Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple Patterns Formation for an Aggregation/Diffusion Predator-Prey
  System   We investigate existence of stationary solutions to an aggregation/diffusion
system of PDEs, modelling a two species predator-prey interaction. In the model
this interaction is described by non-local potentials that are mutually
proportional by a negative constant $-\alpha$, with $\alpha>0$. Each species is
also subject to non-local self-attraction forces together with quadratic
diffusion effects. The competition between the aforementioned mechanisms
produce a rich asymptotic behaviour, namely the formation of steady states that
are composed of multiple bumps, i.e. sums of Barenblatt-type profiles. The
existence of such stationary states, under some conditions on the positions of
the bumps and the proportionality constant $\alpha$, is showed for small
diffusion, by using the functional version of the Implicit Function Theorem. We
complement our results with some numerical simulations, that suggest a large
variety in the possible strategies the two species use in order to interact
each other.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat