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SUMMARY:Beyond Blow-Up for Nonlinear Noisy Leaky Integrate and Fire neuron
 al models: numerical  approach to the &quot\;plateau&quot\; state - Alejan
 dro Ramos-lora (University of Granada)
DTSTART:20220127T133000Z
DTEND:20220127T143000Z
UID:TALK168878@talks.cam.ac.uk
CONTACT:Daniel Boutros
DESCRIPTION:The Nonlinear Noisy Leaky Integrate and Fire neuronal models a
 re mathematical models that describe the activity of neural networks. Thes
 e models have been studied at a microscopic level\, using Stochastic Diffe
 rential Equations\, and at a mesoscopic/macroscopic level\, through the me
 an field limits using Fokker-Planck type equa-\ntions. To advance in the u
 nderstanding of the NNLIF models\, we have analyzed in depth the behaviour
  of the classical and physical solutions of the Stochastic Differential\nE
 quations and we compare it with what is already known about the Fokker-Pla
 nck equation\, using a numerical study of their particle systems. This all
 ows us to under-\nstand what happens in the neural network when an explosi
 on occurs in finite time\, which is one of the most important open problem
 s about this kind of models. This\nallows us to go beyond the mesoscopic/m
 acroscopic description. We answer one of the\nmost important open question
 s about these models: what happens after all the neurons in the network fi
 re at the same time? We find that the neural network converges towards its
  unique steady state\, if the system is weakly connected. Otherwise\, its 
 behaviour is more complex\, tending towards a stationary state or a “pla
 teau” distribution (membrane potentials are uniformly distributed betwee
 n reset and threshold values). To our knowledge\, these distributions have
  not been described before for these nonlinear\nmodels.
LOCATION:Venue to be confirmed
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