强Duffing系统的局部分岔分析<sup>*</sup>

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强Duffing系统的局部分岔分析^*

基金项目: * 国家自然科学基金,博士点基金

摘要: 本文通过坐标变化和近恒等变化,将强Duffing方程化成范式,从而可以得到在不同共振条件下的分合方程以及其近似解,应用奇异性理论研究了强Duffing在开折参数及物理参数平面上的转迁集及其局部分岔图。
- NormalForm理论 /
- 奇异性理论 /
- 普适开折 /
- 转迁集 /
- 强Duffing系统
Abstract: By using coordinate and nearly,identical transformations.the strongly nonlinear Duffing system is reduced to normal form in this paper.and then the bifurcation equations with different resonant conditions and their solutions are obtained.The local bifurcation diagrams and the transition sets on unfolding parmeter and physical parameter plane are analysized by singularity theory.
- normal form theory /
- singularity theory /
- universal unfolding /
- transition set /
- strongly nonlinear Duffing system

[1]	A.H.Nayfeh,D.T.Mook and S.Sridhar,Nonlinear analysis of the forced response of structural elements,J.Acoust.Soc.Am.,55(1974),281-291.
[2]	P.J.Holmes,Averaging and chaotic motion in forced oscillations,SIAM,J.Appl.Math.,38(1980),65-80.
[3]	陈予恕,《非线性振动系统的分岔和混沌理论》,高等教育出版社(lass)
[4]	张建,《周期激励下Duffing系统复杂动力学行为研究》,天津大学硕士论文(1991).
[5]	L.Jezeque and C.H.Lamarque,Analysis of nonlinear dynamical systems by normal form theory,J.Sound Vib.,149(1991),429-459.
[6]	S.N.Chow and J.K.Hale,Methods of Bifurcation Theory,Springer-Verlag(1982).