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Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator

机译:非线性振子的多重屈曲和余维-三岔现象

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In this paper, we investigate the global bifurcations and multiple bucklings of a nonlinear oscillator with a pair of strong irrational nonlinear restoring forces, proposed recently by Han et al. [2012]. The equilibrium stabilities of multiple snap-through buckling system under static loading are analyzed. It is found that complex bifurcations are exhibited of codimension-three with two parameters at the catastrophe point. The universal unfolding for the codimension-three bifurcation is also found to be equivalent to a nonlinear viscous damped system. The bifurcation diagrams and the corresponding codimension-three behaviors are obtained by employing subharmonic Melnikov functions for the existing singular closed orbits of homoclinic, tangent homoclinic, homo-heteroclinic and cuspidal heteroclinic, respectively.
机译:在本文中,我们研究了由Han等人最近提出的具有一对强非理性非线性恢复力的非线性振荡器的整体分叉和多重屈曲。 [2012]。分析了静态载荷作用下多个快速扣紧系统的平衡稳定性。发现在突变点处具有两个参数的余维3表现出复杂的分叉。共维三分叉的普遍展开也被发现等效于非线性粘性阻尼系统。分岔图和相应的余维三性是通过分别利用亚调和的Melnikov函数获得的现有单斜,正切同斜,同异斜和尖齿异斜的奇异闭合轨道的。

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