Warm water in the Pacific Ocean shifts back and forth between the coasts of South America and Indonesia. This phenomenon is called El Niño, and it affects weather across the entire planet. Scientists describe it with equations, but solving them is very hard. So mathematicians came up with a simplification: they represented the ocean as a pendulum that is pushed in rhythm with the seasons, and inside the pendulum there is a switch that triggers with a delay.

This pendulum was solved exactly. It turns out it performs periodic oscillations, and one can calculate under what conditions these oscillations are stable. If the seasonal forcing is strong, the oscillations are stable; if it is weak, they become irregular. Comparison with the original complex model showed that the simple pendulum behaves almost identically.

Now this switch-triggered pendulum can be used as a benchmark for testing complex climate models. It helps explain why El Niño sometimes arrives regularly and sometimes falls out of rhythm.