The classic scenario for the generation of Dansgaard-Oeschger (DO) events assumes a link to changes in the Atlantic Meridional Overturning Circulation (AMOC) induced by North Atlantic freshwater perturbations. Recent proxy data emphasize the existence of leads and lags between DO fingerprints in Greenland and Antarctic records, highlighting the potential of a Southern Hemisphere control on these events. Investigating this possibility, we provide a conceptual model resulting from phase space reconstructions based on the northern and southern ice core records. The resulting patterns closely resemble AMOC hysteresis, consistent with a northern abrupt warming linked to gradual global temperature changes. This suggests that rapid DO warmings associated with abrupt AMOC transitions from a relatively weak (cold stadial) state to a stronger (warm inter-stadial) state can be controlled by global forcing that can be linked to the Southern Hemisphere, rather than by the end of a local temporary forcing in the North Atlantic.