Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronization hypothesis in the Winfree model   We consider $N$ oscillators coupled by a mean field as in the Winfree model.
The model is governed by two parameters: the coupling strength $\kappa$ and the
spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled
regime, $\kappa=0$, each oscillator possesses its own natural frequency, and
the difference between the phases of any two oscillators grows linearly in
time. We say that $N$ oscillators are synchronized if the difference between
any two phases is uniformly bounded in time. We identify a new hypothesis for
the existence of synchronization. The domain in $(\gamma,\kappa)$ of
synchronization contains coupling values that are both weak and strong.
Moreover the domain is independent of the number of oscillators and the
distribution of the frequencies. We give a numerical counter-example which
shows that this hypothesis is necessary for the existence of synchronization.

26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics