Distribution-based prediction of noise-induced tipping

The occurrence of noise-induced tipping often poses a serious threat to the safety and stability of systems. Therefore, achieving early warning of noise-induced tipping is particularly important. Considering that tipping events may be difficult to recover from once they occur, this letter presents a criterion for identifying the occurrence of noise-induced tipping, as well as a method for recording its occurrence time. Taking ecological and engineering systems as examples, the distribution of occurrence time for noise-induced tipping is statistically obtained. Then, the distribution type is examined using the Kolmogorov-Smirnov test and Quantile-Quantile plot. It is found that the occurrence time of noise-induced tipping follows a Gaussian distribution. Based on these results, we can predict the time window of noise-induced tipping and calculate the probability of its occurrence within a certain interval. Our findings provide a new perspective for predicting catastrophic tipping events.