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H 2 Around a Fokker-Planck equation modeling neuronal networks

Auteurs : Salort, Delphine (Auteur de la Conférence)
CIRM (Editeur )

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neuronal network mean field model Fokker-Planck equation blow-up and existence of solution uniform estimates asymptotic dynamic entropy inequalities maximum principle smoothing effect questions

Résumé : In this talk, I will focus on a Fokker-Planck equation modeling interacting neurons in a network where each neuron is governed by an Integrate and Fire dynamic type. When the network is excitatory, neurons that discharge, instantaneously increased the membrane potential of the neurons of the network with a speed which is proportional to the amplitude of the global activity of the network. The self-excitable nature of these neurons in the case of excitatory networks leads to phenomena of blow-up, once the proportion of neurons that are close to their action potential is too high. In this talk, we are interested in understanding the regimes where solutions globally exist. By new methods of entropy and upper-solution, we give criteria where the phenomena of blow-up can not appear and specify, in some cases, the asymptotic behavior of the solution.

integrate-and-fire - neural networks - Fokker-Planck equation - blow-up

Codes MSC :
82C32 - Neural nets
92B20 - Neural networks, artificial life and related topics
35Q84 - Fokker-Planck equations

    Informations sur la Vidéo

    Langue : Français
    Date de publication : 08/01/15
    Date de captation : 11/12/14
    Collection : Research talks ; Partial Differential Equations ; Mathematics in Science and Technology
    Format : QuickTime (.mov) Durée : 00:50:50
    Domaine : PDE ; Mathematics in Science & Technology
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2014-12-11_Salort.mp4

Informations sur la rencontre

Nom de la rencontre : LEM2I international conference / Colloque international du LEM2I
Organisateurs de la rencontre : Benabdallah, Assia ; Dehman, Belhassen ; Dermenjian, Yves ; Lebeau, Gilles ; Pardoux, Etienne
Dates : 08/12/14 - 12/12/14
Année de la rencontre : 2014
URL Congrès : http://lem2i-2014.sciencesconf.org/

Citation Data

DOI : 10.24350/CIRM.V.18652103
Cite this video as: Salort, Delphine (2014). Around a Fokker-Planck equation modeling neuronal networks. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18652103
URI : http://dx.doi.org/10.24350/CIRM.V.18652103

Bibliographie

  • Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with long firing rates. Neural Computation, 11(7), 1621–1671 - http://dx.doi.org/doi:10.1162/089976699300016179

  • Caceres, M.J., & Perthame, B. (2014). Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity. Journal of Theoretical Biology, 350, 81–89. <10.1016/j.jtbi.2014.02.005>. - http://hal.upmc.fr/hal-00874746

  • Caceres, M.J., Carrillo, J.A., & Perthame, B. (2011). Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states, Journal of Mathematical Neuroscience, 1:7 - http://dx.doi.org/10.1186/2190-8567-1-7

  • Carrillo, J.A., Perthame, B., Salort, D., & Smets, D. (2014). Qualitative properties of solutions for the noisy integrate & fire model in computational neuroscience. - https://hal.archives-ouvertes.fr/hal-01079381

  • Carrillo, J.A., Gonzalez, M.d.M., Gualdani, M.P., & Schonbek, M.E. (2013). Classical solutions for a nonlinear Fokker-Planck equation arising in computational neuroscience. Communications in Partial Differential Equations, 38(1-3), 385–409 - http://dx.doi.org/10.1080/03605302.2012.747536

  • Delarue, F., Inglis, J., Rubenthaler, S., & Tanré, E. (2014) Global solvability of a networked integrate-and-fire model of McKean-Vlasov type. - https://hal.inria.fr/hal-00747565



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