Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A prey-predator model with three interacting species   In this paper we consider a class of discrete time prey-predator models with
three interacting species defined on the two-dimensional simplex. For some
choices of parameters of the operator describing the evolution of the relative
frequencies, we show that the ergodic hypothesis does not hold. Moreover, we
prove that any order Ces\`aro mean of the trajectories diverges. For another
class of parameters, we show that all orbits starting from the interior of the
simplex converge to the unique fixed point of the operator while for the
remaining choices of parameters all orbits converge to one of the vertices of
the simplex. Contrary to many authors we study discrete time models but we
include a speed function $f$ in the dynamics which allows us to approximate the
continuous-time case arbitrarily well when $f$ is small.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex