Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toric Differential Inclusions and a Proof of the Global Attractor
  Conjecture   The global attractor conjecture says that toric dynamical systems (i.e., a
class of polynomial dynamical systems on the positive orthant) have a globally
attracting point within each positive linear invariant subspace -- or,
equivalently, complex balanced mass-action systems have a globally attracting
point within each positive stoichiometric compatibility class. A proof of this
conjecture implies that a large class of nonlinear dynamical systems on the
positive orthant have very simple and stable dynamics. The conjecture
originates from the 1972 breakthrough work by Fritz Horn and Roy Jackson, and
was formulated in its current form by Horn in 1974. We introduce toric
differential inclusions, and we show that each positive solution of a toric
differential inclusion is contained in an invariant region that prevents it
from approaching the origin. We use this result to prove the global attractor
conjecture. In particular, it follows that all detailed balanced mass action
systems and all deficiency zero weakly reversible networks have the global
attractor property.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th