Visualizing the Template of a Chaotic Attractor

Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces a novel and unique tool to validate a linking matrix, to opt...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Olszewski, Maya, Meder, Jeff, Kieffer, Emmanuel, Bleuse, Raphaël, Martin, Rosalie, Danoy, Grégoire, Bouvry, Pascal
Format: Article
Language:English
Subjects:
Mathematical analysis
Matrix algebra
Matrix methods
Topology
Toruses
Online Access:Get full text
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Summary:Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces a novel and unique tool to validate a linking matrix, to optimize the compactness of the corresponding template and to draw this template. The article provides a detailed description of the different validation steps and the extraction of an order of crossings from the linking matrix leading to a template of minimal height. Finally, the drawing process of the template corresponding to the matrix is saved in a Scalable Vector Graphics (SVG) file.
ISSN:2331-8422
DOI:10.48550/arxiv.1807.11853