含二次非线性项的受迫振子在主共振曲线上表现的浑沌特性*
Chaotic Behavior of Forced Oscillator Containing a Square Nonlinear Term on Principal Resonance Curves
-
摘要: 本文在[1]的基础上,用多尺度法和数值模拟对含二次非线性项的受迫振子作了进一步研究,探讨了其浑沌域与主共振曲线的关系,通过对主共振曲线稳定性的分析,我们推测浑沌运动将发生在主共振曲线具有垂直切线的频率附近,数值模拟结果证实了这一推测。这就为那些难以用Melnikov方法处理的系统,提供了一条寻求浑沌运动的可行途径。Abstract: Based on [1],we investigate the route to chaos in forced oscillator containing a square nonlinear term on principal resonance curves. And chaotic motion is observed against the background of classical resonance curves,stability limits and jump phenomena.It is shown that chaotic motion appears in the neighbourhood of the point both meeting condition that Melnikov function has simple zero and having the point of vertical tangent of the resonance curves.
-
[1] 裴钦元、李骊,一个非线性振子的浑沌现象,应用数学和力学,14(5)(1993),377-388. [2] Guokenheimer,J.and P.J.Holmes,Nonlinear oscillations,dynamical systems and bifurcations of vector fields. Revised and Corrected,SPringer-Verlay (1986). [3] 李继彬、刘曾荣,一类二次系数周期扰动的浑沌性质,科学通报,7(1985),491-495. [4] 李继彬、刘曾荣,几类非线性受迫振动系统的浑沌性质,数学物理学报,5(1986),195-204. [5] 林常,有限个次谐分叉导致浑沌的一个例子,科学通报,(1985),980-982. [6] Szemplinska-Stupnicka,W.,Bifurcations of harmonic solution leading to chaotic motion in the softening type duffing's oscillator,Int,J. Nonlinear Mechanics,23(1988),257-277 [7] Szemplinska-Stupnicka,W.and P.Niezgodzki,The approximate approach to chaos phenomena in oscillators having single equilibrium position,l ,Sound and Vibraiion,14(1990),181-192. [8] Minorsky,N.,Introduction to Nonlinear Mechanics,J,W,Edwards,Ann,Arbor,Mich,(1947). [9] Nayfeh,A.H. and D,T. Mook,Nonlinear Oscillations,John Wiley,New York.(1979).
点击查看大图
计量
- 文章访问数: 1685
- HTML全文浏览量: 44
- PDF下载量: 438
- 被引次数: 0