Templex-based dynamical units for a taxonomy of chaos - CEA - Commissariat à l’énergie atomique et aux énergies alternatives
Journal Articles Chaos: An Interdisciplinary Journal of Nonlinear Science Year : 2024

Templex-based dynamical units for a taxonomy of chaos

Abstract

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.
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hal-04776002 , version 1 (11-11-2024)

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Caterina Mosto, Gisela Charó, Christophe Letellier, Denisse Sciamarella. Templex-based dynamical units for a taxonomy of chaos. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2024, 34 (11), ⟨10.1063/5.0233160⟩. ⟨hal-04776002⟩
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