Abstract
In this paper, the Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring. Duffing equation after its heteroclinic orbits rupture as the result of a small perturbation. The conditions that limit circles are bifurcated are given, and then their stability and location is determined.
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References
Li Jibin,Chaos and Melnikov Method, Chongqing University Publication (1989) (in Chinese)
T. Gukenheimer and P. Holmes,Nonlinear Oscillations. Dynamical Systems and Bifurcations of Vector Field Springer-Verlag, New York, Berlin, Tokyo (1984).
Shen Jiaqi and Yu Baihua. Chaotic behaviors in nonlinear perturbed equations.Acta Math. Science,31, 2 (1988). 215–220. (in Chinese)
Ye Yanqian,The Theory of Limit Cycles. Revised edition. Shanghai Science and Technology Publication (1984). (in Chinese)
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Communicated by Xu Zhengfan
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Fude, C. Limit circles bifurcated from a soft spring duffing equation under perturbation. Appl Math Mech 19, 129–133 (1998). https://doi.org/10.1007/BF02457680
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DOI: https://doi.org/10.1007/BF02457680