Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilibrium and surviving species in a large Lotka-Volterra system of
  differential equations   Lotka-Volterra (LV) equations play a key role in the mathematical modeling of
various ecological, biological and chemical systems. When the number of species
(or, depending on the viewpoint, chemical components) becomes large, basic but
fundamental questions such as computing the number of surviving species still
lack theoretical answers. In this paper, we consider a large system of LV
equations where the interactions between the various species are a realization
of a random matrix. We provide conditions to have a unique equilibrium and
present a heuristics to compute the number of surviving species. This
heuristics combines arguments from Random Matrix Theory, mathematical
optimization (LCP), and standard extreme value theory. Numerical simulations,
together with an empirical study where the strength of interactions evolves
with time, illustrate the accuracy and scope of the results.

26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc