{"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":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"35 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1552292","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","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：
SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS is published in electronic format only.
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