Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple and Superlattice Turing Patterns in Reaction-Diffusion Systems:
  Bifurcation, Bistability, and Parameter Collapse   This paper investigates the competition between both simple (e.g. stripes,
hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns
in two-component reaction-diffusion systems. ``Superlattice'' patterns are
formed from eight or twelve Fourier modes, and feature structure at two
different length scales. Using perturbation theory, we derive simple analytical
expressions for the bifurcation equation coefficients on both rhombic and
hexagonal lattices. These expressions show that, no matter how complicated the
reaction kinectics, the nonlinear reaction terms reduce to just four effective
terms within the bifurcation equation coefficients. Moreover, at the hexagonal
degeneracy -- when the quadratic term in the hexagonal bifurcation equation
disappears -- the number of effective system parameters drops to two, allowing
a complete characterization of the possible bifurcation results at this
degeneracy. The general results are then applied to specific model equations,
to investigate the stability of different patterns within those models.

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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org