Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mesa-type patterns in the one-dimensional Brusselator and their
  stability   The Brusselator is a generic reaction-diffusion model for a tri-molecular
chemical reaction. We consider the case when the input and output reactions are
slow. In this limit, we show the existence of $K$-periodic, spatially bi-stable
structures, \emph{mesas}, and study their stability. Using singular
perturbation techniques, we find a threshold for the stability of $K$ mesas.
This threshold occurs in the regime where the exponentially small tails of the
localized structures start to interact. By comparing our results with Turing
analysis, we show that in the generic case, a Turing instability is followed by
a slow coarsening process whereby logarithmically many mesas are annihilated
before the system reaches a steady equilibrium state. We also study a
``breather''-type instability of a mesa, which occurs due to a Hopf
bifurcation. Full numerical simulations are shown to confirm the analytical
results.

20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph