一类含三势阱Mathieu-Duffing振子的相对转动系统的分岔和混沌

刘彬; 赵红旭; 侯东晓

doi:10.7498/aps.63.174502

摘要

建立了一类具有三势阱Mathieu-Duffing振子的两质量相对转动系统的非线性动力学方程. 应用多尺度法和奇异性理论分析该系统在非自治情况下的余维3分岔特性. 利用Melnikov方法获得系统在Smale马蹄意义下混沌的阈值. 最后通过数值仿真，研究了系统的混沌行为和安全盆分岔，得到安全盆被侵蚀的过程与系统通向混沌的过程之间密切联系.

关键词:

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:

作者及机构信息

1.
燕山大学电气工程学院, 秦皇岛 066004;

2.
东北大学秦皇岛分校控制工程学院, 秦皇岛 066004

基金项目: 国家自然科学基金（批准号：51405068，51105324）、河北省自然科学基金（批准号：E2014501006，E2012203194）﹑河北省科技支撑计划项目（批准号：13211907D）和河北省高等学校科学技术研究项目（批准号：ZD2014202）资助的课题.

Authors and contacts

1.
College of Electrical Engineering, YanShan University, Qinhuangdao 066004, China;

2.
Department of Control Engineering Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

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).

参考文献

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施引文献

[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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