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

doi:10.1007/s00033-016-0642-2

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	Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones
	Shen, Jun 1; Du, Zhengdong 2
	2016-06-01
发表期刊	ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
ISSN	0044-2275
卷号	67 期号:3 页码:17
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.
关键词	Melnikov method Piecewise smooth system Heteroclinic bifurcation Smale horseshoe Chaos
DOI	10.1007/s00033-016-0642-2
语种	英语
资助项目	NSFC (China)[11371264] ; NSFC (China)[11501549] ; China Postdoctoral Science Foundation[2015M571145]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000378940400008
出版者	SPRINGER BASEL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23098
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.