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File:Circle map bifurcation.jpeg

From Wikipedia, the free encyclopedia

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

This figure shows 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

GNU head 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.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
This licensing tag was added to this file as part of the GFDL licensing update.
date/time username edit summary
05:00, 20 January 2006 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Circle_map_bifurcation.jpeg#Summary" title="Image:Circle map bifurcation.jpeg">→</a>Summary -</span> in-depth explanation of image)
04:44, 20 January 2006 en:User:Linas (<a href="/wiki/Bifurcation_diagram" title="Bifurcation diagram">Bifurcation diagram</a> for the <a href="/wiki/Circle_map" title="Circle map">circle map</a> at Ω=1/3. Original image created by Linas Vepstas <a href="/wiki/User:Linas" title="User:Linas">User:Linas</a> <linas@linas.org>)

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