2024

Caterina Mosto, Gisela D. Charó, Christophe Letellier & Denisse Sciamarella
Templex-based dynamical units for a taxonomy of chaos
Chaos, 34, 113111, 2024 [Online]

• 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.