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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.
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Keywords:
- relatively rotation /
- Mathieu-Duffing /
- triple-well /
- safe basins
[1] Carmeli M 1985 Found. Phys. 15 175
[2] [3] Carmeli M 1986 Int. J. Theor. Phys. 25 89
[4] [5] Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese)[罗绍凯 1996 北京理工大学学报 16(S1) 154]
[6] Luo S K 1998 Appl. Math. Mech. 19 45
[7] [8] Shi P M, Han D Y, Liu B 2010 Chin. Phys. B. 19 90306
[9] [10] [11] Liu Sh, Liu H R, Wen Y, Liu B 2010 Acta Phys. Sin. 59 5223 (in Chinese)[刘爽, 刘浩然, 闻岩, 刘彬 2010 物理学报 59 5223]
[12] Liu Sh, Liu B, Zhang Y K, Wen Y 2010 Acta Phys. Sin. 59 38 (in Chinese)[刘爽, 刘彬, 张业宽, 闻岩 2010 物理学报 59 38]
[13] [14] Rong H W, Wang X D, Xu W, Fang T 2007 Acta Phys. Sin. 56 2005 (in Chinese)[戎海武, 王向东, 徐伟, 方同 2007 物理学报 56 2005]
[15] [16] Tchoukuegno R, Nana Nbendjo B R, Woafo P 2002 Phy. A 304 362
[17] [18] [19] Chen S Y, Tang J Y 2008 J. Sound Vib. 318 1109
[20] Zhang Q Ch, Wang W, Liu F H 2008 Chin. Phys. B 17 4123
[21] [22] Feng J J, Zhang Q Ch, Wang W 2011 Chin. Phys. B 20 090202
[23] [24] Meng Z, Fu L Y, Song M H 2013 Acta Phys. Sin. 62 054501 (in Chinese)[孟宗, 付立元, 宋明厚 2013 物理学报 62 054501]
[25] -
[1] Carmeli M 1985 Found. Phys. 15 175
[2] [3] Carmeli M 1986 Int. J. Theor. Phys. 25 89
[4] [5] Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese)[罗绍凯 1996 北京理工大学学报 16(S1) 154]
[6] Luo S K 1998 Appl. Math. Mech. 19 45
[7] [8] Shi P M, Han D Y, Liu B 2010 Chin. Phys. B. 19 90306
[9] [10] [11] Liu Sh, Liu H R, Wen Y, Liu B 2010 Acta Phys. Sin. 59 5223 (in Chinese)[刘爽, 刘浩然, 闻岩, 刘彬 2010 物理学报 59 5223]
[12] Liu Sh, Liu B, Zhang Y K, Wen Y 2010 Acta Phys. Sin. 59 38 (in Chinese)[刘爽, 刘彬, 张业宽, 闻岩 2010 物理学报 59 38]
[13] [14] Rong H W, Wang X D, Xu W, Fang T 2007 Acta Phys. Sin. 56 2005 (in Chinese)[戎海武, 王向东, 徐伟, 方同 2007 物理学报 56 2005]
[15] [16] Tchoukuegno R, Nana Nbendjo B R, Woafo P 2002 Phy. A 304 362
[17] [18] [19] Chen S Y, Tang J Y 2008 J. Sound Vib. 318 1109
[20] Zhang Q Ch, Wang W, Liu F H 2008 Chin. Phys. B 17 4123
[21] [22] Feng J J, Zhang Q Ch, Wang W 2011 Chin. Phys. B 20 090202
[23] [24] Meng Z, Fu L Y, Song M H 2013 Acta Phys. Sin. 62 054501 (in Chinese)[孟宗, 付立元, 宋明厚 2013 物理学报 62 054501]
[25]
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