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SUMMARY:Nonlinear non-local Fokker-Planck equations modelling networks of 
 integrate and fire neurons at the mesoscopic scale - Pierre Roux (Universi
 ty of Oxford)
DTSTART:20220428T133000Z
DTEND:20220428T143000Z
UID:TALK171890@talks.cam.ac.uk
DESCRIPTION:The emergence of patterned activity in a neural network are ke
 y processes in human and animal brains. However\, since they often arise f
 rom the interplay between a large number of cells\, these mechanisms are v
 ery difficult to encompass whithout the use of simple\, consistent and sel
 f-contained mathematical models. In this talk\, I shall present some nonli
 near partial differential models obtained from mean-field techniques appli
 ed to particle systems. I will be focussing in particular on the so-called
  Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model (a non-linear non-
 local Fokker-Planck-type equation) for which we have\, my collaborators an
 d myself\, obtained some new results and insights about the convergence to
  stationary states (desynchronisation)\, the emergence and the shape of pe
 riodic self-sustained oscillations and the finite-time blow-up (synchronis
 ation).
LOCATION:Seminar Room 1\, Newton Institute
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