Mode Locking

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for strong couplings between natural and forcing oscillation frequencies.

The phenomenon can be exemplified in the circle map when, after  iterations of the map, the new angle differs from the initial value by a rational number

This is the form of the unperturbed circle map with the map winding number

For  not a rational number, the trajectory is quasiperiodic.