Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One-Dimensional Population Density Approaches to Recurrently Coupled
  Networks of Neurons with Noise   Mean-field systems have been previously derived for networks of coupled,
two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting
exponential (AdEx) and quartic integrate and fire (QIF), among others.
Unfortunately, the mean-field systems have a degree of frequency error and the
networks analyzed often do not include 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 of integrate-and-fire neurons with white noise inputs. The PDE has
substantially less frequency error than the mean-field system, and provides a
great deal more information, at the cost of analytical tractability. The
convergence properties of the mean-field system in the low noise limit are
elucidated. A novel method for the analysis of the stability of the
asynchronous tonic firing solution is also presented and implemented. Unlike
previous attempts at stability analysis with these network types, information
about the marginal densities of the adaptation variables is used. This method
can in principle be applied to other systems with nonlinear partial
differential equations.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol