基于 Templex 的混沌分类动态单元。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0233160
Caterina Mosto, Gisela D Charó, Christophe Letellier, Denisse Sciamarella
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引用次数: 0

摘要

区分不同类型的混沌仍然是一个极具挑战性的课题,即使对于耗散三维系统来说,最先进的工具也是模板。然而,根据定义,获得模板仅限于基于结理论的三维对象。为了处理更高维的混沌,我们最近推出了将面向流动的 BraMAH 单元复合体与有向图(数字图)相结合的 templex。Templex 的概念没有维度限制。在这里,我们展示了 templex 可以自动简化为一种 "最小 "形式,从而为混沌吸引子的主要特性提供一个全面的综合视角。通过这种还原,我们可以根据两个基本单元:振荡单元(O-单元)和开关单元(S-单元),对混沌进行分类。我们将这种方法应用于各种著名的吸引子(罗斯勒吸引子、洛伦兹吸引子、伯克肖吸引子)以及一种非三维的四维吸引子。我们还讨论了环状混沌(Deng)的一个案例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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