Anticipating the occurrence and type of critical transitions

Chun-Wei Chang and Chih-hao Hsieh

Prof. Chih-hao Hsieh from the Institute of Oceanography and Prof. Chun-Wei Chang from the Institute of Fishery Sciences, NTU lead an international team and develop a novel method that successfully anticipates the occurrence and type of a variety of critical transition events. This study, published in Science Advances (Jan 2023), overcomes the long-lasting challenge in revealing a quantitative threshold as well as distinguishing types of critical transition by early warning signals using empirical data collected in real-world systems. The proposed method also provides a powerful tool to track the change of system resilience that potentially leads to catastrophic shift in socio-economically important systems.

A critical threshold can be found (i.e., tipping point) in various real-world systems, at which systems suddenly shift to a distinct, usually an undesirable state. This phenomenon, named critical transitions (or regime shifts), initiated by local bifurcation in nonlinear dynamical systems. The occurrence of critical transition, due to its rapidness and low predictability, often causes tremendous damages and losses in environmental, economic, and public health resource. Thus, it is important for various scientific fields and in many applications to forecast occurrence and consequence of critical transitions. Here, the research team developed a novel early warning signal (EWS) for the occurrence of critical transition, named Dynamical Eigen-Value (DEV), that is rooted in bifurcation theory of dynamical systems and enables to quantitatively predict the occurrence condition as well as the types of critical transition. Applying this approach, the research team successfully forecast a variety of critical transition events occurred in theoretical models and many real-world systems (Fig. 1).

The proposed methodological framework fulfills the public needs in many fields for anticipating the occurrence of critical transition. The proposed DEV method has a quantitatively defined critical threshold indicating the occurrence condition of critical transition; this is in contrast to previous EWS that only warn critical transition based on a qualitative increasing trend of EWS without telling how large the raised EWS shall be. Moreover, the ability of DEV on predicting various transition types improves our capacity in adopting various corresponding managements to minimize potential losses caused by various types of critical transition.

Figure 1. A novel method, Dynamical Eigen-Value (DEV) analysis, is proposed to predict the occurrence and type of critical transition. Three of the empirical cases analyzed in the study, including 1) cyanobacteria microcosm, 2) voice onset, 3) the end of last greenhouse earth, were presented as examples. The DEV method is conducted in the framework of empirical dynamic modeling, which computes a key quantitative measure, DEV as a proxy of the dominant eigenvalue of Jacobian, for predicting the upcoming critical transition in mathematical bifurcation theory. By tracking the temporal dynamics of DEV, critical transition occurs when DEV approaches 1. Moreover, various critical transition types can be identified from the location of DEV on the complex plane. Here, the systems 1) and 3) underwent fold bifurcation; the system 2) presented clear Neimark-Sacker bifurcation.

Grziwotz F., C. W. Chang, V. Dakos, E. H. van Nes, M. Schwarzländer, O. Kamps, M. Heßler, I. T. Tokuda, A. Telschow*, C. h Hsieh*. (2023) Anticipating the occurrence and type of critical transitions. Science Advances. 9, eabq4558. (Equally contributed)