Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topologically robust zero-sum games and Pfaffian orientation -- How
  network topology determines the long-time dynamics of the antisymmetric
  Lotka-Volterra equation   To explore how the topology of interaction networks determines the robustness
of dynamical systems, we study the antisymmetric Lotka-Volterra equation
(ALVE). The ALVE is the replicator equation of zero-sum games in evolutionary
game theory, in which the strengths of pairwise interactions between strategies
are defined by an antisymmetric matrix such that typically some strategies go
extinct over time. Here we show that there also exist topologically robust
zero-sum games, such as the rock-paper-scissors game, for which all strategies
coexist for all choices of interaction strengths. We refer to such zero-sum
games as coexistence networks and construct coexistence networks with an
arbitrary number of strategies. By mapping the long-time dynamics of the ALVE
to the algebra of antisymmetric matrices, we identify simple graph-theoretical
rules by which coexistence networks are constructed. Examples are
triangulations of cycles characterized by the golden ratio $\varphi =
1.6180...$, cycles with complete subnetworks, and non-Hamiltonian networks. In
graph-theoretical terms, we extend the concept of a Pfaffian orientation from
even-sized to odd-sized networks. Our results show that the topology of
interaction networks alone can determine the long-time behavior of nonlinear
dynamical systems, and may help to identify robust network motifs arising, for
example, in ecology.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an