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Lozi Map

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LoziMap

The Lozi map modifies the two-dimensional Hénon map by replacing the term -alphax_n^2 with -alpha|x_n|. It is given by the equations

x_(n+1)=1-alpha|x_n|+y_n
(1)
y_(n+1)=betax_n.
(2)

The strange attractor illustrated above results from alpha=1.4, beta=0.3.

The Lozi map has been applied to global optimization, synchronization of coupled dynamical systems, and cryptography (Lozi 2023).

See also

Gingerbreadman Map, Hénon Map, Quadratic Map, Strange Attractor

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References

Dickau, R. M. "Lozi Attractor." https://www.robertdickau.com/lozi.html.Lozi, R. "Un attracteur étrange (?) du type attracteur de Hénon." J. Phys. Colloques 39, C5-9-C5-10, 1978. https://doi.org/10.1051/jphyscol:1978505.Lozi, R. "Survey of Recent Applications of the Chaotic Lozi Map." Algorithms 16, 491, 2023. https://doi.org/10.3390/a16100491.Peitgen, H.-O.; Jürgens, H.; and Saupe, D. §12.1 in Chaos and Fractals: New Frontiers of Science. New York: Springer-Verlag, p. 672, 1992.

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Lozi Map

Cite this as:

Weisstein, Eric W. "Lozi Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LoziMap.html

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