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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.


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.


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


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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> <>)

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