- 必威体育下载

姓名
邮箱
手机号码
标题
留言内容
验证码

Abstract

The dynamic equation of a nonlinear relative rotation system with a triple-well Mathieu-Duffing oscillator is investigated. Firstly, a codimension three-bifurcation characteristic is deduced by combining with the multi-scale method and singularity theory under the condition of nonautonomy. Secondly, the threshold value of chaos about Smale horseshoe commutation is given from Melnikov method. Finally, the numerical simulation exhibits safe basins and chaos, and the erosion process of safe basins, which is closely related to the process, leading to chaos.

Keywords:

Authors and contacts

1.
2.
Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 51405068, 51105324), the Natural Science Foundation of Hebei Province, China (Grant Nos. E2014501006, E2012203194), the Hebei Province Science and Technology Support Program (Grant No. 13211907D), and the Colleges and Universities Research Fund of Hebei Province (Grant No. ZD2014202).

References

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]

Cited By

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]

[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]	Shang Hui-Lin, Han Yuan-Bo, Li Wei-Yang.Suppression of chaos and basin erosion in a nonlinear relative rotation system by delayed position feedback. Acta Physica Sinica, 2014, 63(11): 110502.doi:10.7498/aps.63.110502
[3]	Zhang Wen-Ming, Li Xue, Liu Shuang, Li Ya-Qian, Wang Bo-Hua.Chaos and the control of multi-time delay feedback for some nonlinear relative rotation system. Acta Physica Sinica, 2013, 62(9): 094502.doi:10.7498/aps.62.094502
[4]	Meng Zong, Fu Li-Yuan, Song Ming-Hou.Bifurcation of a kind of nonlinear-relative rotational system with combined harmonic excitation. Acta Physica Sinica, 2013, 62(5): 054501.doi:10.7498/aps.62.054501
[5]	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
[6]	Tang Rong-Rong.The renormalization solution for a class of relative rotation nonlinear dynamic model with multi-frequency excitation. Acta Physica Sinica, 2012, 61(20): 200201.doi:10.7498/aps.61.200201
[7]	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
[8]	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
[9]	Liu Shuang, Liu Bin, Zhang Ye-Kuan, Wen Yan.Hopf bifurcation and stability of periodic solutions in a nonlinear relative rotation dynamical system with time delay. Acta Physica Sinica, 2010, 59(1): 38-43.doi:10.7498/aps.59.38
[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]	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
[12]	Hou Dong-Xiao, Liu Bin, Shi Pei-Ming.The bifurcation of a kind of relative rotational dynamic equation with hysteresis and its approximate solution. Acta Physica Sinica, 2009, 58(9): 5942-5949.doi:10.7498/aps.58.5942
[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]	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
[15]	Shi Pei-Ming, Liu Bin, Hou Dong-Xiao.Chaotic motion of some relative rotation nonlinear dynamic system. Acta Physica Sinica, 2008, 57(3): 1321-1328.doi:10.7498/aps.57.1321
[16]	Wang Hai-Lei, Yang Shi-Ping.Switch effect of Bose-Einstein condensates in a triple-well potential. Acta Physica Sinica, 2008, 57(8): 4700-4705.doi:10.7498/aps.57.4700
[17]	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
[18]	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
[19]	Zhao Wu, Liu Bin.Series solution for relative-rotation motion equation. Acta Physica Sinica, 2005, 54(10): 4543-4548.doi:10.7498/aps.54.4543
[20]	Dong Quan-Lin, Wang Kun, Zhang Chun-Xi, Liu Bin.An integral solution for the relative-rotation dynamic equation of a cylinder. Acta Physica Sinica, 2004, 53(2): 337-342.doi:10.7498/aps.53.337

Catalog

Vol. 63, Issue 17 - 2014-09-05

Metrics

Abstract views:6042
PDF Downloads:437
Cited By:0

Search

Article

留言板

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About