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高维非线性系统的全局分岔和混沌动力学研究

张伟 姚明辉 张君华 李双宝

张伟, 姚明辉, 张君华, 李双宝. 高维非线性系统的全局分岔和混沌动力学研究[J]. 力学进展, 2013, 43(1): 63-90. doi: 10.6052/1000-0992-12-053
引用本文: 张伟, 姚明辉, 张君华, 李双宝. 高维非线性系统的全局分岔和混沌动力学研究[J]. 力学进展, 2013, 43(1): 63-90. doi: 10.6052/1000-0992-12-053
ZHANG Wei, YAO Minghui, ZHANG Junhua, LI Shangbao. Study of global bifurcations and chaotic dynamics for high-dimensional nonlinear systems[J]. Advances in Mechanics, 2013, 43(1): 63-90. doi: 10.6052/1000-0992-12-053
Citation: ZHANG Wei, YAO Minghui, ZHANG Junhua, LI Shangbao. Study of global bifurcations and chaotic dynamics for high-dimensional nonlinear systems[J]. Advances in Mechanics, 2013, 43(1): 63-90. doi: 10.6052/1000-0992-12-053

高维非线性系统的全局分岔和混沌动力学研究

doi: 10.6052/1000-0992-12-053
基金项目: 国家自然科学基金项目(11290152,11072008,11172009,10732020,10872010)资助
详细信息
    作者简介:

    张伟, 北京工业大学机电学院教授、博士生导师. 1997 年在天津大学力学系一般力学专业获得博士学位, 1997 年破格晋升为教授. 2004 年获得国家杰出青年科学基金项目, 2003 年获得海外青年学者合作研究基金项目, 2007 年获得国家自然科学基金重点项目. 加拿大西安大略大学博士后,加拿大多伦多大学机械与工业工程系访问教授, 香港城市大学访问教授. 2010 入选北京市属高等学校人才强教深化计划\高层次人才资助计划". 2007 年入选北京市属高等学校人才强教计划"学术创新团队". 发表学术论文300 多篇, 其中在国际学术期刊发表学术论文100 多篇, 100 多篇论文被SCI 收录, 150 多篇论文被EI 收录. 在科学出版社出版学术专著3 本. 主要研究领域包括新型材料结构的高维非线性系统的全局分岔和混沌动力学, 规范形的理论和应用, 高维非线性系统的全局摄动法, 航空航天飞行器结构非线性动力学, 非线性连续系统的全局动力学, 混沌运动的控制, 减振器的非线性动力学, 流体诱发的结构系统的非线性动力学, 可变体飞行器的非线性动力学与控制.

    通讯作者:

    张伟

  • 中图分类号: O322

Study of global bifurcations and chaotic dynamics for high-dimensional nonlinear systems

Funds: The project was supported by the National Natural Science Foundation of China (11290152, 11072008, 11172009, 10732020, 10872010).
More Information
    Corresponding author: ZHANG Wei
  • 摘要:

    综述了Melnikov方法的发展历史, 从1963年苏联学者Melnikov提出该方法开始, 一直到目前广义Melnikov方法的提出和发展. Melnikov方法的发展历程可以概括为3 个阶段, 分别综述了每一个阶段Melnikov方法的扩展和应用, 论述了国内外在该方向的研究现状和所获得的主要结果, 指出了各种Melnikov方法之间的联系、存在的问题和不足. 为了对比两种研究高维非线性系统多脉冲混沌动力学的理论, 本文综述了另外一种全局摄动理论, 即能量相位法, 总结了该方法十几年来的发展历史以及国内外的理论研究成果和工程应用实例, 阐述了能量相位法发展的根源以及与Melnikov方法的内在联系, 比较了能量相位法和广义Melnikov方法两种理论研究对象的差别, 以及各自所存在的不足和问题. 简要论述了能量相位法和广义Melnikov方法的理论体系, 并利用广义Melnikov方法分析了四边简支矩形薄板的多脉冲混沌动力学, 数值模拟进一步验证了理论研究的结果. 最后, 详细综述了两种理论的缺点和不足, 说明今后全局摄动理论的发展方向.

     

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  • 收稿日期:  2012-04-06
  • 修回日期:  2012-12-14
  • 刊出日期:  2013-01-24

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