Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase models and clustering in networks of oscillators with delayed
  coupling   We consider a general model for a network of oscillators with time delayed,
circulant coupling. We use the theory of weakly coupled oscillators to reduce
the system of delay differential equations to a phase model where the time
delay enters as a phase shift. We use the phase model to study the existence
and stability of cluster solutions. Cluster solutions are phase locked
solutions where the oscillators separate into groups. Oscillators within a
group are synchronized while those in different groups are phase-locked. We
give model independent existence and stability results for symmetric cluster
solutions. We show that the presence of the time delay can lead to the
coexistence of multiple stable clustering solutions. We apply our analytical
results to a network of Morris Lecar neurons and compare these results with
numerical continuation and simulation studies.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph