The stability of parametrically forced coupled oscillators in sum resonance

The stability of parametrically forced coupled oscillators in sum resonance
复制标题

和谐振中参量强制耦合振荡器的稳定性

DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
M. Ruijgrok
M. Ruijgrok
中科院分区：
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文献类型：
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作者：
I. Hoveijn;M. Ruijgrok

文献摘要

被引文献

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对于两个有阻尼的参数化强迫振子的和共振系统，强迫的振幅与频率的平面稳定性图在阻尼为零处显示出不连续。这是一种众所周知的现象，我们对此作了几何解释。一个线性稳定性分析就足够了。我们证明了这个问题的一般（即结构稳定）矩阵展开需要四个参数，这表明稳定性图实际上是四维的。稳定区域在参数空间上的边界是奇异的，这为平面稳定性图的不连续提供了几何解释。
For a system of two damped parametrically forced oscillators in sum resonance the planar stability diagram of amplitude versus frequency of the forcing shows a discontinuity at damping zero. This is a well known phenomenon, for which we give a geometrical explanation. A linear stability analysis suffices. We show that a versal (i.e. a structurally stable) matrix unfolding for this problem needs four parameters, indicating that the stability diagram is actually four dimensional. The boundary of the stability region in parameter space is singular, this provides a geometric explanation of the discontinuity in the planar stability diagram.