Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A general framework for stochastic traveling waves and patterns, with
  application to neural field equations   In this paper we present a general framework in which to rigorously study the
effect of spatio-temporal noise on traveling waves and stationary patterns. In
particular the framework can incorporate versions of the stochastic neural
field equation that may exhibit traveling fronts, pulses or stationary
patterns. To do this, we first formulate a local SDE that describes the
position of the stochastic wave up until a discontinuity time, at which point
the position of the wave may jump. We then study the local stability of this
stochastic front, obtaining a result that recovers a well-known deterministic
result in the small-noise limit. We finish with a study of the long-time
behavior of the stochastic wave.

33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th