Abstract
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.
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References
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).
Liu Zeng-rong, About some complex Phenomena in the chaos,ICNM symposium (1985).
Gucknheimer, J. and P.Holmes,Nonlinear Oscillation, Dynamical, and Bifurcation of Vector Fields, Springer-Verlag (1983).
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Communicated by Xu Zheng-fan
We would like to thank our teacher Xu Zheng-fan for his valuable and constant help during our writing.
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Zhen-yuan, X., Zeng-rong, L. Some phenomena for weak spring Duffing equation in subharmonic and ultrasubharmonic region. Appl Math Mech 8, 427–431 (1987). https://doi.org/10.1007/BF02019629
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DOI: https://doi.org/10.1007/BF02019629