Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic Determination of the Critical Coupling for Oscillators in a
  Ring   We study a model of coupled oscillators with bidirectional first nearest
neighbours coupling with periodic boundary conditions. We show that a stable
phase-locked solution is decided by the oscillators at the borders between the
major clusters, which merge to form a larger one of all oscillators at the
stage of complete synchronization. We are able to locate these four oscillators
as well as the size of major clusters in the vicinity of the stage of full
synchronization which we show to depend only on the set of initial frequencies.
Using the method presented here, we are able to obtain an analytic form of the
critical coupling, at which the complete synchronization state occurs.

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The categories of this paper are: math
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci