Summary

Transferred from en.wikipedia to Commons by Maksim.

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

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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

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Original upload log

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

Click on date to download the file or see the image uploaded on that date.

• (del) (cur) 05:05, 20 January 2006 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 450x900 (120433 bytes) (Reverted to earlier revision)
• (del) (rev) 05:04, 20 January 2006 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 450x900 (120130 bytes) (Reverted to earlier revision)
• (del) (rev) 05:03, 20 January 2006 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 450x900 (120433 bytes) ( en:Bifurcation_diagram Bifurcation diagram for the en:Circle_map circle map at &Omega;=1/3. Original image created by Linas Vepstas en:User:Linas User:Linas <linas@linas.org> on 19 January 2006.)
• (del) (rev) 04:44, 20 January 2006 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 450x900 (120130 bytes) ( en:Bifurcation_diagram Bifurcation diagram for the en:Circle_map circle map at &Omega;=1/3. Original image created by Linas Vepstas en:User:Linas User:Linas <linas@linas.org>)