通过两重快速相位随机化
Fast phase randomisation via two-folds
摘要：
二重是分段光滑向量场的不连续曲面上的一个奇点，在该点处，向量场在两侧与不连续曲面相切。如果一个轨道在稳定到规则的周期运动之前通过一个不可见的二重（也称为特谢拉奇点），那么该运动的相位不能从初始条件确定，并且在存在小噪声的情况下，大量样本解的渐近相位是高度随机的。在本文中，我们展示了如何的概率分布的渐近相位依赖于全球的非线性动力学。我们还展示了如何通过应用一个简单的不连续控制律，产生一个看不见的双重平滑振荡器的相位可以随机化。我们建议，这样的控制律可以用来descruise振荡器的集合，这种方式的相位随机化是快速相比，现有的方法（使用不动点作为相位奇点），因为没有放缓的动力学附近的两倍。
英文摘要：
A two-fold is a singular point on the discontinuity surface of a piecewise-smooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If an orbit passes through an invisible two-fold (also known as a Teixeira singularity) before settling to regular periodic motion, then the phase of that motion cannot be determined from initial conditions, and in the presence of small noise the asymptotic phase of a large number of sample solutions is highly random. In this paper we show how the probability distribution of the asymptotic phase depends on the global nonlinear dynamics. We also show how the phase of a smooth oscillator can be randomised by applying a simple discontinuous control law that generates an invisible two-fold. We propose that such a control law can be used to desynchronise a collection of oscillators, and that this manner of phase randomisation is fast compared to existing methods (which use fixed points as phase singularities) because there is no slowing of the dynamics near a two-fold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
