Dynamical Systems on Graph Limits and Their Symmetries

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-23 DOI:10.1007/s10884-023-10334-7

引用次数: 0

Abstract

The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and the dynamics thereon. We elucidate the symmetry properties of dynamical systems on graph limits—including graphons and graphops—and analyze how the symmetry shapes the dynamics, for example through invariant subspaces. In addition to traditional symmetries, dynamics on graph limits can support generalized noninvertible symmetries. Moreover, as asymmetric networks can have symmetric limits, we note that one can expect to see ghosts of symmetries in the dynamics of large but finite asymmetric networks.

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图极限上的动力系统及其对称性

摘要网络上相互作用的动态单元的集体动力学在很大程度上取决于网络结构的特性。人们通常不考虑大型但有限的图来捕捉网络，而是求助于图极限及其上的动力学。我们阐明了图极限（包括图子和图顶）上动力学系统的对称特性，并分析了对称性如何塑造动力学，例如通过不变子空间。除了传统的对称性，图极限上的动力学还支持广义的非可逆对称性。此外，由于非对称网络可以有对称极限，我们注意到，在大型但有限的非对称网络的动力学中，我们可以看到对称的幽灵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.