Anticipating the occurrence and type of critical transitions

Abstract A critical transition can occur in many real-world systems and the ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWS) have been developed to anticipate a critical transition or distinguish types of transitions. However, there is no effective method to establish practical thresholds indicating the condition when a critical transition is most likely to occur. Here, we introduce a powerful EWS, named Dynamical Eigen-Value (DEV), rooted in bifurcation theory of dynamical systems, that estimates the dominant eigen-value of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, whereas its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and in addition we test the DEV approach on various critical transitions in real-world systems.