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作者:

Li, Shuangbao (Li, Shuangbao.) | Ma, Wensai (Ma, Wensai.) | Zhang, Wei (Zhang, Wei.) (学者:张伟) | Hao, Yuxin (Hao, Yuxin.)

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Scopus SCIE

摘要:

In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed planar hybrid piecewise-smooth systems. In this class, the switching manifold is a straight line which divides the plane into two zones, and the dynamics in each zone is governed by a smooth system. When a trajectory reaches the separation line, then a reset map is applied instantaneously before entering the trajectory in the other zone. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise-smooth homoclinic solution transversally crossing the switching manifold. Then, we study the persistence of the homoclinic orbit under a nonautonomous periodic perturbation and the reset map. To achieve this objective, we obtain the Melnikov function to measure the distance of the perturbed stable and unstable manifolds and present the theorem for homoclinic bifurcations for the class of planar hybrid piecewise-smooth systems. Furthermore, we employ the obtained Melnikov function to detect the chaotic boundaries for a concrete planar hybrid piecewise-smooth system.

关键词:

piecewise-smooth homoclinic solutions switching manifold Melnikov method planar hybrid piecewise-smooth systems homoclinic bifurcations chaotic boundaries

作者机构:

  • [ 1 ] [Li, Shuangbao]Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China
  • [ 2 ] [Ma, Wensai]Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China
  • [ 3 ] [Zhang, Wei]Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China
  • [ 4 ] [Hao, Yuxin]Beijing Informat Sci & Technol Univ, Coll Mech Engn, Beijing 100192, Peoples R China

通讯作者信息:

  • [Li, Shuangbao]Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

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来源 :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

年份: 2016

期: 2

卷: 26

2 . 2 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:71

中科院分区:3

被引次数:

WoS核心集被引频次: 7

SCOPUS被引频次: 22

ESI高被引论文在榜: 0 展开所有

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中文被引频次:

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