{"title":"Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems","authors":"Hong Tang, Alan Champneys","doi":"10.1137/23m1552292","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3320-3357, December 2023. <br/> 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.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1552292","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.
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