基于Templex的动态单元用于混沌分类
Templex-based dynamical units for a taxonomy of chaos
AI总结：
本文提出基于Templex的动态单元方法，用于对混沌进行分类，通过减少Templex到最小形式，引入振荡和切换单元，应用于多种已知吸引子及四维吸引子。
摘要：
区分不同类型的混沌仍然是一个非常具有挑战性的话题，即使对于耗散的三维系统而言，最先进的工具仍然是模板。然而，获取模板本质上受限于三维对象，因为其基于结论理论。为了解决高维混沌问题，我们最近引入了结合以流为导向的BraMAH细胞复形和有向图（有向图）的Templex。Templex的概念没有维度限制。在此，我们证明Templex可以自动减少到“最小”形式，以提供对混沌吸引子主要属性的全面和综合的视角。这种减少允许以两个基本单元：振荡单元（O单元）和切换单元（S单元）来开发混沌的分类。我们应用这种方法到各种著名的吸引子（Rossler、Lorenz和Burke-Shaw）以及一个非平凡的四维吸引子。还处理了环形混沌（Deng）的情况。这项工作献给Otto E. Rossler。
英文摘要：
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, since based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented {\sc 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. This work is dedicated to Otto E. Rössler.
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