Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological synchronization: explosive transition and rhythmic phase   Topological signals defined on nodes, links and higher dimensional simplices
define the dynamical state of a network or of a simplicial complex. As such,
topological signals are attracting increasing attention in network theory,
dynamical systems, signal processing and machine learning. Topological signals
defined on the nodes are typically studied in network dynamics, while
topological signals defined on links are much less explored. Here we
investigate topological synchronization, describing locally coupled topological
signals defined on the nodes and on the links of a network, and treated using
the recently proposed topological Dirac operator. The dynamics of signals
defined on the nodes is affected by a phase lag depending on the dynamical
state of nearby links and vice versa, the dynamics of topological signals
defined on the links is affected by a phase lag depending on the dynamical
state of nearby nodes. We show that topological synchronization on a fully
connected network is explosive with an hysteresis loop characterized by a
discontinuous forward transition and a continuous backward transition. The
analytical investigation of the phase diagram provides a theoretical
understanding of this topological explosive synchronization. The model also
displays an exotic coherent synchronized phase, also called rhythmic phase,
characterized by non-stationary order parameters which can shed light on
topological mechanisms for the emergence of brain rhythms.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess