使用Perron-Frobenius和Koopman算子的对称混沌分类

IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Jaime Cisternas
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引用次数: 0

摘要

等变耗散动力系统的吸引子的对称性可以遭受改变对称性的分岔,这种分岔可以用成熟的方法检测和分类。新的数据驱动方法,如Koopman和Perron-Frobenius算子,除了将任何非线性系统简化为线性系统外,还可以应用于等变动力系统的分析和分类问题。在本文中,我们研究了这些无限维算子的矩阵近似,它们尊重原始对称性,并引入了一个具有清晰解释的集合矩阵。它的稀疏模式揭示了多个共轭吸引子的存在,并指出了它们对称子群的结构。我们将这些思想应用于由三个非线性等变系统产生的数据,寻找非平凡子群的吸引子并检测改变对称的分岔。该方法可与现有的非线性等变系统的分析、预测和控制计算过程相结合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Classification of symmetric chaos using the Perron–Frobenius and Koopman operators
The symmetry properties of the attractors of equivariant dissipative dynamical systems can suffer symmetry-changing bifurcations, that can be detected and classified using well-established methods. Novel data-driven methods, such as the Koopman and Perron–Frobenius operators, besides reducing any nonlinear system to a linear one, can also be applied to the analysis of equivariant dynamical systems and the classification problem. In this article, we study matrix approximations of these infinite-dimensional operators that respect the original symmetry and introduce an aggregate matrix that has a clear interpretation. Its sparsity pattern reveals the presence of multiple conjugate attractors and indicates the structure of their symmetry subgroup. We apply these ideas to data generated by three nonlinear equivariant systems, finding attractors of non-trivial subgroups and detecting symmetry-changing bifurcations. The proposed method can be incorporated into existing computational processes for the analysis, prediction and control of nonlinear equivariant systems.
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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