Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

doi:10.1088/1674-1056/23/10/104502

›› 2014, Vol. 23 ›› Issue (10): 104502-104502.doi: 10.1088/1674-1056/23/10/104502

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

刘爽^{a b}, 李雪^a, 谈书贤^a, 李海滨^a

a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China

收稿日期:2014-03-15 修回日期:2014-04-11 出版日期:2014-10-15 发布日期:2014-10-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090).

Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

Liu Shuang (刘爽)^{a b}, Li Xue (李雪)^a, Tan Shu-Xian (谈书贤)^a, Li Hai-Bin (李海滨)^a

a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China

Received:2014-03-15 Revised:2014-04-11 Online:2014-10-15 Published:2014-10-15
Contact: Li Hai-Bin E-mail:hbli@ysu.edu.cn
About author:45.20.dc; 05.45.-a
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090).

摘要/Abstract

摘要： This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.

关键词: relative rotation, coupled nonlinear system, bifurcation, time delay

Abstract: This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.

Key words: relative rotation, coupled nonlinear system, bifurcation, time delay

中图分类号: (Rotational dynamics)

45.20.dc

05.45.-a (Nonlinear dynamics and chaos)

刘爽, 李雪, 谈书贤, 李海滨. Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks[J]. , 2014, 23(10): 104502-104502.

Liu Shuang (刘爽), Li Xue (李雪), Tan Shu-Xian (谈书贤), Li Hai-Bin (李海滨). Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks[J]. Chin. Phys. B, 2014, 23(10): 104502-104502.

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Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

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