What is common to the self-combustion of grain dust in a storage silo and the bursting activity of neurons? In both cases a quick time evolution follows a period of quiescence during which a key parameter is slowly varying. It can be the surrounding temperature in the case of the grain storage silo or the concentration of calcium ions that turns the neuronal activity on and off. These dramatic changes are possible because a slowly varying parameter passes a limit or bifurcation point of a fast dynamical system. But because of the system's inertia close to the bifurcation point, the expected jump or bifurcation transition is delayed. This delay has raised considerable interest not only for lasers but in other areas as well, such as fluid mechanics and chemistry. In mechanical engineering, slow passage problems are referred to as “nonstationary processes”. They occur in the start-up and shut-down of engines or in high-rise building elevators when the length of the rope is slowly changing. Although most delay effects are now well understood and illustrated by simple first or second order equations, the study of slow passage problems remains a fascinating topic of research for mathematicians, biologists, and students learning bifurcation theory in the laboratory.

Quantitative comparisons between experiments and theory for slow passage problems are always delicate. The evolution equations of a real physical system cannot be reduced to a simple equation if the rate of change is gradually increased, and we often need to take into account the effect of noise present in experiments.