Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system

Zuohuan Zheng; Guanrong Chen

doi:10.1016/j.jmaa.2005.09.087

Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system

Zuohuan Zheng, Guanrong Chen

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

37 Citations (Scopus)

Abstract

In this paper, the existence of heteroclinic orbits of Shil'nikov type in a three-dimensional quadratic autonomous system is proved. Four heteroclinic orbits and four critical points together constitute two cycles simultaneously. The dynamical behaviors of the system are also studied. © 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	106-119
Journal	Journal of Mathematical Analysis and Applications
Volume	315
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2005.09.087
Publication status	Published - 1 Mar 2006

Research Keywords

Behavior of trajectory
Heteroclinic orbit
Invariant set
Shil'nikov map

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title = "Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system",

abstract = "In this paper, the existence of heteroclinic orbits of Shil'nikov type in a three-dimensional quadratic autonomous system is proved. Four heteroclinic orbits and four critical points together constitute two cycles simultaneously. The dynamical behaviors of the system are also studied. {\textcopyright} 2005 Elsevier Inc. All rights reserved.",

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author = "Zuohuan Zheng and Guanrong Chen",

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T1 - Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system

AU - Zheng, Zuohuan

AU - Chen, Guanrong

PY - 2006/3/1

Y1 - 2006/3/1

N2 - In this paper, the existence of heteroclinic orbits of Shil'nikov type in a three-dimensional quadratic autonomous system is proved. Four heteroclinic orbits and four critical points together constitute two cycles simultaneously. The dynamical behaviors of the system are also studied. © 2005 Elsevier Inc. All rights reserved.

AB - In this paper, the existence of heteroclinic orbits of Shil'nikov type in a three-dimensional quadratic autonomous system is proved. Four heteroclinic orbits and four critical points together constitute two cycles simultaneously. The dynamical behaviors of the system are also studied. © 2005 Elsevier Inc. All rights reserved.

KW - Behavior of trajectory

KW - Heteroclinic orbit

KW - Invariant set

KW - Shil'nikov map

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U2 - 10.1016/j.jmaa.2005.09.087

DO - 10.1016/j.jmaa.2005.09.087

M3 - RGC 21 - Publication in refereed journal

SN - 0022-247X

VL - 315

SP - 106

EP - 119

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system

Abstract

Research Keywords

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