  A complete bifurcation analysis of explicit dynamical equations for the
periodically forced Kuramoto model was performed in [L. M. Childs and S. H.
Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the
model. We show that the phase diagram predicted by this analysis is incomplete.
Our numerical analysis of the equations reveals that the model can also undergo
an abrupt phase transition from oscillations to wobbly rotations of the order
parameter under increasing field frequency or decreasing field strength. This
transition was not revealed by bifurcation analysis because it is not caused by
a bifurcation, and can neither be classified as first nor second-order since it
does not display critical phenomena characteristic of either transition. We
discuss the topological origin of this transition and show that it is
determined by a singular point in the order-parameter space.
