Onset of bubbling, i.e., a sudden appearance of high frequency oscillations disrupting the waveform of a slowly oscillating signal in a restricted phase interval, is a serious problem for many applications in the field of power electronics. It has been shown in many publications that the appearance of bubbling is typically associated with a classical (smooth) bifurcation, as for example a pitchfork or a flip, but the mechanism leading to this phenomenon remained unclear. In the present work we focus on bubbling in nonautonomous models given by 1D maps. Using the recently developed cobweb diagrams for such maps, we suggest a novel geometric approach to deal with this phenomenon. As a first step, we explain the onset of bubbling in a model where it is not related to any smooth bifurcation. As a second step, we demonstrate that the provided explanation holds also for models where the onset of bubbling follows such a bifurcation. We show that bubbling does indeed appear soon, but not immediately, after a smooth bifurcation and explain why this fact has been overlooked before.

对于电力电子领域中的许多应用而言，起泡的开始，即高频振荡的突然出现破坏了在有限的相位间隔中的缓慢振荡的信号的波形，是一个严重的问题。在许多出版物中已经表明，鼓泡的外观通常与经典的（光滑的）分叉有关，例如干草叉或翻转，但导致这种现象的机理仍不清楚。在当前的工作中，我们专注于一维映射给出的非自治模型中的冒泡。使用最近开发的此类地图的蜘蛛网图，我们建议一种新颖的几何方法来处理这种现象。第一步，我们说明在与任何平滑分叉都不相关的模型中起泡的发生。第二步 我们证明，所提供的解释也适用于其中冒泡发生在这种分叉之后的模型。我们表明，在平稳的分叉之后，冒泡确实确实会很快出现，但不会立即出现，并解释为什么以前忽略了这个事实。