Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Synchronization of Pulse-Coupled Oscillators Interacting on Cycle
  Graphs   The importance of pulse-coupled oscillators (PCOs) in biology and engineering
has motivated research to understand basic properties of PCO networks. Despite
the large body of work addressing PCOs, a global synchronization result for
networks that are more general than all-to-all connected is still unavailable.
In this paper we address global synchronization of PCO networks described by
cycle graphs. It is shown for the bidirectional cycle case that as the number
of oscillators in the cycle grows, the coupling strength must be increased in
order to guarantee synchronization for arbitrary initial conditions. For the
unidirectional cycle case, the strongest coupling cannot ensure global
synchronization yet a refractory period in the phase response curve is
sufficient to enable global synchronization. Analytical findings are confirmed
by numerical simulations.

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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th