Maître de Conférences HDR
Université d'Evry Val d'Essonne
Laboratoire de Mathématiques et Modélisation d'Évry (LaMME, UMR 8071)
Département de Mathématiques
Email : Alexandre.Vidal[at]univ-evry.fr
Les documents de présentation de la Licence de Mathématiques 2020-24 de l'UEVE sont disponibles dans la dernière section ci-dessous.
Cliquer sur les titres des sections pour montrer/cacher leur contenu.
Analyse qualitative des systèmes dynamiques, Dynamiques à plusieurs échelles de temps:
Dynamiques non-linéaire, Bifurcations, Perturbations singulières, Désingularisation, Méthodes Numériques,
Analyse dynamique des oscillations complexes, Mixed-Mode Oscillations, Bursting,
Analyse de synchronisation d'oscillateurs couplés, Réseau d'oscillateurs.
Modélisation, analyse et réduction de modèles en Sciences du Vivant :
Neurosciences, Neuro-endocrinologie, Dynamiques de Populations.
Analyse des signaux expérimentaux à l'appui de modèles.
Analyse des mécanismes biologiques induisant des dynamiques complexes.
Identification et estimation des paramètres des modèles.
A. Bandera, S. Fernandez-Garcia, M. Gomez-Marmol, A. Vidal.
Automatic Proper Orthogonal Block Decomposition method for network dynamical systems with multiple timescales.
Communications in Nonlinear Science and Numerical Simulation 131: 107844, 2024. https://doi.org/10.1016/j.cnsns.2024.107844
A. Bandera, S. Fernandez-Garcia, M. Gomez-Marmol, A. Vidal.
A Multiple Timescale Network Model of Intracellular Calcium Concentrations in Coupled Neurons: Insights from ROM Simulations.
Math. Model. Nat. Phenom. 17(11), 2022. https://doi.org/10.1051/mmnp/2022016
A. Bandera, S. Fernandez-Garcia, M. Gomez-Marmol, A. Vidal.
Numerical Simulation by ROM of a Network Model of Intracellular Calcium Concentration in Neurons.
Proc. XXVI Congress of Differential Equations and Applications, 2021 (sous presse).
O.B.K. Ali, A. Vidal, C. Grova, and H. Benali.
Glial glutamate regulation, critical determinant of whole brain physiology: a computational study.
Proc. Annual Meeting of OHBM (Organization for Human Brain Mapping), 2020. Preprint
S. Fernandez-Garcia, and A. Vidal.
Symmetric coupling of multiple timescale systems with Mixed-Mode Oscillations and synchronization.
Physica D: Nonlinear Phenomena, 401, 132129, 2020. https://doi.org/10.1016/j.physd.2019.05.009
E. Koksal, A. Vidal, and F. Clément.
Coupled multiple timescale dynamics in populations of endocrine neurons: Pulsatile and surge patterns of GnRH secretion.
SIAM Journal of Applied Dynamical Systems, 17(1):1052–1090, 2018. https://doi.org/10.1137/16M1103695
J. Rubin, J. Signerska-Rynkowska, J. Touboul, and A. Vidal.
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike adding and chaos.
Discrete and Continuous Dynamical Systems Series B, 22(10), 2017. https://dx.doi.org/10.3934/dcdsb.2017204
J. Rubin, J. Signerska-Rynkowska, J. Touboul, and A. Vidal.
Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-Mode Oscillations.
Discrete and Continuous Dynamical Systems Series B, 22(10), 2017. https://dx.doi.org/10.3934/dcdsb.2017205
A. Garnier, A. Vidal, and H. Benali.
A theoretical study on the role of astrocytic activity in neuronal hyperexcitability by a novel neuron-glia mass model.
Journal of Mathematical Neuroscience, 6(10), 2016. http://dx.doi.org/10.1186/s13408-016-0042-0
A. Garnier, A. Vidal, C. Huneau, and H. Benali.
A neural mass model with direct and indirect excitatory feedback loops: identification of bifurcations and temporal dynamics.
Neural Computation, 27:329–364, 2015. http://dx.doi.org/10.1162/NECO_a_00696
P.A. Fletcher, F. Clément, A. Vidal, J. Tabak, and R. Bertram.
Interpreting frequency responses to dose-conserved pulsatile input signals in simple cell signaling motifs.
PloS one, 9(4):e95613, 2014. http://dx.doi.org/10.1371/journal.pone.0095613
A. Garnier, C. Huneau, A. Vidal, F. Wendling, and H. Benali.
Identification of dynamical behaviors in epileptic discharges using a neural mass model with double excitatory feedbacks.
Proceedings of ICCSA 2014, Normandie University, Le Havre, France, pages 205–210, 2014. http://www.hal.inserm.fr/inserm-01154781/document
M. Krupa, A. Vidal, and F. Clément.
A network model of the periodic synchronization process in the dynamics of calcium concentration in GnRH neurons.
Journal of Mathematical Neuroscience, 3(4), 2013. http://dx.doi.org/10.1186/2190-8567-3-4
M. Krupa, A. Vidal, M. Desroches, and F. Clément.
Mixed-mode oscillations in a multiple time scale phantom bursting system.
SIAM Journal on Applied Dynamical Systems, 11:1458–1498, 2012. http://dx.doi.org/10.1137/110860136
A. Vidal, Q. Zhang, C. Médigue, St. Fabre, and F. Clément.
Dynpeak: An algorithm for pulse detection and frequency analysis in hormonal time series.
PloS one, 7(7):e39001, 2012. http://dx.doi.org/10.1371/journal.pone.0039001
A. Vidal and J.-P. Françoise.
Canard cycles in global dynamics.
International Journal of Bifurcation and Chaos, 22(02):1250026, 2012. http://dx.doi.org/10.1142/S0218127412500265
F. Clément and A. Vidal.
Foliation-based parameter tuning in a model of the GnRH pulse and surge generator.
SIAM Journal on Applied Dynamical Systems, 8(4):1591–1631, 2009. http://dx.doi.org/10.1137/080732237
A. Vidal, C. Médigue, B. Malpaux, and F. Clément.
Endogenous circannual rhythm in LH secretion: insight from signal analysis coupled with mathematical modelling.
Philosophical Transactions of the Royal Society A, 367:4759–4777, 2009. http://dx.doi.org/10.1098/rsta.2009.0136
J.-P. Françoise, C. Piquet, and A. Vidal.
Enhanced delay to bifurcation.
Bulletin of the Belgian Mathematical Society Simon Stevin, 15:825–831, 2008. http://projecteuclid.org/euclid.bbms/1228486410
A. Vidal.
Stable periodic orbits associated with bursting oscillations in population dynamics.
Lecture Notes in Control and Information Sciences, 341:439–446, 2006. https://link.springer.com/book/9783540347712