Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kuramoto model with additional nearest-neighbor interactions: Existence
  of a nonequilibrium tricritical point   A paradigmatic framework to study the phenomenon of spontaneous collective
synchronization is provided by the Kuramoto model comprising a large collection
of limit-cycle oscillators of distributed frequencies that are globally coupled
through the sine of their phase differences. We study here a variation of the
model by including nearest-neighbor interactions on a one-dimensional lattice.
While the mean-field interaction resulting from the global coupling favors
global synchrony, the nearest-neighbor interaction may have cooperative or
competitive effects depending on the sign and the magnitude of the
nearest-neighbor coupling. For unimodal and symmetric frequency distributions,
we demonstrate that as a result, the model in the stationary state exhibits in
contrast to the usual Kuramoto model both continuous and first-order
transitions between synchronized and incoherent phases, with the transition
lines meeting at a tricritical point. Our results are based on numerical
integration of the dynamics as well as an approximate theory involving
appropriate averaging of fluctuations in the stationary state.

16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph