desroches, Serafim Rodrigues. A modular architecture for transparent computation in recurrent neural networks. Neural Networks, Elsevier, 2017, 85 (1), pp.85-105. ⟨10.1016/j.neunet.2016.09.001⟩. ⟨hal-01386281⟩
  • Elif Köksal Ersöz, Mathieu Desroches, Martin Krupa. Synchronization of weakly coupled canard oscillators. Physica D: Nonlinear Phenomena, Elsevier, 2017, 349, pp.46-61. ⟨10.1016/j.physd.2017.02.016⟩. ⟨hal-01558897⟩
  • Daniele Avitabile, Mathieu Desroches, Edgar Knobloch, Martin Krupa. Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2017, 473 (2207), pp.20170018. ⟨10.1098/rspa.2017.0018⟩. ⟨hal-01243304⟩
  • Elif Köksal Ersöz, Mathieu Desroches, Maciej Krupa, Frédérique Clément. Canard-Mediated (De)Synchronization in Coupled Phantom Bursters. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2016, 15 (1), pp.580-608. ⟨10.1137/15M101840X⟩. ⟨hal-01256389⟩
  • Serafim Rodrigues, Mathieu Desroches, Martin Krupa, Jesus Cortes, Terrence J. Sejnowski, et al.. Time-coded neurotransmitter release at excitatory and inhibitory synapses. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2016, 113 (8), pp.E1108-E1115. ⟨10.1073/pnas.1525591113⟩. ⟨hal-01386149⟩
  • Mathieu Desroches, Soledad Fernández-García, Martin Krupa. Canards and spike-adding transitions in a minimal piecewise-linear Hindmarsh-Rose square-wave burster. Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2016, 26 (7), pp.073111. ⟨10.1063/1.4958297⟩. ⟨hal-01243302⟩
  • Mathieu Desroches, Martin Krupa, Serafim Rodrigues. Spike-adding mechanism in parabolic bursters: the role of folded-saddle canards. Physica D: Nonlinear Phenomena, Elsevier, 2016, 331 (1), pp.58-70. ⟨10.1016/j.physd.2016.05.011⟩. ⟨hal-01136874⟩
  • John Burke, Mathieu Desroches, Albert Granados, Tasso J. Kaper, Martin Krupa, et al.. From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation. Journal of Nonlinear Science, Springer Verlag, 2016, 26 (2), pp.405-451. ⟨10.1007/s00332-015-9279-0⟩. ⟨hal-01242892⟩
  • Mathieu Desroches, Olivier Faugeras, Martin Krupa. Slow-fast transitions to seizure states in the Wendling-Chauvel neural mass model. Opera Medica et Physiologica, UNN Press 2016. ⟨hal-01404623⟩
  • Mathieu Desroches, Antoni Guillamon, Enrique Ponce, Rafel Prohens, Serafim Rodrigues, et al.. Canards, folded nodes and mixed-mode oscillations in piecewise-linear slow-fast systems. SIAM Review, Society for Industrial and Applied Mathematics, 2016, 58 (4), pp.653-691. ⟨10.1137/15M1014528⟩. ⟨hal-01243289⟩
  • Soledad Fernández-García, Mathieu Desroches, Martin Krupa, Antonio Teruel. Canard solutions in planar piecewise linear systems with three zones. Dynamical Systems, Taylor & Francis, 2015, pp.25. ⟨10.1080/14689367.2015.1079304⟩. ⟨hal-01244978⟩
  • Eric Benoît, Morten Brøns, Mathieu Desroches, Martin Krupa. Extending the zero-derivative principle for slow–fast dynamical systems. Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2015, 66 (5), pp.2255-2270. ⟨10.1007/s00033-015-0552-8⟩. ⟨hal-01243307⟩
  • Jonathan Touboul, Maciej Krupa, Mathieu Desroches. Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales . SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2015, 75 (5), pp.26. ⟨hal-01253417⟩
  • Morten Brøns, Mathieu Desroches, Maciej Krupa. Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model. Mathematical Population Studies, Taylor & Francis (Routledge), 2014, pp.1-22. ⟨hal-00924098⟩
  • Jan Sieber, Alain Rapaport, Serafim Rodrigues, Mathieu Desroches. A method for the reconstruction of unkwnown non-monotonic growth functions in the chemostat. Bioprocess and Biosystems Engineering, Springer Verlag, 2013, 36 (10), pp.1496-1507. ⟨10.1007/s00449-013-0912-8⟩. ⟨hal-00860573⟩
  • Jesus M Cortes, Mathieu Desroches, Serafim Rodrigues, Romain Veltz, Miguel A Munoz, et al.. Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2013, 110 (41), pp.16610-16615. ⟨hal-00936308⟩
  • Mathieu Desroches, Emilio Freire, John Hogan, Enrique Ponce, Phanikhrisna Thota. Canards in piecewise-linear systems: explosions and super-explosions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2013, 469 (2154), pp.20120603. ⟨10.1098/rspa.2012.0603⟩. ⟨hal-00844799⟩
  • Mathieu Desroches, Tasso J. Kaper, Maciej Krupa. Mixed-Mode Bursting Oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster. Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2013, 23 (4), pp.046106. ⟨10.1063/1.4827026⟩. ⟨hal-00932344⟩
  • Peter de Maesschalck, Mathieu Desroches. Numerical continuation techniques for planar slow-fast systems. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2013, 12 (3), pp.1159-1180. ⟨10.1137/120877386⟩. ⟨hal-00844785⟩
  • Jesus Cortes, Mathieu Desroches, Serafim Rodrigues, Romain Veltz, Miguel Muñoz, et al.. Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2013. ⟨hal-00857699⟩
  • Maciej Krupa, Alexandre Vidal, Mathieu Desroches, Frédérique Clément. Mixed-mode oscillations in a multiple time scale phantom bursting system. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2012, 11 (4), pp. 1458-1498. ⟨10.1137/110860136⟩. ⟨hal-00669486⟩
  • Daniele Avitabile, Mathieu Desroches, Serafim Rodrigues. On the numerical continuation of isolas of equilibria. International journal of bifurcation and chaos in applied sciences and engineering , World Scientific Publishing, 2012, 22 (11), 12 p. ⟨10.1142/S021812741250277X⟩. ⟨hal-00765172⟩
  • Mathieu Desroches, John Burke, Tasso J. Kaper, Mark A. Kramer. Canards of mixed type in a neural burster. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 85 (2), 6 p. ⟨10.1103/PhysRevE.85.021920⟩. ⟨hal-00765223⟩
  • John Burke, Mathieu Desroches, Anna M. Barry, Tasso J. Kaper, Mark A. Kramer. A showcase of torus canards in neuronal bursters. Journal of Mathematical Neuroscience, BioMed Central, 2012, 2 (3), ⟨10.1186/2190-8567-2-3⟩. ⟨hal-00765229⟩
  • Daniele Linaro, Alan Champneys, Mathieu Desroches, Marco Storace. Codimension-Two Homoclinic Bifurcations Underlying Spike Adding in the Hindmarsh-Rose Burster. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2012, 11 (3), pp.939-962. ⟨10.1137/110848931⟩. ⟨hal-00765189⟩
  • Mathieu Desroches, Maciej Krupa, Serafim Rodrigues. Inflection, canards and excitability threshold in neuronal models. Journal of Mathematical Biology, Springer Verlag (Germany), 2012, ⟨10.1007/s00285-012-0576-z⟩. ⟨hal-00765148⟩
  • Mathieu Desroches, John Guckenheimer, Bernd Krauskopf, Christian Kuehn, Hinke M. Osinga, et al.. Mixed-Mode Oscillations with Multiple Time Scales. SIAM Review, Society for Industrial and Applied Mathematics, 2012, 54 (2), pp.211-288. ⟨10.1137/100791233⟩. ⟨hal-00765216⟩

Book sections1 document

  • Mathieu Desroches, Soledad Fernández-García, Martin Krupa, Rafel Prohens, Antonio Teruel. Piecewise-linear (PWL) canard dynamics : Simplifying singular perturbation theory in the canard regime using piecewise-linear systems. Nonlinear Systems, 1, Springer, 2018, Mathematical Theory and Computational Methods, 978-3-319-66765-2. ⟨10.1007/978-3-319-66766-9_3⟩. ⟨hal-01651907⟩

Conference papers7 documents

  • Mathieu Desroches. Mixed-Mode Bursting Oscillations (MMBOs): slow passage through spike-adding canard explosion.. Multi-Scale Models, Slow-Fast Differential Equations, Averaging in Ecology and Neuroscience, Nov 2014, Bernoulli Centre, EPFL, Lausanne, Switzerland. ⟨hal-01091242⟩
  • Mathieu Desroches. Canards in 3D piecewise-linear slow-fast systems, application to neuron models.. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Jul 2014, Madrid, Spain. ⟨hal-01091239⟩
  • Alain Rapaport, Jan Sieber, Serafim Rodrigues, Mathieu Desroches. Extremum seeking via continuation techniques for optimizing biogas production in the chemostat. 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013), Sep 2013, Toulouse, France. pp.152-157, ⟨10.3182/20130904-3-FR-2041.00053⟩. ⟨hal-00787510v2⟩
  • Mathieu Desroches. Inflection lines near canards in 2D and 3D systems. Workshop on Slow-Fast Dynamics: Theory, Numerics and Application to Earth and Life Sciences, Jun 2013, Barcelona, Spain. ⟨hal-00854374⟩
  • Mathieu Desroches. Inflection methods for singular perturbation problems. SIAM Conference on Applications of Dynamical Systems, May 2013, Snowbird, United States. ⟨hal-00854373⟩
  • Jan Sieber, Alain Rapaport, Serafim Rodrigues, Mathieu Desroches. A new method for the reconstruction of unknown non-monotonic growth function in the chemostat. 20th IEEE Mediterranean Conference on Control and Automation (MED '12), Jul 2012, Barcelona, Spain. pp.169 - 175, ⟨10.1109/MED.2012.6265633⟩. ⟨hal-02748259⟩
  • Mathieu Desroches. Canards, inflection and excitability threshold. 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Jul 2012, Orlando, United States. ⟨hal-00854372⟩

Preprints, Working Papers, ...4 documents

  • Louisiane Lemaire, Mathieu Desroches, Martin Krupa, Lara Pizzamiglio, Paolo Scalmani, et al.. Modeling NaV1.1/SCN1A sodium channel mutations in a microcircuit with realistic ion concentration dynamics suggests differential GABAergic mechanisms leading to hyperexcitability in epilepsy and migraine. 2021. ⟨hal-03191275⟩
  • Emre Baspinar, Daniele Avitabile, Mathieu Desroches. Canonical models for torus canards in elliptic bursters. 2020. ⟨hal-03045649⟩
  • Oana Chever, Sarah Zerimech, Paolo Scalmani, Louisiane Lemaire, Alexandre Loucif, et al.. GABAergic neurons and Na V 1.1 channel hyperactivity: a novel neocortex-specific mechanism of Cortical Spreading Depression. 2020. ⟨hal-03045625⟩
  • Jan Sieber, Alain Rapaport, Mathieu Desroches, Serafim Rodrigues. A new method for the reconstruction of unknown non-monotonic growth functions in the chemostat. 2012. ⟨hal-00723246⟩

Habilitation à diriger des recherches1 document

  • Mathieu Desroches. Complex oscillations with multiple timescales - Application to neuronal dynamics . Dynamical Systems [math.DS]. Universite Pierre et Marie Curie, 2015. ⟨tel-01254956⟩