Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of twisted states in the Kuramoto model on Cayley and random
  graphs   The Kuramoto model (KM) of coupled phase oscillators on complete, Paley, and
Erdos-Renyi (ER) graphs is analyzed in this work. As quasirandom graphs, the
complete, Paley, and ER graphs share many structural properties. For instance,
they exhibit the same asymptotics of the edge distributions, homomorphism
densities, graph spectra, and have constant graph limits. Nonetheless, we show
that the asymptotic behavior of solutions in the KM on these graphs can be
qualitatively different. Specifically, we identify twisted states, steady state
solutions of the KM on complete and Paley graphs, which are stable for one
family of graphs but not for the other. On the other hand, we show that the
solutions of the IVPs for the KM on complete and random graphs remain close on
finite time intervals, provided they start from close initial conditions and
the graphs are sufficiently large. Therefore, the results of this paper
elucidate the relation between the network structure and dynamics in coupled
nonlinear dynamical systems. Furthermore, we present new results on
synchronization and stability of twisted states for the KM on Cayley and random
graphs.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an