Lozi Attractor

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The French mathematician René Lozi introduced a piecewise linear version of the Hénon map [1] with applications in secure communications [2]. It is a 2D invertible iterated map that yields a chaotic attractor. Selecting "attractor" shows the iterates of this map with initial value , and selecting "iterations to escape" colors points in the plane based on how long it takes the sequence of iterates with that initial value to escape the region .

Contributed by: Enrique Zeleny (March 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The map is defined by

,

,

where usually and are positive.

References

[1] H-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, New York: Springer-Verlag, 1992 p. 672 (§12.1).

[2] Z. Elhadj and J. C. Sprott, "A Unified Piecewise Smooth Chaotic Mapping That Contains the Hénon and the Lozi Systems," Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, 1, 2012 pp. 50–60. www.arctbds.com/Volume1/4-A %20 unified %20 chaotic %20 mapping.pdf.



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