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Coexistence of Thread and Sheet Chaotic Attractors for Three Dimensional Lozi Map
Version 1
: Received: 10 May 2023 / Approved: 11 May 2023 / Online: 11 May 2023 (03:48:45 CEST)
A peer-reviewed article of this Preprint also exists.
Lozi, R. Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map. Dynamics 2023, 3, 315-344. Lozi, R. Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map. Dynamics 2023, 3, 315-344.
Abstract
Since its original publication 1 in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications analyze its particular structure or apply its properties in many fields (electronic devices like memristor, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial two-dimensional map into multidimensional one. However, they do not respect the original constraint that allows this map to be one of the few strictly hyperbolic: a constant Jacobian. In this paper we introduce a three-dimensional piece-wise linear extension respecting this constraint and we explore a special property never highlighted for chaotic mappings: the coexistence of thread-chaotic attractors (i.e., attractors which are formed by collection of lines) and sheet-chaotic attractors (i.e., attractors which are formed by collection of planes). This new 3-dimensional mapping can generate a large variety of chaotic and hyperchaotic attractors. We give five examples of such behavior in this article. In the first three examples, there is coexistence of thread and sheet-chaotic attractors. However, their shape are different and they are constituted by a different number of pieces. In the two last examples, the blow up of the attractors with respect to parameter a and b is highlighted.
Keywords
chaotic attractor; hyperchaotic attractor; Lozi map; sheet-attractor; thread-attractor
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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