Bifurcation Diagram of the Hénon Map

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The Hénon map is the two-dimensional map described by the equations

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,

.

The plot shows the last 36 coordinates after iterations of the Hénon map using the initial point .

To obtain an interesting region of periodic and chaotic behavior, we use values between 0.91 and 1.41 with . Changing these values will give very similar results.

You can click anywhere in the diagram to see a magnified inset in the lower-left corner.

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Contributed by: Erik Mahieu  (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Using the lowest values for and will let you quickly find an appropriate region to inspect. Larger values will show a cleaner, more detailed plot.

The idea for the Locator-magnifier was taken from Ed Pegg Jr.



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