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


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


For Omega not a rational number, the trajectory is quasiperiodic.

See also

Chaos, Quasiperiodic Function

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Cite this as:

Weisstein, Eric W. "Mode Locking." From MathWorld--A Wolfram Web Resource.

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