Applied Mathematics and Mechanics

, Volume 8, Issue 5, pp 427–431 | Cite as

Some phenomena for weak spring Duffing equation in subharmonic and ultrasubharmonic region

  • Xu Zhen-yuan
  • Liu Zeng-rong


In this paper the situation in which weak spring Duffing equation gets into the chaos on account of small perturbation is discussed with Melnikov-Holmes' method, and some phenomena in which the different subharmonic and the ultrasubharmonic coexist with the chaos are discovered.


Mathematical Modeling Industrial Mathematic Small Perturbation Duffing Equation Weak Spring 
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  1. [1]
    Liu Zeng-rong, Yao Wei-guo, and Zhu Zhao-xuan, The way getting into chaos for solution of weak spring Duffing equation,J. Appl. Math. and Mech,7, 2 (1986).Google Scholar
  2. [2]
    Liu Zeng-rong, About some complex Phenomena in the chaos,ICNM symposium (1985).Google Scholar
  3. [3]
    Gucknheimer, J. and P.Holmes,Nonlinear Oscillation, Dynamical, and Bifurcation of Vector Fields, Springer-Verlag (1983).Google Scholar

Copyright information

© Shanghai University of Technology 1987

Authors and Affiliations

  • Xu Zhen-yuan
    • 1
  • Liu Zeng-rong
    • 2
  1. 1.Department of MathematicsAnhui Huainan Normal CollegeHuainan
  2. 2.Anhui UniversityHefei

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