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File:Bifurcations and crises of Ikeda attractor.png

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English: Bifurcation diagram and basins of attraction for attractors of the Ikeda map.

The top diagram shows how the real part of iterates change depending on the control parameter. Period doubling bifurcations are clearly visible. For some parameter values multiple attractors coexist, and as the parameters change they suddenly appear or disappear (a crisis). In particular, the top attractor suffers a crisis near 1.56, merging with another attractor. This one disappears in a crisis near 1.59. A large strange attractor appears through a crisis near 1.79.

The diagrams below show the basins of attraction (colour) and the attractors (white) for selected parameter values.The colours are calculated based on the mean orbit of points starting in a particular location: the swirls inside a basin seen for some parameter values indicate long chaotic transients.
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Author Anders Sandberg

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current11:27, 14 December 2011Thumbnail for version as of 11:27, 14 December 20112,532 × 1,821 (1.47 MB)Anders Sandberg (talk | contribs)

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