Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the dynamics of random neuronal networks   We study the mean-field limit and stationary distributions of a pulse-coupled
network modeling the dynamics of a large neuronal assemblies. Our model takes
into account explicitly the intrinsic randomness of firing times, contrasting
with the classical integrate-and-fire model. The ergodicity properties of the
Markov process associated to finite networks are investigated. We derive the
limit in distribution of the sample path of the state of a neuron of the
network when its size gets large. The invariant distributions of this limiting
stochastic process are analyzed as well as their stability properties. We show
that the system undergoes transitions as a function of the averaged
connectivity parameter, and can support trivial states (where the network
activity dies out, which is also the unique stationary state of finite networks
in some cases) and self-sustained activity when connectivity level is
sufficiently large, both being possibly stable.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci