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Chin. Phys. B, 2014, Vol. 23(10): 104502    DOI: 10.1088/1674-1056/23/10/104502
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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
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.
Keywords:  relative rotation      coupled nonlinear system      bifurcation      time delay  
Received:  15 March 2014      Revised:  11 April 2014      Accepted manuscript online: 
PACS:  45.20.dc (Rotational dynamics)  
  05.45.-a (Nonlinear dynamics and chaos)  
Fund: 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).
Corresponding Authors:  Li Hai-Bin     E-mail:  hbli@ysu.edu.cn
About author:  45.20.dc; 05.45.-a

Cite this article: 

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 2014 Chin. Phys. B 23 104502

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