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

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

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

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