Lozi Attractor

view

attractor

iterations to escape

α

1.7

β

0.5

steps

4000

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

(0,0)

, 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

[-10,10]

.

Details

The map is defined by

x

n+1

=1-α|

x

n

|+β

y

n

,

y

n+1

=

x

n

,

where usually

α

and

β

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.

External Links

Invertible (Wolfram MathWorld)

Lozi Map (Wolfram MathWorld)

Hénon Map (Wolfram MathWorld)

Permanent Citation

Enrique Zeleny

"Lozi Attractor"
http://demonstrations.wolfram.com/LoziAttractor/
Wolfram Demonstrations Project
Published: March 21, 2013