  The Kuramoto model is a system of nonlinear differential equations that
models networks of coupled oscillators and is often used to study
synchronization among the oscillators. In this paper we study steady state
solutions of the Kuramoto model by assigning to each steady state a tuple of
integers which records how the state twists around the cycles in the network.
We then use this new classification of steady states to obtain a "Weyl" type of
asymptotic estimate for the number of steady states as the number of
oscillators becomes arbitrarily large while preserving the cycle structure. We
further show how this asymptotic estimate can be maximized, and as a special
case we obtain an asymptotic lower bound for the number of stable steady states
of the model.
