Distribution-based prediction of noise-induced tipping

¹ School of Mathematics and Statistics, Shanxi University - Taiyuan 030006, China
² School of Mathematics and Statistics, Shaanxi Normal University - Xi'an 710119, China
³ School of Science, Xi'an University of Posts and Telecommunications - Xi'an 710121, China
⁴ Department of Physics, Humboldt University of Berlin - Berlin 12489, Germany
⁵ Potsdam Institute for Climate Impact Research - Potsdam 14412, Germany
⁶ School of Mathematics and Statistics, Northwestern Polytechnical University - Xi'an 710072, China
⁷ MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University Xi'an 710072, China

Received: 28 November 2025
Accepted: 13 March 2026

Abstract

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.