Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-06 DOI:10.1137/23m1552292

Hong Tang, Alan Champneys

引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3320-3357, December 2023.
Abstract. A semianalytical method is derived for finding the existence and stability of single-impact periodic orbits born in a boundary equilibrium bifurcation in a general [math]-dimensional impacting hybrid system. Known results are reproduced for planar systems and general formulae derived for three-dimensional (3D) systems. A numerical implementation of the method is illustrated for several 3D examples and for an 8D wing-flap model that shows coexistence of attractors. It is shown how the method can easily be embedded within numerical continuation, and some remarks are made about necessary and sufficient conditions in arbitrary dimensional systems.

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撞击混合系统中边界平衡的极限循环分岔

SIAM 应用动力系统期刊》，第 22 卷第 4 期，第 3320-3357 页，2023 年 12 月。摘要。推导了一种半解析方法，用于求解一般[数学]维碰撞混合系统中边界平衡分岔所产生的单碰撞周期轨道的存在性和稳定性。已知结果用于平面系统，一般公式用于三维（3D）系统。针对几个三维实例和一个显示吸引子共存的 8D 翼瓣模型，对该方法的数值实现进行了说明。图中展示了如何将该方法轻松嵌入数值延续中，并对任意维度系统中的必要条件和充分条件做了一些说明。

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.