Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The existence of localized vegetation patterns in a systematically
  reduced model for dryland vegetation   In this paper we consider the 2-component reaction-diffusion model that was
recently obtained by a systematic reduction of the 3-component Gilad et al.
model for dryland ecosystem dynamics. The nonlinear structure of this model is
more involved than other more conceptual models, such as the extended
Klausmeier model, and the analysis a priori is more complicated. However, the
present model has a strong advantage over these more conceptual models in that
it can be more directly linked to ecological mechanisms and observations.
Moreover, we find that the model exhibits a richness of analytically tractable
patterns that exceeds that of Klausmeier-type models. Our study focuses on the
4-dimensional dynamical system associated with the reaction-diffusion model by
considering traveling waves in 1 spatial dimension. We use the methods of
geometric singular perturbation theory to establish the existence of a
multitude of heteroclinic/homoclinic/periodic orbits that `jump' between
(normally hyperbolic) slow manifolds, representing various kinds of localized
vegetation patterns. The basic 1-front invasion patterns and 2-front spot/gap
patterns that form the starting point of our analysis have a direct ecological
interpretation and appear naturally in simulations of the model. By exploiting
the rich nonlinear structure of the model, we construct many multi-front
patterns that are novel, both from the ecological and the mathematical point of
view. In fact, we argue that these orbits/patterns are not specific for the
model considered here, but will also occur in a much more general (singularly
perturbed reaction-diffusion) setting. We conclude with a discussion of the
ecological and mathematical implications of our findings.

5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th