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 $\mathrm{XY}$ 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.

• Received 10 January 2001

DOI:https://doi.org/10.1103/PhysRevB.64.014305