Signatures consistent with multi-frequency tipping in the Atlantic meridional overturning circulation

Abstract

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 and are often associated with hysteresis loops. 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, 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 behaviour 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.