Si'lnikov-type orbits of Lorenz-family systems

Wang, Junwei, Zhao, Meichun, Zhang, Yanbin and Xiong, Xiaohua (2007) Si'lnikov-type orbits of Lorenz-family systems. Physica A-statistical Mechanics And Its Applications, 375 2: 438-446. doi:10.1016/j.physa.2006.10.007

Author Wang, Junwei
Zhao, Meichun
Zhang, Yanbin
Xiong, Xiaohua
Title Si'lnikov-type orbits of Lorenz-family systems
Journal name Physica A-statistical Mechanics And Its Applications   Check publisher's open access policy
ISSN 0378-4371
Publication date 2007-03-01
Sub-type Article (original research)
DOI 10.1016/j.physa.2006.10.007
Volume 375
Issue 2
Start page 438
End page 446
Total pages 9
Place of publication Amsterdam, The Netherlands
Publisher Elsevier Science Bv
Language eng
Subject 0105 Mathematical Physics
0104 Statistics
Abstract This paper studies the Lorenz-family system which is known to establish a topological connection among the Lorenz, Chen and Lii systems in the parametric space. The existence of Si'Inikov heterclinic orbits is proved using an undetermined coefficient method. As a consequence, the Si'Inikov criterion along with some technical conditions guarantees that the Lorenz-family system has both Smale horseshoes and horseshoe type of chaos. It is this heteroclinic orbit that determines the geometric structure of the corresponding chaotic attractor. (c) 2006 Elsevier B.V. All rights reserved.
Keyword Physics, Multidisciplinary
Lorenz-family system
heteroclinic orbit
Si'lnikov criterion
undetermined coefficient method
Attractor Exists
Chaotic System
Canonical Form
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mechanical & Mining Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 28 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 36 times in Scopus Article | Citations
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Created: Fri, 25 Jan 2008, 17:01:43 EST