Journal Articles  ·  Book Chapters  ·  Proceedings Papers  ·  Other Publications  ·  Theses  ·  Preprints

Journal Articles

• Discontinuity-induced dynamics in the Conductance-Based Adaptive Exponential Integrate-and-Fire Model    
  M. Desroches, P. Kowalczyk, and S. Rodrigues
  Bulletin of Mathematical Biology 87(2), 2025.
  
• Dynamics of a piecewise-linear Morris-Lecar model: bifurcations and spike adding     
  J. Penalva Vadell, M. Desroches, A. E. Teruel and C. Vich
  Journal of Nonlinear Science 34(3): 52, 2024.
  
• Viruses - a major cause of amyloid deposition in the brain    
  T. Fülöp (...), M. Desroches, S. Rodrigues, K. Bourgade, A. A. Cohen and J. M. Witkowski
  Expert Review on Neurotherapeutics 23(9): 775-790, 2023.
  
• Synchronization in STDP-driven memristive neural networks with time-varying topology    
  M. E. Yamakou, M. Desroches and S. Rodrigues
  Journal of Biological Physics 49: 483-507, 2023.
  
• Slow-fast dynamics in a neurotransmitter release model: delayed response to a time-dependent input signal    
  M. Sensi, M. Desroches and S. Rodrigues
  Physica D: Nonlinear Phenomena 455: 133887, 2023.
  
• From integrator to resonator neurons: A multiple-timescale scenario     
  G. Girier, M. Desroches and S. Rodrigues
  Nonlinear Dynamics 111: 16545-16556, 2023.
  
• Single-compartment model of a pyramidal neuron, fitted to recordings with current and conductance injection     
  A. V. Chizhov, D. V. Amakhin, A. Erdem Sagtekin and M. Desroches
  Biological Cybernetics 117: 433-451, 2023.
  
• Idealized multiple-timescale model of CSD initiation and pre-epileptic hyperexcitability caused by NaV1.1/SCN1A mutations     
  L. Lemaire, M. Desroches, M. Krupa and M. Mantegazza
  Journal of Mathematical Biology 86(1): 92, 2023.
• Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of Bipolar Disorder    
  E. Pavlidis, F. Campillo, A. Goldbeter and M. Desroches
  Cognitive Neurodynamics (accepted), 2022.
• Slow passage through a Hopf-like bifurcation in piecewise linear systems: application to elliptic bursting    
  J. Penalva, M. Desroches, A. E. Teruel and C. Vich
  Chaos 32(12): 123109, 2022.
• Geometry of spiking patterns in early visual cortex: a Topological Data Analytic approach      
  A. Guidolin, M. Desroches, J. D. Victor, K. P. Purpura and S. Rodrigues
  Journal of the Royal Society Interface 19(196): 20220677, 2022.
• Cross-scale excitability in networks of quadratic integrate-and-fire neurons      
  D. Avitabile, M. Desroches and G. B. Ermentrout
  PLoS Computational Biology 18(10): e1010569, 2022.
• Interaction Mechanism Between the HSV-1 Glycoprotein B and the Antimicrobial Peptide Amyloid-β    
  K. Bourgade, (...), M. Desroches, S. Rodrigues and T. Fülöp
  Journal of Alzheimer's Disease Reports 6(1): 599-606, 2022.
  
• Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach       
  H. Taher, D. Avitabile and M. Desroches
  Nonlinear Dynamics 108: 4261-4285, 2022.
  
• A phenomenological model for interfacial water near hydrophilic polymers    
  A. Earls, M.-C. Calderer, M. Desroches, A. Zarnescu and S. Rodrigues
  Journal of Physics: Condensed Matter 34: 355102, 2022.
  
• Immunosenescence and Altered Vaccine Efficiency in Older Subjects: A Myth Difficult to Change    
  T. Fülöp, S. Rodrigues, M. Desroches et al.
  Vaccines 10(4): 10040607, 2022.
  
• Classification of bursting patterns: A tale of two ducks    
  M. Desroches, J. Rinzel and S. Rodrigues
  PLoS Computational Biology 18(2): e1009752, 2022.
  
• Initiation of migraine-related cortical spreading depolarization by hyperactivity of GABAergic neurons and NaV1.1 channels     
  O. Chever, S. Zerimech, P. Scalmani, L. Lemaire, A. Loucif, M. Ayrault, M. Krupa, M. Desroches, F. Duprat, S. Cestèle and M. Mantegazza
  The Journal of Clinical Investigation 131(21): e142203, 2021.
  
• Modeling NaV1.1/SCN1A sodium channel mutations in a microcircuit with realistic ion concentration dynamics (...)    
  L. Lemaire, M. Desroches, M. Krupa, L. Pizzamiglio, P. Scalmani and M. Mantegazza
  PLoS Computational Biology 17(7): e1009239, 2021.
  
• Hyperactivation of monocytes and macrophages in MCI patients contributes to the progression of Alzheimer's Disease    
  U. Munawara, (...), S. Rodrigues, M. Desroches and T. Fülöp
  Immunity and Ageing 18: 29, 2021.
  
• Targeting Impaired Antimicrobial Immunity in the Brain for the Treatment of Alzheimer’s Disease    
  T. Fülöp, S. Tripathi, S. Rodrigues, M. Desroches et al.
  Neuropsychiatric Disease and Treatment 17: 1311-1339, 2021.
  
• Canonical models for torus canards in elliptic bursters    
  E. Baspinar, D. Avitabile and M. Desroches
  Chaos 31(6): 063129, 2021.
  
• Spike-adding and reset-induced canard cycles in adaptive integrate and fire models    
  M. Desroches, P. Kowalczyk and S. Rodrigues
  Nonlinear Dynamics 104(3): 2451-2470, 2021.
  
• Why we should use topological data analysis in ageing: Towards defining the “topological shape of ageing”    
  T. Fülöp, M. Desroches, A. A. Cohen, F. A. N. Santos and S. Rodrigues
  Mechanisms of Ageing and Development 192: 111390, 2020.
  
• Inflection, canards and folded singularities in excitable systems – Application to a 3D FitzHugh-Nagumo model    
  J. Uria Albizuri, M. Desroches, M. Krupa and S. Rodrigues
  Journal of Nonlinear Science 30(6): 3265-3291, 2020.
  
• Targeting Infectious Agents as a Therapeutic Strategy in Alzheimer’s Disease    
  T. Fülöp, U. Munawara, A. Larbi, M. Desroches, S. Rodrigues et al.
  CNS Drugs 34(7): 673–695, 2020.
  
• Local theory for spatio-temporal canards and delayed bifurcations    
  D. Avitabile, M. Desroches, R. Veltz and M. Wechselberger
  SIAM Journal on Mathematical Analysis 52(6): 5703-5747, 2020.
  
• Canard-induced complex oscillations in an excitatory network    
  E. Köksal-Ersöz, M. Desroches, A. Guillamon, J. Rinzel and J. Tabak
  Journal of Mathematical Biology 80(7): 2075-2107, 2020.
  
• Modeling cortical spreading depression induced by the hyperactivity of interneurons    
  M. Desroches, O. Faugeras, M. Krupa and M. Mantegazza
  Journal of Computational Neuroscience 47(2-3): 125-140, 2019.
  
• Conductance-Based Refractory Density Approach for a Population of Bursting Neurons    
  A. Chizhov, F. Campillo, M. Desroches, A. Guillamon and S. Rodrigues
  Bulletin of Mathematical Biology 81(10): 4124-4143, 2019.
  
• Metastable resting state brain dynamics    
  P. beim Graben, A. Jimenez-Marin, I. Diez, J. M. Cortes, M. Desroches and S. Rodrigues
  Frontiers in Computational Neuroscience 13: 62, 2019.
  
• Parabolic bursting, spike-adding, dips and slices in a minimal model    
  M. Desroches, J.-P. Françoise and M. Krupa
  Mathematical Modelling of Natural Phenomena 14(4), 2019.
  
• Anticipation via canards in excitable systems    
  E. Köksal-Ersöz, M. Desroches, C. Mirasso and S. Rodrigues
  Chaos 29(1): 013111, 2019.
  
• Spike-adding in a canonical three time scale model: superslow explosion & folded-saddle canards    
  M. Desroches and V. Kirk
  SIAM Journal on Applied Dynamical Systems 17(3): 1989-2017, 2018.
  
• Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system    
  D. Avitabile, M. Desroches, E. Knobloch and M. Krupa
  Proceedings of the Royal Society A 473(2207): 20170018, 2017.
  
• Spatio-temporal canards in neural field equations    
  D. Avitabile, M. Desroches and E. Knobloch
  Physical Review E 95(4): 042205, 2017.
  
• Synchronization of weakly coupled canard oscillators    
  E. Köksal-Ersöz, M. Desroches and M. Krupa
  Physica D: Nonlinear Phenomena 349: 46-61, 2017.
  
• A modular architecture for transparent computation in recurrent neural networks    
  G. Carmantini, P. beim Graben, M. Desroches and S. Rodrigues
  Neural Networks 85(1): 85-105, 2017.
  
• Canards, folded nodes and mixed-mode oscillations in piecewise-linear slow-fast systems    
  M. Desroches, A. Guillamon, E. Ponce, R. Prohens, S. Rodrigues and A. E. Teruel
  SIAM Review 58(4): 653-691, 2016.
  
• Time-coded neurotransmitter release at excitatory and inhibitory synapses    
  S. Rodrigues*, M. Desroches*, M. Krupa*, J. M. Cortes, T. J. Sejnowski and A. B. Ali*      (* joint first author)
  Proceedings of the National Academy of Sciences of the USA 113(8): E1108-E1115, 2016.
  
• Spike-adding in parabolic bursters: the role of folded-saddle canards    
  M. Desroches, M. Krupa and S. Rodrigues
  Physica D: Nonlinear Phenomena 331: 58-70, 2016.
  
• Slow-fast transitions to seizure states in the Wendling-Chauvel neural mass model    
  M. Desroches, O. Faugeras and M. Krupa
  Opera Medica & Physiologica 2(3): 228--234, 2016.
  
• Canards in a minimal piecewise-linear square-wave burster    
  M. Desroches, S. Fernández-García and M. Krupa
  Chaos 26(7): 073111, 2016.
  
• Canard-mediated (de)synchronisation in coupled phantom bursters    
  E. Köksal-Ersöz, M. Desroches, M. Krupa and F. Clément
  SIAM Journal on Applied Dynamical Systems 15(1): 580-608, 2016.
  
• From canards of folded singularities to torus canards in a forced van der Pol equation    
  J. Burke, M. Desroches, A. Granados, T. J. Kaper, M. Krupa and T. Vo
  Journal of Nonlinear Science 26(2): 405-451, 2016.
  
• Canard solutions in planar piecewise linear systems with three zones    
  S. Fernández-García, M. Desroches, M. Krupa and A. E. Teruel
  Dynamical Systems: An International Journal 31(2): 173-197, 2015.
  
• Extending the zero-derivative principle for slow-fast dynamical systems    
  E. Benoît, M. Brøns, M. Desroches and M. Krupa
  Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 66(5): 2255-2270, 2015.
  
• A multiple timescale coupling of piecewise-linear oscillators. Application to a neuroendocrine system    
  S. Fernández-García, M. Desroches, M. Krupa and F. Clément
  SIAM Journal on Applied Dynamical Systems 14(2): 643-673, 2015.
  
• Noise-induced Canard and Mixed-Mode Oscillations in Large-Scale Stochastic Networks    
  J. Touboul, M. Krupa and M. Desroches
  SIAM Journal on Applied Mathematics 75(5): 2024-2049, 2015.
  
• Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model    
  M. Brøns, M. Desroches and M. Krupa
  Mathematical Population Studies 22(5): 71-79, 2015.
  
• On the dynamics of the Adenylate Energy System: Homeorhesis vs Homeostasis    
  I. M. De la Fuente, J. M. Cortes, E. Valero, M. Desroches, S. Rodrigues, I. Malaina and L. Martinez
  PLoS one 9(10): e108676, 2014.
  
• Mixed-Mode Bursting Oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster     
  M. Desroches, T. J. Kaper and M. Krupa
  Chaos 23(4): 046106, 2013.
  
• Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics    
  J. M. Cortes*, M. Desroches*, S. Rodrigues*, R. Veltz, M. A. Muñoz and T. J. Sejnowski      (* joint first author)
  Proceedings of the National Academy of Sciences of the USA 110(41): 16610-16615, 2013.
  
• Numerical continuation techniques for planar slow-fast systems    
  P. De Maesschalck and M. Desroches
  SIAM Journal on Applied Dynamical Systems 12(3): 1159-1180, 2013.
  
• A method for the reconstruction of unknown non-monotonic growth functions in the chemostat    
  J. Sieber, A. Rapaport, S. Rodrigues and M. Desroches
  Bioprocess and Biosystems Engineering 36(10): 1497-1507, 2013.
  
• Canards in piecewise-linear systems: explosions and super-explosions    
  M. Desroches, E. Freire, S. J. Hogan, E. Ponce and P. Thota
  Proceedings of the Royal Society A 469(2154): 20120603, 2013.
  
• Inflection, canards and excitability threshold in neuronal models    
  M. Desroches, M. Krupa and S. Rodrigues
  Journal of Mathematical Biology 67(4): 989-1017, 2013.
  
• Mixed-mode oscillations in a multiple time scale phantom bursting system    
  M. Krupa, A. Vidal, M. Desroches and F. Clément
  SIAM Journal on Applied Dynamical Systems 11(4): 1458-1498, 2012.
  
• On the numerical continuation of isolas of equilibria    
  D. Avitabile, M. Desroches and S. Rodrigues
  International Journal of Bifurcation and Chaos 22(11): 1250277, 2012.
  
• Spike-adding and codimension-two homoclinic bifurcations in the Hindmarsh-Rose burster    
  D. Linaro, A. R. Champneys, M. Desroches and M. Storace
  SIAM Journal on Applied Dynamical Systems 11(3): 939-962, 2012.
  
• Mixed-mode oscillations with multiple time scales    
  M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga and M. Wechselberger
  SIAM Review 54(2): 211-288, 2012.
  
• Canards of mixed type in a neural burster    
  M. Desroches, J. Burke, T. J. Kaper and M. A. Kramer
  Physical Review E 85(2): 021920, 2012.
  
• A showcase of torus canards in neuronal bursters    
  J. Burke, M. Desroches, A. M. Barry, T. J. Kaper and M. A. Kramer
  The Journal of Mathematical Neuroscience 2: 3, 2012.
  
• Canard and curvature: the “smallness of ε” in slow-fast dynamics  
  M. Desroches and M. R. Jeffrey
  Proceedings of the Royal Society A 467(2132): 2404-2421, 2011.
  
• Canard and curvature: nonsmooth approximation by pinching  
  M. Desroches and M. R. Jeffrey
  Nonlinearity 24(5): 1655-1682, 2011.
  
• Canard cycles in aircraft ground dynamics  
  J. Rankin, M. Desroches, B. Krauskopf and M. Lowenberg
  Nonlinear Dynamics 66(4): 681-688, 2011.
  
• Numerical continuation of canard orbits in slow-fast dynamical systems  
  M. Desroches, B. Krauskopf and H. M. Osinga
  Nonlinearity 23(3): 739-765, 2010.
  
• The geometry of mixed-mode oscillations in the Olsen model for the Peroxidase-Oxidase reaction  
  M. Desroches, B. Krauskopf and H. M. Osinga
  Discrete and Continuous Dynamical Systems - S 2(4): 807-827, 2009.
  
• The geometry of slow manifolds near a folded node  
  M. Desroches, B. Krauskopf and H. M. Osinga
  SIAM Journal on Applied Dynamical Systems 7(4): 1131-1162, 2008.
  
• Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system  
  M. Desroches, B. Krauskopf and H. M. Osinga
  Chaos 18(1): 015107, 2008.
  

Book chapters

• Infection, Neuroinflammation and Interventions for Healthy Brain and Longevity    
  T. Fülöp, C. Ramassamy, G. Lacombe, E. H. Frost, A. A. Cohen, S. Rodrigues, M. Desroches, K. Hirokawa, B. Laurent and J. M. Witkowski
  In: Brain and Mental Health in Ageing
  G. Kaur and S. I. S. Rattan, Eds., Springer, 2024, pp. 255--275.
  
• Piecewise-linear (PWL) canard dynamics : Simplifying singular perturbation theory in the canard regime using piecewise-linear systems    
  M. Desroches, S. Fernández-García, M. Krupa, R. Prohens and A. E. Teruel
  In: Nonlinear Systems, Vol. 1 : Mathematical Theory and Computational Methods
  V. Carmona, J. Cuevas-Maraver, F. Fernández-Sánchez and E. García-Medina, Eds., Springer, 2018, pp. 67--86.
  


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Proceedings papers

• Turing computation with recurrent artificial neural networks
  G. Carmantini, P. beim Graben, M. Desroches and S. Rodrigues
  NIPS workshop -- Cognitive Computation: Integrating Neural and Symbolic Approaches, Montréal (Canada), December 2015.
• Canard-induced loss of stability across a homoclinic bifurcation
  M. Desroches, J.-P. Françoise and L. Mégret
  ARIMA, Volume 20, Colloquium in honor of Éric Benoît (La Rochelle, France, 16-18 December 2013), 2015, pp. 47--62.
• Extremum Seeking Via Continuation Techniques for Optimizing Biogas Production in the Chemostat
  A. Rapaport, J. Sieber, S. Rodrigues and M. Desroches
  NOLCOLS 2013, 9th IFAC Symposium on Nonlinear Control Systems, Toulouse (France), September 2013.
• A new method for the reconstruction of unknown non-monotonic growth functions in the chemostat
  J. Sieber, A. Rapaport, S. Rodrigues and M. Desroches
  Proceedings of the IEEE Mediterranean Conference on Control and Automation (MED), Barcelona (Spain), July 2012.
• Numerical continuation of isolas of equilibria
  D. Avitabile, M. Desroches and S. Rodrigues
  7th European Nonlinear Oscillations Conference (ENOC), Rome (Italy), July 2011.
• Numerical continuation of canard-like orbits in piecewise-linear dynamical systems
  P. Thota and M. Desroches
  7th European Nonlinear Oscillations Conference (ENOC), Rome (Italy), July 2011.


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Other Publications

• Building Bridges through Science  
  T. Lissek et al.
  Neuron 96(4): 730-735, 2017.
  


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Theses

• Complex oscillations with multiple timescales - Application to neuronal dynamics   
  Habilitation thesis (HDR), Université Pierre et Marie Curie (Paris, France), 2015.
  
• Numerical continuation methods for slow-fast dynamical systems  
  PhD thesis, University of Bristol (UK), 2009.
  


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Preprints

• GABAergic neurons can facilitate the propagation of cortical spreading depolarization: experiments in mouse neocortical slices and a novel neural field computational model  
  E. Baspinar, M. Simonti, H. Srour, M. Desroches, D. Avitabile and M. Mantegazza
  Submitted preprint, 2024.
  
• Modeling impairment of ionic regulation with extended Adaptive Exponential integrate-and-fire models  
  D. Depannemaecker, F. Tesler, M. Desroches, V. Jirsa, and A. Destexhe
  Submitted preprint, 2024.
  
• Complex excitability and "flipping" of granule cells: an experimental and computational study  
  J. Danielewicz, G. Girier, A. Chizhov, M. Desroches, J. M. Encinas and S. Rodrigues
  Submitted preprint, 2024.
  
• Observing hidden neuronal states in experiments  
  D. Amakhin, A. Chizhov, G. Girier, M. Desroches, J. Sieber and S. Rodrigues
  Submitted preprint, 2024.
  


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