Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation

Cheng Fude

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Cheng Fude. Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation[J]. Applied Mathematics and Mechanics, 1998, 19(2): 121-125.

Citation:

Cheng Fude. Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation[J]. Applied Mathematics and Mechanics, 1998, 19(2): 121-125.

Citation:

Cheng Fude. Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation[J]. Applied Mathematics and Mechanics, 1998, 19(2): 121-125.

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Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation

Cheng Fude

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

Received Date: 1996-04-29
Publish Date: 1998-02-15

Abstract

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

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References(4)

References

[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).