不变子空间的分岔定理

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-21 DOI:10.1137/23m1595540

John M. Neuberger, Nándor Sieben, James W. Swift

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引用次数: 0

摘要

SIAM 应用动力系统学报》第 23 卷第 2 期第 1610-1635 页，2024 年 6 月。摘要：简单特征值分岔（BSE）定理是单参数函数族稳态分岔理论的基础。当对称性导致特征值的多重性大于 1 时，通常可以应用等变分支两难（Equivariant branching lemma，EBL）来预测解的分支。EBL 可以解释为 BSE 定点子空间定理的应用。有些函数的不变线性子空间不是由对称性引起的。例如，完全相同的耦合单元网络通常具有这样的不变子空间。我们提出了对 EBL 的一种概括，即将 BSE 定理应用于嵌套不变子空间。我们称其为不变子空间分岔稃（BLIS）。我们给出了几个分岔的例子，并确定 BSE、EBL 或 BLIS 是否适用。我们扩展了之前的自动分岔分析算法，使用 BLIS 简化并改进了对分岔处产生的分支的检测。

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A Bifurcation Lemma for Invariant Subspaces

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1610-1635, June 2024.
Abstract.The bifurcation from a simple eigenvalue (BSE) theorem is the foundation of steady-state bifurcation theory for one-parameter families of functions. When eigenvalues of multiplicity greater than one are caused by symmetry, the equivariant branching lemma (EBL) can often be applied to predict the branching of solutions. The EBL can be interpreted as the application of the BSE theorem to a fixed point subspace. There are functions which have invariant linear subspaces that are not caused by symmetry. For example, networks of identical coupled cells often have such invariant subspaces. We present a generalization of the EBL, where the BSE theorem is applied to nested invariant subspaces. We call this the bifurcation lemma for invariant subspaces (BLIS). We give several examples of bifurcations and determine if BSE, EBL, or BLIS applies. We extend our previous automated bifurcation analysis algorithms to use the BLIS to simplify and improve the detection of branches created at bifurcations.

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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.