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Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones
Shen, Jun1; Du, Zhengdong2
2016-06-01
Source PublicationZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
ISSN0044-2275
Volume67Issue:3Pages:17
AbstractWe discuss heteroclinic bifurcation in a class of periodically excited planar piecewise smooth systems with discontinuities on finitely many smooth curves intersecting at the origin. Assume that the unperturbed system has a hyperbolic saddle in each subregion, and those saddles are connected by a heteroclinic cycle that crosses every switching curve transversally exactly once. We present a method of Melnikov type to derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally. Such transversal intersections imply that the corresponding Poincare map has a transverse heteroclinic cycle. As applications, we present examples with 2 and 4 switching curves respectively. Our numerical simulations suggest that such transversal intersections result in the appearance of chaotic motions in those example systems.
KeywordMelnikov method Piecewise smooth system Heteroclinic bifurcation Smale horseshoe Chaos
DOI10.1007/s00033-016-0642-2
Language英语
Funding ProjectNSFC (China)[11371264] ; NSFC (China)[11501549] ; China Postdoctoral Science Foundation[2015M571145]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000378940400008
PublisherSPRINGER BASEL AG
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23098
Collection中国科学院数学与系统科学研究院
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China
Recommended Citation
GB/T 7714
Shen, Jun,Du, Zhengdong. Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,2016,67(3):17.
APA Shen, Jun,&Du, Zhengdong.(2016).Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones.ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,67(3),17.
MLA Shen, Jun,et al."Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones".ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 67.3(2016):17.
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