软弹簧型Duffing方程在摄动下分支出的极限环

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Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation

Department of Mathematics, Hubei Normal University, Huangshi 435002, P. R. China

摘要: 在这篇文章中,作者用Melnikov函数方法分析了软弹簧型Duffing方程[1]在摄动下异宿轨道破裂后稳定流形与不稳定流形的相对位置,给出了方程在不同摄动下分支出极限环的条件与极限环的位置.
- 极限环 /
- 异宿轨道 /
- Melnikov函数
Abstract: In this paper,foe Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring Duffing equation^[1] after its heteroclinic orbits rupture as the result of a small perturbation.The conditionsthat limit circles are bifurcated are given,and the their stability and location isdetermined.
- limit circle /
- heteroclinic orbit /
- Melnikov function

[1]	李继彬,《浑沌与Melnikov 方法》,重庆大学出版社(1989).
[2]	T.Gukenheimer and P.Holmes,Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Field,Spring-Verlag.New York.Berlin.Tokyo(1984).
[3]	沈家骐、俞伯华,非线性扰动方程的紊动性态,数学学报,31(2)(1988),215-220.(in Chinese).
[4]	叶彦谦,《极限环论》,(修改版),上海科学技术出版社(1984).