Nonuniqueness Phenomena in Discontinuous Dynamical Systems and Their Regularizations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-30 DOI:10.1137/23m1587488

Alessia Andò, Roderick Edwards, Nicola Guglielmi

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引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1345-1371, June 2024.
Abstract.In a recent article by Guglielmi and Hairer [SIAM J. Appl. Dyn. Syst., 14 (2015), pp. 1454–1477], an analysis in the [math] limit was proposed of regularized discontinuous ODEs in codimension-2 switching domains; this was obtained by studying a certain 2-dimensional system describing the so-called hidden dynamics. In particular, the existence of a unique limit solution was not proved in all cases, a few of which were labeled as ambiguous, and it was not clear whether or not the ambiguity could be resolved. In this paper, we show that it cannot be resolved in general. A first contribution of this paper is an illustration of the dependence of the limit solution on the form of the switching function. Considering the parameter dependence in the ambiguous class of discontinuous systems, a second contribution is a bifurcation analysis, revealing a range of possible behaviors. Finally, we investigate the sensitivity of solutions in the transition from codimension-2 domains to codimension-3 when there is a limit cycle in the hidden dynamics.

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非连续动态系统中的非唯一性现象及其正则化

SIAM 应用动力系统期刊》，第 23 卷第 2 期，第 1345-1371 页，2024 年 6 月。摘要.Guglielmi 和 Hairer 最近的一篇文章[SIAM J. Appl. Dyn. Syst., 14 (2015), pp.特别是，并不是在所有情况下都能证明唯一极限解的存在，其中有几种情况被标记为含糊不清，而且不清楚是否能解决这种含糊不清。在本文中，我们证明在一般情况下无法解决这一问题。本文的第一个贡献是说明了极限解对开关函数形式的依赖性。考虑到非连续系统模糊类别中的参数依赖性，本文的第二个贡献是进行了分岔分析，揭示了一系列可能的行为。最后，我们研究了当隐藏动力学中存在极限循环时，解在从标度-2 域向标度-3 域过渡时的敏感性。

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.