To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

# File:Circle map bifurcation.jpeg

Transferred from en.wikipedia to Commons by Maksim.

The original description page was here. All following user names refer to en.wikipedia.
Circle map showing mode-locked regions or Arnold tongues in black. Ω varies from 0 to 1 along the x-axis, and K varies from 0 at the bottom to 4π at the top.

## Summary

The image shows the en:bifurcation diagram for the iterated en:circle map. The circle map is given by iterating on the map

${\displaystyle \theta _{n+1}=\theta _{n}+\Omega -{\frac {K}{2\pi }}\sin(2\pi \theta _{n}).}$

This figure shows ${\displaystyle \theta _{n}\mod 1}$ along the x-axis, with coupling constant K ranging from 0 at the bottom to 4π at the top. The frequency Ω is held constant at 1/3.

Chaotic regions are interspersed with stable region are clearly visible. By comparing this image to the image showing Arnold tongues, and aligning along the Ω=1/3 slice, it becomes apparent that the stable regions correspond to the Arnold tongues, that is, to the regions where the map is mode-locked.

## Summary

en:Bifurcation diagram for the en:circle map at Ω=1/3. Original image created by Linas Vepstas en:User:Linas <linas@linas.org> on 19 January 2006.

## Licensing

 Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.