Tilted washboard potential ($V=-\omega \theta -ϵ\cos \theta$)

A periodic corrugation plus a uniform tilt. For the Adler phase equation, $V(\theta )=-\omega \theta -ϵ\cos \theta$ gives force $-V^{\prime }=\omega -ϵ\sin \theta$ and $V(\theta +2\pi )-V(\theta )=-2\pi \omega$. It has wells when $|\omega |<ϵ$ and no extrema when $|\omega |>ϵ$. It is a potential on the unwrapped phase, not a single-valued periodic potential on the circle.