受迫Holmes-Duffing系统安全域分形及时滞速度反馈控制

尚慧琳

doi:10.7498/aps.61.180506

摘要

以受迫Holmes-Duffing系统为研究对象, 对系统施加时滞速度反馈控制, 研究周期激励引起的系统安全域的分形侵蚀及时滞速度反馈对分形侵蚀安全盆的控制作用. 利用Melnikov函数法给出时滞受控系统的安全盆的边界分形条件. 再以时滞量为变参数, 运用四阶Runge-Kutta方法和点映射方法数值研究了时滞对受控系统安全盆的影响规律. 结果表明在弱反馈下, 时滞量的增大能够提高安全盆边界分形的阈值, 从而抑制安全盆的分形侵蚀. 说明时滞速度反馈能够有效抑制系统的安全盆侵蚀.

关键词:

Abstract

A forced Holmes-Duffing system is considered in this paper. A delayed velocity feedback is opplied to the system. The erosion of safe basin, caused by the periodic excitation, and the effects of delayed velocity feedback on the controlling of the fractal eroded safe basin are investigated. The conditions of fractal erosion of the basin boundary are obtained by the Melnikov method. Then considering the time delay as a variable parameter, the evolutions of safe basin with time delay are presented numerically by the 4th Runge-Kutta and the point-to-point mapping method. It is found that the increase of time delay can enhance the threshold of the fractal erosion of the basin boundary under a weak and positive feedback gain so as to reduce the basin erosion. These imply that the delayed velocity feedback can control the basin erosion of the system effectively.

Keywords:

作者及机构信息

尚慧琳

1.
上海应用技术学院, 机械工程学院, 上海 200235

基金项目: 国家自然科学基金(批准号: 10902071);上海市教委晨光计划(批准号: 11CG61);上海应用技术学院科学技术发展基金(批准号: KJ2011-06)和上海市教育委员会重点学科建设项目(批准号: J51501)资助的课题.

Authors and contacts

Shang Hui-Lin

1.
School of Mechanical Engineering, Shanghai Institute of Technology, Shangha 200235, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10902071), the "Twilight" Program of Shanghai Education Commission, China (Grant No. 11CG61), Foundation of Science and Technology of Shanghai Institute of Technology, China (Grant No. KJ2011-06), and Shanghai Leading Academic Discipline Program, China (Grant No. J51501).

参考文献

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[11]	Shang H L, Xu J 2009 Chaos, Solitons and Fractals 41 1880
[12]	Shang H L 2011 Chin. Phys. Lett. 28 010502
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施引文献

[1]	Thompson J M T, Rainey F C T, Soliman M S 1995 Philosophical Transactions of the Royal Society 332 149
[2]	Soliman M S 1995 J. Sound Vib. 182 618
[3]	Gu J Y, Miao Z H 2005 Journal of Jiangsu University of Science and Technology (Natural Science Edition) 19 6 (in Chinese) [谷家扬, 缪振华 2005 江苏科技大学学报(自然科学版) 19 6]
[4]	Long Z J, Lee S K, Kim J Y 2010 Ocean Engineering 37 418
[5]	Marcos S H C, Lopes S R, Viana R L 2003 Chaos, Solitons and Fractals 15 417
[6]	Lewis C P, Ucar A, Bishop S R 1998 Transactions of the Institute of Measurement and Control 20 29
[7]	Zhang Q, Wang B H, Yang C W 2005 Power System Technology 29 63 (in Chinese) [张强, 王宝华, 杨成梧 2005 电网技术 29 63]
[8]	Fadi M A, Mohammad I Y, Hassen M O 2009 Smart Material Structure 19 045013
[9]	Lenci S, Rega G 2006 J. Micromechanics and Microengineering 16 390
[10]	Fadi M A, Mohammad I Y 2010 Smart Material Structure 19 035016
[11]	Shang H L, Xu J 2009 Chaos, Solitons and Fractals 41 1880
[12]	Shang H L 2011 Chin. Phys. Lett. 28 010502
[13]	Shang H L 2011 Acta Phys. Sin. 60 070501 (in Chinese) [尚慧琳 2011 物理学报 60 070501]
[14]	Sun Z K, Xu W, Yang X L, Fang T 2006 Chaos, Solitons and Fractals 27 705
[15]	Gan C B 2006 Nonlin. Dyn. 45 305
[16]	Gan C B, He S M 2007 Acta Mech. Sin. 23 577
[17]	Stephen W 2003 Introduction to Applied Nonlinear Dynamical Systems and Chaos (2nd Ed.) (New York: Springer-Verlag) p62
[18]	Hu H Y 2000 Applied Nonlinear Dynamics (Beijing: Aviation Industry Press) p176 (in Chinese) [胡海岩 2000 应用非线性动力学 (北京: 航空工业出版社) 第176页]

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