Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience

The Noisy Integrate-and-Fire equation is a standard non-linear Fokker-Planck equation used to describe the activity of a homogeneous neural network characterized by its connectivity b (each neuron connected to all others through synaptic weights); b  >  0 describes excitatory networks and b  ...

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Bibliographic Details
Published in:Nonlinearity 2015-09, Vol.28 (9), p.3365-3388
Main Authors: Antonio Carrillo, José, Perthame, Benoît, Salort, Delphine, Smets, Didier
Format: Article
Language:English
Subjects:
Analysis of PDEs
blow-up
Excitation
Fires
Fokker-Planck equation
global existence
Mathematical analysis
Mathematical models
Mathematics
Networks
neural network
Neural networks
Neurons
Nonlinearity
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Summary:The Noisy Integrate-and-Fire equation is a standard non-linear Fokker-Planck equation used to describe the activity of a homogeneous neural network characterized by its connectivity b (each neuron connected to all others through synaptic weights); b  >  0 describes excitatory networks and b  
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/9/3365