## 留言板

 引用本文: 刘延彬, 陈予恕, 曹庆杰. 无小参数系统的混沌与亚谐共振[J]. 应用数学和力学, 2011, 32(1): 1-10.
LIU Yan-bin, CHEN Yu-shu, CAO Qing-jie. Chaos and Sub-Harmonic Resonance of Nonlinear System Without Small Parameters[J]. Applied Mathematics and Mechanics, 2011, 32(1): 1-10. doi: 10.3879/j.issn.1000-0887.2011.01.001
 Citation: LIU Yan-bin, CHEN Yu-shu, CAO Qing-jie. Chaos and Sub-Harmonic Resonance of Nonlinear System Without Small Parameters[J]. Applied Mathematics and Mechanics, 2011, 32(1): 1-10.

## 无小参数系统的混沌与亚谐共振

##### doi: 10.3879/j.issn.1000-0887.2011.01.001

###### 作者简介:刘延彬(1974- ),男,哈尔滨人,博士(E-mail:d_lyb@126.com);陈予恕(1932- ),男,山东肥城人,教授,院士(联系人.E-mail:yschen@hit.edu.cn).
• 中图分类号: O193；O322

## Chaos and Sub-Harmonic Resonance of Nonlinear System Without Small Parameters

• 摘要: Melnikov方法是判别混沌和亚谐共振的一种重要方法．传统的Melnikov方法依赖于小参数，在大多数实际物理系统中，小参数是不存在的．因此，传统的Melnikov方法不能应用于强非线性系统．为了摆脱小参数对Melnikov方法的限制，采用同伦分析将Melnikov方法拓展到强非线性系统，且采用该方法研究了一个强非线性系统的亚谐共振与混沌，解析结果和数值结果相互吻合，说明了该方法的有效性．
•  [1] CHEN Yu-shu, Leung Andrew Y T. Bifurcation and Chaos in Engineering[M]. New York: Springer ,1998. [2] Wiggins S.Introduction to Applied Nonlinear Dynamical Systems and Chaos[M].New York:Springer-Verlag,1990. [3] Greenspan B D, Holmes P J.Homoclinic orbits, subharmonics and global bifurcations in forced oscillations[C] Barenblatt G, Iooss G, Joseph D D. Nonlinear Dynamics and Turbulence. London: Pitman, 1983: 172-214. [4] Wiggins S. Global Bifurcations and Chaos[M].New York:Springer-Verlag,1988. [5] Liao S J. Beyond Perturbation：Introduction to Homotopy Analysis Method[M]. Bpca Taton: Chapmaen Hall/CRC Press, 2003. [6] Liao S J. The proposed homotopy analysis techniques for the solution of nonlinear problems[D]. Ph D dissertation. Shanghai: Shanghai Jiao Tong University, 1992. [7] Liao S J. On the homotopy analysis method for nonlinear problems[J].Appl Math Comput, 2004,147(2): 499-513. [8] Liao S J. A kind of approximate solution technique which does not depend upon small parameters—Ⅱ:an application in fluid mechanics[J]. Int J Non-Linear Mech, 1997, 32(4):815-822. [9] Liao S J. An explicit, totally analytic approximation of Blasius viscous flow problems[J]. Int J Non-Linear Mech, 1999,34(4):759-785

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##### 出版历程
• 收稿日期:  2010-09-15
• 修回日期:  2010-12-07
• 刊出日期:  2011-01-15

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