Multi-folds in an Lozi-type map

Aziz Alaoui, M.A.
Depart. of Math., Labo. of Mechanics, Le Havre University, France.

in preparation

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.

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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