Every winter, the water off the coast of Peru turns warmer or cooler than usual. The warm state is called El Niño, the cold one La Niña. Both phenomena influence weather across the globe: they bring droughts in some regions and floods in others. And both most often reach their greatest strength in December.

The ocean behaves like a swing with a delay: if the water warms up today, the effects won't show up right away but several months later. That's why scientists describe this phenomenon with an equation that has memory. In such a model, the rate of temperature change depends not only on what's happening now but also on what happened before. The seasonal cycle, that is, the changing of the seasons, acts as a rhythmic external push.

The mathematicians added seasonal forcing to the equation and mapped how the system behaves under different conditions. It turned out that the regions of rhythm synchronization are very narrow. That's why real El Niño doesn't repeat strictly every year, although it does tend to peak in December. The scientists also found that the model doesn't capture all the chaos of the real climate, so it needs to be made more complex for accurate forecasts.