Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect cycles in the synchronous Heider dynamics in complete network   We discuss a cellular automaton simulating the process of reaching Heider
balance in a fully connected network. The dynamics of the automaton is defined
by a deterministic, synchronous and global update rule. The dynamics has a very
rich spectrum of attractors including fixed points and limit cycles, the length
and number of which change with the size of the system. In this paper we
concentrate on a class of limit cycles that preserve energy spectrum of the
consecutive states. We call such limit cycles perfect. Consecutive states in a
perfect cycle are separated from each other by the same Hamming distance. Also
the Hamming distance between any two states separated by $k$ steps in a perfect
cycle is the same for all such pairs of states. The states of a perfect cycle
form a very symmetric trajectory in the configuration space. We argue that the
symmetry of the trajectories is rooted in the permutation symmetry of vertices
of the network and a local symmetry of a certain energy function measuring the
level of balance/frustration of triads.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex