Arnold Tongues

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

K

between

0

and

4π

, versus the driving phase

Ω

from

0

to

1

.

Details

The circle map is given by

θ

n+1

=

θ

n

+Ω-

K

2π

sin(2π

θ

n

)

,

where

θ

n+1

is computed mod 1 and

K

is a constant.

External Links

Circle Map (Wolfram MathWorld)

Arnold Tongue (Wolfram MathWorld)

Map Winding Number (Wolfram MathWorld)

Mode Locking (Wolfram MathWorld)

Permanent Citation

Enrique Zeleny

"Arnold Tongues"
http://demonstrations.wolfram.com/ArnoldTongues/
Wolfram Demonstrations Project
Published: May 31, 2013