  A topological argument is constructed and applied to explain subharmonic mode
locking in a system of coupled oscillators with inertia. Via a series of
transformations, the system is shown to be described by a classical XY model
with periodic bond angles, which is in turn mapped onto a tight-binding
particle in a periodic gauge field. It is then revealed that subharmonic
quantization of the average phase velocity follows as a manifestation of
topological invariance. Ubiquity of multistability and associated hysteresis
are also pointed out.
