缓慢变化强迫下的静摩擦振荡器：利用爆破揭示小尺度现象
A stiction oscillator under slowly varying forcing: Uncovering small scale phenomena using blowup
摘要：
在本文中，我们考虑一个质量弹簧摩擦振子与摩擦建模的正则化静摩擦模型的限制，其中的自然弹簧频率和强迫频率的比例是在同一数量级的规模与正则化静摩擦模型。研究这种情况的动机来自于\cite{bossolini2017b}，它证明了在这种状态下的新摩擦现象。Bossolini等人2017年的结果导致了一些开放的问题，我们在本文中解决了这些问题。特别是，使用GSPT和blowup，我们提供了一个简单的几何描述的分歧的粘滑极限环通过组合的鸭式和全球返回机制。我们还表明，这种组合导致鸭式马蹄，因此能够证明在这个基本的振荡器系统的混沌存在。
英文摘要：
In this paper, we consider a mass-spring-friction oscillator with the friction modelled by a regularized stiction model in the limit where the ratio of the natural spring frequency and the forcing frequency is on the same order of magnitude as the scale associated with the regularized stiction model. The motivation for studying this situation comes from \cite{bossolini2017b} which demonstrated new friction phenomena in this regime. The results of Bossolini et al 2017 led to some open problems, that we resolve in this paper. In particular, using GSPT and blowup we provide a simple geometric description of the bifurcation of stick-slip limit cycles through a combination of a canard and a global return mechanism. We also show that this combination leads to a canard-based horseshoe and are therefore able to prove existence of chaos in this fundamental oscillator system.
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