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Abstract
Hopf bifurcation in a nonlinear relative-rotation system with time delay is considerd, and the critical time delay associated with Hopf bifurcation is found. The time delays influence on the direction and stability of bifurcation are analyzed under the primary resonance condition with the aid of multiple scales. Finally, numerical simulations are performed to verify the analytical results.

Keywords:
relativel rotation/

time delay/

Hopf bifurcation/

stability
Authors and contacts
Liu Shuang²,

Liu Bin¹,

Zhang Ye-Kuan¹,

Wen Yan³
References

Cited By

[1]	Liu Bin, Zhao Hong-Xu, Hou Dong-Xiao, Liu Hao-Ran.Bifurcation and chaos of some strongly nonlinear relative rotation system with time-varying clearance. Acta Physica Sinica, 2014, 63(7): 074501.doi:10.7498/aps.63.074501
[2]	Zhu Lin-He, Zhao Hong-Yong.Stability and bifurcation control in inertial neuron networks with delays. Acta Physica Sinica, 2014, 63(9): 090203.doi:10.7498/aps.63.090203
[3]	Hou Dong-Xiao, Zhao Hong-Xu, Liu Bin.Bifurcation and chaos in some relative rotation systems with Mathieu-Duffing oscillator. Acta Physica Sinica, 2013, 62(23): 234501.doi:10.7498/aps.62.234501
[4]	Li Xiao-Jing, Chen Xuan-Qing, Yan Jing.Hopf bifurcation and the problem of periodic solutions in a recharge-discharge oscillator model for El Niño and southern oscillation with time delay. Acta Physica Sinica, 2013, 62(16): 160202.doi:10.7498/aps.62.160202
[5]	Li Hai-Bin, Wang Bo-Hua, Zhang Zhi-Qiang, Liu Shuang, Li Yan-Shu.Combination resonance bifurcations and chaos of some nonlinear relative rotation system. Acta Physica Sinica, 2012, 61(9): 094501.doi:10.7498/aps.61.094501
[6]	Xu Chang-Jin.Bifurcation analysis for a delayed sea-air oscillator coupling model for the ENSO. Acta Physica Sinica, 2012, 61(22): 220203.doi:10.7498/aps.61.220203
[7]	Zhao Hong-Yong, Chen Ling, Yu Xiao-Hong.Bifurcation and control of a class of inertial neuron networks. Acta Physica Sinica, 2011, 60(7): 070202.doi:10.7498/aps.60.070202
[8]	Li Ji-Zhao, Liu Bin, Han Dong-Ying, Shi Pei-Ming.Stability and time-delayed feedback control of a relative-rotation nonlinear dynamical system under quasic-periodic parametric excitation. Acta Physica Sinica, 2011, 60(9): 094501.doi:10.7498/aps.60.094501
[9]	Zhang Li-Ping, Xu Min, Wang Hui-Nan.Hybrid control of bifurcation in a predator-prey system with three delays. Acta Physica Sinica, 2011, 60(1): 010506.doi:10.7498/aps.60.010506
[10]	Liu Hao-Ran, Liu Bin, Liu Shuang, Wen Yan.Hopf bifurcation control in a coupled nonlinear relative rotation dynamical system. Acta Physica Sinica, 2010, 59(8): 5223-5228.doi:10.7498/aps.59.5223
[11]	Liu Hao-Ran, Zhu Zhan-Long, Shi Pei-Ming.Stability analysis of a relative rotation time-delay nonlinear dynamic system. Acta Physica Sinica, 2010, 59(10): 6770-6777.doi:10.7498/aps.59.6770
[12]	Shi Pei-Ming, Jiang Jin-Shui, Liu Bin.Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms. Acta Physica Sinica, 2009, 58(4): 2147-2154.doi:10.7498/aps.58.2147
[13]	Liu Shuang, Liu Bin, Shi Pei-Ming.Nonlinear feedback control of Hopf bifurcation in a relative rotation dynamical system. Acta Physica Sinica, 2009, 58(7): 4383-4389.doi:10.7498/aps.58.4383
[14]	Liu Su-Hua, Tang Jia-Shi.Anti-control of Hopf bifurcation at zero equilibrium of 4D Qi system. Acta Physica Sinica, 2008, 57(10): 6162-6168.doi:10.7498/aps.57.6162
[15]	Meng Zong, Liu Bin.Stability of equilibrium state of a kind of nonlinear relative rotation dynamic system and associated harmonic approximate solution. Acta Physica Sinica, 2008, 57(3): 1329-1334.doi:10.7498/aps.57.1329
[16]	Shi Pei-Ming, Liu Bin, Liu Shuang.Stability and approximate solution of a relative-rotation nonlinear dynamical system under harmonic excitation. Acta Physica Sinica, 2008, 57(8): 4675-4684.doi:10.7498/aps.57.4675
[17]	Wang Zuo-Lei.Stability and Hopf bifurcation of the simplified Lang-Kobayashi equation. Acta Physica Sinica, 2008, 57(8): 4771-4776.doi:10.7498/aps.57.4771
[18]	Shi Pei-Ming, Liu Bin.Stability of nonlinear dynamical system of relative rotation and approximate solution under forced excitation. Acta Physica Sinica, 2007, 56(7): 3678-3682.doi:10.7498/aps.56.3678
[19]	Meng Zong, Liu Bin.Stability of relativistic rotational nonlinear dynamic equation and solution for a kind of nonlinear elastic coefficients. Acta Physica Sinica, 2007, 56(11): 6194-6198.doi:10.7498/aps.56.6194
[20]	Zhao Wu, Liu Bin, Shi Pei-Ming, Jiang Jin-Shui.Analysis of stability of the equilibrium state of periodic motion in a nonlinear relative-rotation system. Acta Physica Sinica, 2006, 55(8): 3852-3857.doi:10.7498/aps.55.3852

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Vol. 59, Issue 1 - 2010-01-05

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