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:
- Slow recovery from perturbations: The recovery rate after small perturbations decreases when the system is close to the bifurcation.
- 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.
- Increasing variance: The accumulating impact of the non-decaying shocks prior to the transition increases the variance of the state variable.
- Increasing skewness: The system spends more time close to border between two alternative states, resulting in a highly skewed distribution of the state variable.
- 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.