Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transitions in a Logistic Metapopulation Model with Nonlocal
  Interactions   The presence of one or more species at some spatial locations but not others
is a central matter in ecology. This phenomenon is related to ecological
pattern formation. Nonlocal interactions can be considered as one of the
mechanisms causing such a phenomenon. We propose a single-species, continuous
time metapopulation model taking nonlocal interactions into account. Discrete
probability kernels are used to model these interactions in a patchy
environment. A linear stability analysis of the model shows that solutions to
this equation exhibit pattern formation if the dispersal rate of the species is
sufficiently small and the discrete interaction kernel satisfies certain
conditions. We numerically observe that traveling and stationary wave type
patterns arise near critical dispersal rate. We use weakly nonlinear analysis
to better understand the behavior of formed patterns. We show that observed
patterns arise through both supercritical and subcritical bifurcations from
spatially homogeneous steady state. Moreover, we observe that as the dispersal
rate decreases, amplitude of the patterns increases. For discontinuous
transitions to instability, we also show that there exists a threshold for the
amplitude of the initial condition, above which pattern formation is observed.

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg