The orchestra plays in harmony, but the conductor gradually loses control. First one musician lags slightly, then another speeds up, and soon each is playing at their own tempo, even though a minute ago they all followed the same melody. This is roughly what happens in the El Niño climate system: two independent rhythms—the ocean's own rhythm and the imposed seasonal cycle—can coexist for years, then suddenly fall out of sync.

Inside this system, a simple equation with memory operates: the rate of change of the warm layer's depth depends on what it was almost a year ago. When parameters enter a special region where two feedback cycles fit exactly into seven years, tori emerge in phase space—surfaces along which the system moves like a thread winding around a doughnut, looping with two different periods.

Previously, it was unclear how such tori break apart in equations with memory. Now, for the first time, the authors have numerically reproduced the full picture: when two tori approach each other, they disappear, and instead of a smooth transition, the system lurches into a sharp switch, as if the orchestra didn't gradually go out of tune but suddenly broke into cacophony. This finding could help in searching for precursors of abrupt climate shifts, though there is no direct practical application yet.