Templex-based dynamical units for a taxonomy of chaos
Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to three-dimensional objects based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented BraMAH cell complex and a directed graph (a digraph). There is no dimensional limitation in the concept of templex. Here, we show that a templex can be automatically reduced into a "minimal" form to provide a comprehensive and synthetic view of the main properties of chaotic attractors. This reduction allows for the development of a taxonomy of chaos in terms of two elementary units: the oscillating unit (O-unit) and the switching unit (S-unit). We apply this approach to various well-known attractors (Rössler, Lorenz, and Burke-Shaw) as well as a non-trivial four-dimensional attractor. A case of toroidal chaos (Deng) is also treated.
Authors
- Gisela D. Charó (ORCID: https://orcid.org/0000-0001-5798-0933)
- Denisse Sciamarella (ORCID: https://orcid.org/0000-0001-5218-3708)
- Christophe Letellier (ORCID: https://orcid.org/0000-0003-3603-394X)
- Caterina Mosto (ORCID: https://orcid.org/0000-0001-9452-5622)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Consejo Nacional de Investigaciones Científicas y Técnicas (AR)
- Université de Versailles Saint-Quentin-en-Yvelines (FR)
- Universidad de Buenos Aires (AR)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Université Paris-Saclay (FR)
- Centre National pour la Recherche Scientifique et Technique (CNRST) (MA)
- Complexe de Recherche Interprofessionnel en Aérothermochimie (FR)
- Normandie Université (FR)
- Laboratoire des Sciences du Climat et de l'Environnement (FR)
- CEA Paris-Saclay (FR)
- Institute of Astronomy and Space Physics (AR)
- Instituto Franco-Argentino sobre Estudios de Clima y sus Impactos (AR)
- Université de Rouen Normandie (FR)
Publication Details
- Journal
- Chaos An Interdisciplinary Journal of Nonlinear Science
- Published
- 2024-11-01
- DOI
- https://doi.org/10.1063/5.0233160
- Citations
- 5
- Primary Topic
- Nonlinear Dynamics and Pattern Formation
- Type
- article
- Field-Weighted Citation Impact
- 1.74
Funders
- Agence Nationale de la Recherche
- Consejo Nacional de Investigaciones Científicas y Técnicas