Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the problem of synchronization of identical dynamical systems: The
  Huygens's clocks   In 1665, Christiaan Huygens reported the observation of the synchronization
of two pendulum clocks hanged on the wall of his workshop. After
synchronization, the clocks swung exactly in the same frequency and $180^{o}$
out of phase -- anti-phase synchronization. Here, we propose and analyze a new
interaction mechanism between oscillators leading to exact anti-phase and
in-phase synchronization of pendulum clocks, and we determine a sufficient
condition for the existence of an exact anti-phase synchronization state. We
show that exact anti-phase and in-phase synchronization states can coexist in
phase space, and the periods of the synchronized states are different from the
eigen-periods of the individual oscillators. We analyze the robustness of the
system when the parameters of the individual pendulum clocks are varied, and we
show numerically that exact anti-phase and in-phase synchronization states
exist in systems of coupled oscillators with different parameters.

5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int