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Synchronization of Heterogeneous Kuramoto Oscillators with Arbitrary Topology
We study synchronization of coupled Kuramoto oscillators with heterogeneous
inherent frequencies and general underlying connectivity. We provide conditions
on the coupling strength and the initial phases which guarantee the existence
of a Positively Invariant Set (PIS) and lead to synchronization. Unlike
previous works that focus only on analytical bounds, here we introduce an
optimization approach to provide a computational-analytical bound that can
further exploit the particular features of each individual system such as
topology and frequency distribution. Examples are provided to illustrate our
results as well as the improvement over previous existing bounds
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