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 multi-frequency 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 work provides a path towards identifying possible early-warning signs of tipping in multiple-frequency systems.

中文翻译：

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与大西洋子午倾覆环流中多频倾翻相符的特征

临界点的早期检测描述了快速脱离稳定状态，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（M-tipping），这是由于吸引圆环的消失而引起的小费。M倾斜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，因此与多种感兴趣的系统相关。我们表明，涉及M小费的更复杂的分叉序列为大西洋子午翻转循环气候模型中的小费附近观察到的尚未解释的行为提供了可能的一致解释。更普遍，