Arnold Tongues

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Vladimir Arnold first investigated Arnold tongues in a model for kicked rotors. They are domains of stability with periodic motion around rational values for a circle map. These domains are mode-locked to an irrational driving frequency and have a constant rational winding number. A plot is shown of the coupling strength between and , versus the driving phase from to .

Contributed by: Enrique Zeleny (May 2013)
Open content licensed under CC BY-NC-SA



The circle map is given by


where is computed mod 1 and is a constant.

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