Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coupled cell networks: semigroups, Lie algebras and normal forms   We introduce the concept of a semigroup coupled cell network and show that
the collection of semigroup network vector fields forms a Lie algebra. This
implies that near a dynamical equilibrium the local normal form of a semigroup
network is a semigroup network itself. Networks without the semigroup property
will support normal forms with a more general network architecture, but these
normal forms nevertheless possess the same symmetries and synchronous solutions
as the original network. We explain how to compute Lie brackets and normal
forms of coupled cell networks and we characterize the SN-decomposition that
determines the normal form symmetry. This paper concludes with a generalization
to nonhomogeneous networks with the structure of a semigroupoid.

8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat