Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Waves and distributions connected to systems of interacting populations   We discuss two cases that can be connected to the dynamics of interacting
populations: (I.) density waves for the case or negligible random fluctuations
of the populations densities, and (II.) probability distributions connected to
the model equations for of spatially averaged populations densities for the
case of significant random fluctuations of the independent quantity that can be
associated with the population density. For the case (I.) we consider model
equations containing polynomial nonlinearities. Such nonlinearities can arise
as a consequence of interaction among the populations (for the case of large
population densities) or as a result of a Taylor series expansion (for the case
of small density of interacting populations). In the both cases we can apply
the modified method of simplest equation to obtain exact traveling-wave
solutions connected to migration of population members. Such solutions are
obtained for systems consisting of 1 or 3 populations respectively. For the
case (II.) we discuss model equations of the Fokker-Planck kind for the
evolution of the statistical distributions of population densities. We derive
several stationary distributions for the population density and calculate the
expected exit time connected to the extinction of the studied population.

18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph