The early detection of tipping points, which describe a rapid departure from a stable state, is an important theoretical and practical challenge. Tipping points are most commonly associated with the disappearance of steady-state or periodic solutions at fold bifurcations. We discuss here multifrequency tipping ($M$ tipping), which is tipping due to the disappearance of an attracting torus. $M$ tipping is a generic phenomenon in systems with at least two intrinsic or external frequencies that can interact and, hence, is relevant to a wide variety of systems of interest. We show that the more complicated sequence of bifurcations involved in $M$ tipping provides a possible consistent explanation for as yet unexplained behavior observed near tipping in climate models for the Atlantic meridional overturning circulation. More generally, this Letter provides a path toward identifying possible early warning signs of tipping in multiple-frequency systems.

中文翻译：

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大西洋子午倾覆环流中与多频倾翻一致的特征

临界点的早期检测描述了从稳定状态的快速偏离，这是一个重要的理论和实践挑战。临界点最常与折叠分叉处的稳态或周期解消失有关。我们在这里讨论多频小费（$\mathrm{中号}$ 小费），这是由于吸引的圆环的消失而导致的小费。 $\mathrm{中号}$倾翻是具有至少两个可以交互作用的固有或外部频率的系统中的一种普遍现象，因此与各种感兴趣的系统相关。我们表明，涉及的更复杂的分叉序列$\mathrm{中号}$倾角为大西洋子午倾覆环流的气候模型在倾角附近观察到的尚未解释的行为提供了可能的一致解释。更一般而言，这封信提供了一条途径，以识别多频系统中可能发生的倾翻预警迹象。