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Multi-folds in an Lozi-type map

Aziz Alaoui, M.A.

Depart. of Math., Labo. of Mechanics, Le Havre University, France.

in preparation

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Abstract

We present and analyze a modified version of a piecwise-linear Lozi map.
Lozi [1978] studied the following map :

x_{n+1} = y_n+1-a.|x| ,
y_{n+1} = b.x_n
(a and b are the parameters).
By modifying the nonlinear term (|x|) of this map, we obtain
some new strange attractors with many folds (interest: secure
communication for example),, (... asap ! for the paper ):

See the following figures.

See also multi-folds attractors like Hénon's

A classical Lozi attractor

A 3-folds strange attractor exhibited by the modified Lozi's map

A 4-folds strange attractor exhibited by the modified Lozi's map

A 8-folds strange attractor exhibited by the modified Lozi's map

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