A cartographer walking along a mountain trail notes the passes, the places where the path turns sharply. In the science of dynamical systems, such passes are called bifurcations: when a parameter changes smoothly, the system's behavior suddenly changes qualitatively, for instance, a calm equilibrium gives way to oscillations.

When a system has a delay, meaning its response depends on the past, mapping these passes becomes very difficult. The computer program DDE-BIFTOOL comes to the rescue. It slowly varies the parameter and watches for a bifurcation. This approach allowed researchers to study the El Niño model: the program found oscillations with a period of about 3–4 years, matching real observations.

Such a tool is useful for climatologists, neuroscientists, and engineers: it lets them know in advance where a system might suddenly change behavior, so they can prepare for that pass.