一个非线性振子的浑沌现象*
The Chaotic Behavior of a Nonlinear Oscillator
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摘要: 本文利用Mel'nikov方法和数值模拟对含二次非线性项的受迫振动系统=fcosωτ的分叉与浑沌进行了研究。
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关键词:
- 非线性振动 /
- 数值模拟 /
- Mel’nikov方法 /
- 浑沌运动
Abstract: Behavior of bifurcation and chaos in a forced oscillator =fcosωτ containing a square nonlinear term is investigated by using Mel nikov method and digital computer simulations.-
Key words:
- nonlinear vibration /
- digital computer simulation /
- Mel’nikov method /
- chaotic motion
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[1] Holmes,P.J.,A nonlinear oscillation with a strange attractor,Phil.Trans.Roy.Soc.London,AI,394(1979),419-448. [2] Holmes,P.J.and F.C.Moon,Strange attractors and chaos in nonlinear mechanics,ASME J.Appl.Mech.,12(1983),1021-1032. [3] 李继彬、刘曾荣,几类非线性受迫浑沌性质,数学物理学报,5(1986),195-204. [4] Nestor N.S.and A.H.Nayfeh,Prediction of bifurcations in a parametrically excited duffing Oscillator,Int.J.Non-linear Mechanics,25(1990),163-176. [5] Minorsky N.,Introduction to Nonlinear Mechanics,J.W.Edwards.Ann.Arbor,Mich.,(1947). [6] 倪皖荪、魏荣爵,含二次作线性项受迫振动系统的分叉和浑沌现象.物理学报,34(1985), 503-511 [7] Guckenheimer,J.and P.J.Holmes,Nonlinear Oscillations,Dynamical Systems and Bifurcation of Vector Field Springer-Verlag,(1983). [8] 郝柏林,分叉、浑沌、奇怪吸引子、湍流和其他,物理学进展,3(1983), 329-416 -
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