Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The impact of advection on the stability of stripes on lattices near
  planar Turing instabilities   Striped patterns are known to bifurcate in reaction-diffusion systems with
differential isotropic diffusions at a supercritical Turing instability. In
this paper we study the impact of weak anisotropy by directional advection on
the stability of stripes with respect to various lattice modes, and the role of
quadratic terms therein. We focus on the generic form of planar
reaction-diffusion systems with two components near such a bifurcation. Using
centre manifold reduction we derive a rigorous parameter expansion for the
critical eigenvalues for lattice mode perturbations, specifically nearly square
and nearly hexagonal ones. This provides detailed formulae for the loci of
stability boundaries under the influence of the advection and quadratic terms.
In particular, the well known destabilising effect of quadratic terms can be
counterbalanced by advection, which leads to intriguing arrangements of
stability boundaries. We illustrate these results numerically by a specific
example. Finally, we show numerical computations of these stability boundaries
in the extended Klausmeier model for vegetation patterns and show stripes
bifurcate stably in the presence of sufficiently strong advection.

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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ