Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

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Title:	Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states
Author:	Cáceres, María J.; Carrillo de la Plata, José Antonio; Perthame, Benoît; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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.
Subject(s):	-Xarxes neurals (Informàtica)
Rights:	open access Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús https://creativecommons.org/licenses/by-nc-nd/2.5/
Document type:	Article Prepublicació
Published by:	Centre de Recerca Matemàtica
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Uri:	https://ddd.uab.cat/record/70562