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SUMMARY:Nonlinear integrate and fire neuron models: analysis and numerics 
 - Carrillo\, JA (ICREA)
DTSTART:20101130T140000Z
DTEND:20101130T144500Z
UID:TALK28202@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Abstract: Nonlinear Noisy Leaky Integrate and Fire (NNLIF) mod
 els for neurons networks can be written as Fokker-Planck-Kolmogorov equati
 ons on the probability density of neurons\, the main parameters in the mod
 el being the connectivity of the network and the noise. We analyse several
  aspects of the NNLIF model: the number of steady states\, a priori estima
 tes\, blow-up issues and convergence toward equilibrium in the linear case
 . In particular\, for excitatory networks\, blow-up always occurs for init
 ial data concentrated close to the firing potential. These results show ho
 w critical is the balance between noise and excitatory/inhibitory interact
 ions to the connectivity parameter. This is a work in collaboration with M
 . J. Cceres and B.\nPerthame.\n
LOCATION:Seminar Room 1\, Newton Institute
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