Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spot Patterns in the 2-D Schnakenberg Model with Localized
  Heterogeneities   A hybrid asymptotic-numerical theory is developed to analyze the effect of
different types of localized heterogeneities on the existence, linear
stability, and slow dynamics of localized spot patterns for the two-component
Schnakenberg reaction-diffusion model in a 2-D domain. Two distinct types of
localized heterogeneities are considered: a strong localized perturbation of a
spatially uniform feed rate and the effect of removing a small hole in the
domain, through which the chemical species can leak out. Our hybrid theory
reveals a wide range of novel phenomena such as, saddle-node bifurcations for
quasi-equilibrium spot patterns that otherwise would not occur for a
homogeneous medium, a new type of spot solution pinned at the concentration
point of the feed rate, spot self-replication behavior leading to the creation
of more than two new spots, and the existence of a creation-annihilation
attractor with at most three spots. Depending on the type of localized
heterogeneity introduced, localized spots are either repelled or attracted
towards the localized defect on asymptotically long time scales. Results for
slow spot dynamics and detailed predictions of various instabilities of
quasi-equilibrium spot patterns, all based on our hybrid asymptotic-numerical
theory, are illustrated and confirmed through extensive full PDE numerical
simulations.

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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org