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Nonlinear integrate and fire neuron models: analysis and numerics

Presented by: 
JA Carrillo ICREA
Date: 
Tuesday 30th November 2010 - 14:00 to 14:45
Venue: 
INI Seminar Room 1
Seminar Series: 
Abstract: 
Abstract: Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter. This is a work in collaboration with M. J. Cáceres and B. Perthame.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons