Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cluster singularity: the unfolding of clustering behavior in globally
  coupled Stuart-Landau oscillators   The ubiquitous occurrence of cluster patterns in nature still lacks a
comprehensive understanding. It is known that the dynamics of many such natural
systems is captured by ensembles of Stuart-Landau oscillators. Here, we
investigate clustering dynamics in a mean-coupled ensemble of such limit-cycle
oscillators. In particular we show how clustering occurs in minimal networks,
and elaborate how the observed 2-cluster states crowd when increasing the
number of oscillators. Using persistence, we discuss how this crowding leads to
a continuous transition from balanced cluster states to synchronized solutions
via the intermediate unbalanced 2-cluster states. These cascade-like
transitions emerge from what we call a cluster singularity. At this
codimension-2 point, the bifurcations of all 2-cluster states collapse and the
stable balanced cluster state bifurcates into the synchronized solution
supercritically. We confirm our results using numerical simulations, and
discuss how our conclusions apply to spatially extended systems.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph