Paper Info
Title
One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise
Abstract
Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fireneurons such as the Izhikevich, adapting exponential, and quartic integrate-and-fire, among others.Unfortunately, the mean-field systems have a degree of frequency error, and the networks analyzed often do notinclude noise when there is adaptation. Here, we derive a one-dimensional partial differential equation (PDE)approximation for the marginal voltage density under a first order moment closure for coupled networks ofintegrate-and-fire neurons with white noise inputs. The PDE has substantially less frequency error than themean-field system and provides a great deal more information, at the cost of analytical tractability. Theconvergence properties of the mean-field system in the low noise limit are elucidated. A novel method for theanalysis of the stability of the asynchronous tonic firing solution is also presented and implemented. Unlikein previous attempts at stability analysis with these network types, information about the marginal densities ofthe adaptation variables is used. This method can in principle be applied to other systems with nonlinear PDEs.
Year
DOI
Venue
2015
10.1137/140995738
SIAM Journal of Applied Mathematics
Keywords
Field
DocType
neural networks,population density equations,bifurcation analysis,moment-closure reductions,mean-field systems
Convergence (routing),Mathematical optimization,Exponential function,Nonlinear system,Moment closure,Mathematical analysis,White noise,Quartic function,Artificial neural network,Partial differential equation,Mathematics
Journal
Volume
Issue
ISSN
75
5
0036-1399
Citations 
PageRank 
References 
5
0.41
21
Authors
3
Name
Order
Citations
PageRank
wilten nicola1303.36
Cheng Ly2193.50
sue ann campbell335465.15