Early-warning indicators for rate-induced tipping

摘要: A dynamical system is said to undergo rate-induced tipping when it fails track its quasi-equilibrium state due an above-critical-rate change of parameters. We study a prototypical model for tipping, the saddle-node normal form subject time-varying equilibrium drift and noise. find that both most commonly used early-warning indicators, increase in variance autocorrelation, occur not fastest but with delay. explain this delay by demonstrating likely trajectory also crosses threshold therefore itself delayed. solutions variational problem determining path using numerical continuation techniques. The result systematic time plane two parameters, distance from noise intensity.