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Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones

文献类型：期刊论文

作者Shen, Jun1; Du, Zhengdong2
刊名ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
出版日期2016-06-01
卷号67期号:3页码:17
ISSN号0044-2275
关键词Melnikov method Piecewise smooth system Heteroclinic bifurcation Smale horseshoe Chaos
DOI10.1007/s00033-016-0642-2
英文摘要We 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.
资助项目NSFC (China)[11371264] ; NSFC (China)[11501549] ; China Postdoctoral Science Foundation[2015M571145]
WOS研究方向Mathematics
语种英语
出版者SPRINGER BASEL AG
WOS记录号WOS:000378940400008
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/23097]  
专题中国科学院数学与系统科学研究院
通讯作者Du, Zhengdong
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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