The ocean plays with three hands. One hand is fast: the surface temperature of the Pacific Ocean changes over weeks. Another hand is medium: the depth of the warm layer rearranges over months. The third hand is slow: the entire system tilts toward warm El Niño or cold La Niña, and that takes years. Three tempos weave into a rhythm that is sometimes steady, sometimes jagged, like a jazz improvisation.

Previously, this rhythm was described with two hands. A fast variable and a slow one, while the medium one went unnoticed. But the ocean does not play with two hands. In the new work from Edinburgh, the El Niño model gained three tempos, and it immediately became clear that earlier calculations missed entire classes of motions.

The key image is the equilibrium surface. Imagine a stretched fabric over which a ball slides. As long as the fabric is flat, the ball crawls slowly. But in some places the fabric dips, and the ball falls off. In the model, there are several such dips, and they determine which type of oscillation arises. If there is one dip, the system accumulates stress and releases it in a sharp jump, which is a relaxation oscillation. If there are more dips, the trajectory may get stuck on a shelf: barely moving for a long time, then suddenly falling off. That is a plateau.

The numbers in the paper are small but important. The small parameters δ and ρ equal 0.01, meaning fast processes are a hundred times faster than slow ones. And parameter a in one example reaches 25.55, and at that value the system's behavior changes qualitatively. It is here that oscillations without plateaus are born, which were not seen before.

The same geometry appears in ecology. The predator-prey model is structured similarly: populations change at different rates, and there too are equilibrium surfaces with dips. Therefore, results from climate transfer to biology almost unchanged.

The ocean continues to play with three hands. Now we have the notes for all three, and we can hear where exactly the rhythm falters. This is not a weather forecast for tomorrow, but an understanding of why tomorrow might not look like today.