Tipping point detection

Tipping points (or critical transitions) can be in theory detected by the use of so-called generic early warning signals. These signals are based on common mathematical properties of phenomena that change in characteristic ways in a broad range of systems as they approach a critical transition. The most well studied of these signals within our program are:

1. Slow recovery from perturbations: The recovery rate after small perturbations decreases when the system is close to the bifurcation.
2. Increasing autocorrelation: The state of the system becomes more and more like its past state. The highly correlated time series close to the transition can be quantified as an increase in autocorrelation.
3. Increasing variance: The accumulating impact of the non-decaying shocks prior to the transition increases the variance of the state variable.
4. Increasing skewness: The system spends more time close to border between two alternative states, resulting in a highly skewed distribution of the state variable.
5. Flickering: The probability that stochastic forcing may temporarily shift a system back and forth between alternative basins of attraction is higher close to a bifurcation. As a result, the variance and skewness of the frequency distribution of the state variable increases.