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 $q$ iterations of the map, the new angle differs from the initial value by a Rational Number

$$\theta_{n+q} = \theta_n+{p\over q}.$$

This is the form of the unperturbed Circle Map with the Winding Number

$$\Omega={p\over q}.$$

For $\Omega$ not a Rational Number, the trajectory is Quasiperiodic.

See also Chaos, Quasiperiodic Function