• Complex
  • Title
  • Keyword
  • Abstract
  • Scholars
  • Journal
  • ISSN
  • Conference
搜索

Author:

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

Indexed by:

Scopus SCIE

Abstract:

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.

Keyword:

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

Author Community:

  • [ 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

Reprint Author's Address:

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

Show more details

Related Keywords:

Source :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

Year: 2016

Issue: 2

Volume: 26

2 . 2 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:71

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count: 9

SCOPUS Cited Count: 25

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 13

Online/Total:451/10704041
Address:BJUT Library(100 Pingleyuan,Chaoyang District,Beijing 100124, China Post Code:100124) Contact Us:010-67392185
Copyright:BJUT Library Technical Support:Beijing Aegean Software Co., Ltd.