Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System

被引：2

作者：

Du, Wenju ^{[1
]}

Chu, Yandong ^{[1
]}

Zhang, Jiangang ^{[1
]}

Chang, Yingxiang ^{[1
]}

Yu, Jianning ^{[1
]}

An, Xinlei ^{[1
]}

机构：

[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

来源：

JOURNAL OF APPLIED MATHEMATICS | 2014年

关键词：

D O I：

10.1155/2014/726491

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the bifurcations and sliding mode control of chaotic vibrations in an autonomous system. More precisely, a Hopf bifurcation controller is designed so as to control the unstable subcritical Hopf bifurcation to the stable supercritical Hopf bifurcation. Research result shows that the control method can work very well in Hopf bifurcation control. Besides, we controlled the system to any fixed point and any periodic orbit to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller.

引用

页数：14

共 26 条

[1] TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS [J].

Amaral, Fabiolo M. ;

Alberto, Luis F. C. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (01)

[2]

[Anonymous], 2004, ELEMENTS APPL BIFURC

[3] Sliding mode control of chaotic vibrations of spinning disks with uncertain parameter under bounded disturbance [J].

Chen Di-Yi ;

Shen Tao ;

Ma Xiao-Yi .

ACTA PHYSICA SINICA, 2011, 60 (05)

[4]

Chen Diyi, 2011, Proceedings of the CSEE, V31, P113

[5] Yet another chaotic attractor [J].

Chen, GR ;

Ueta, T .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (07) :1465-1466

[6] Linearizability and local bifurcation of critical periods in a cubic Kolmogorov system [J].

Chen, Xingwu ;

Huang, Wentao ;

Romanovski, Valery G. ;

Zhang, Weinian .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 245 :86-96

[7] Nonlinear dynamics analysis of a new autonomous chaotic system [J].

Chu, Yan-Dong ;

Li, Xian-Feng ;

Zhang, Jian-Gang ;

Chang, Ying-Xiang .

JOURNAL OF ZHEJIANG UNIVERSITY-SCIENCE A, 2007, 8 (09) :1408-1413

[8]

Di-Yi C., 2011, CHINESE PHYS B, V20

[9] Nonlinear analysis in a Lorenz-like system [J].

Dias, Fabio Scalco ;

Mello, Luis Fernando ;

Zhang, Jian-Gang .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) :3491-3500

[10] Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems [J].

El-Dessoky, M. M. ;

Yassen, M. T. ;

Saleh, E. ;

Aly, E. S. .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (24) :11859-11870

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