Early warning signals for critical transitions in complex systems

Abstract

In this topical review, we present a brief overview of the different methods and measures to detect the occurrence of critical transitions in complex systems. We start by introducing the mechanisms that trigger critical transitions, and how they relate to early warning signals (EWS) and briefly mention the conventional measures based on critical slowing down, as computed from data and applied to real systems. We then present in detail the approaches for multivariate data, including those defined for complex networks. More recent techniques like the warning signals derived from the recurrence pattern underlying the data, are presented in detail as measures from recurrence plots and recurrence networks. This is followed by a discussion on how methods based on machine learning are used most recently, to detect critical transitions
in real and simulated data. Towards the end, we summarise the challenges involved while computing the EWS from real-world data and conclude with our outlook and perspective on future trends in this area.

Effective precursors for self-organization of complex systems into a critical state based on dynamic series data

“…Variance, kurtosis, skewness, autocorrelation at lag-1 and power-law scaling exponent (β) of the power spectral density (PSD) are window EWMs, the features of changes in which as the system approaches τ c are interpreted by its critical slowing down (e.g., see the paper [15]). Thus, a precursor of the critical transition of the system is a sharp increase in the values of the variance and autocorrelation series, as well as a sharp increase followed by a sharp decrease in the values of the kurtosis and skewness series.…”

“…The rationale for this behavior is presented in the context of the critical slowing down. The justification of such behavior is presented in the papers [14,15]. Critical slowing down is also accompanied by an increase in "memory", which is reflected in the increase in autocorrelation at lag-1.…”

“…One of the problems in the development of early warning systems, which has not been finally solved, is finding effective precursors of the system transition to a critical state, known as the early warning signals (e.g., see papers [14][15][16][17][18][19][20]). First of all, it is the search for precursors based on the analysis of the observed sequence of values of a macroscopic variable, usually an order parameter, generated by the system in real time.…”

“…This is known as the phenomena of critical slowing down (e.g., see the paper [21]). EWMs have also been proposed that are not directly related to this phenomenon, but their characteristic change near the critical point can be considered as the early warning signals for the critical transition (e.g., see the paper [15]). The number of EWMs and systems for which EWMs give good results in predicting critical points is regularly growing.…”

An improved FMECA method for equipment reliability based on information fusion

“…With the continuous improvement of the automation level of mechanical systems, their system complexity is also constantly increasing [1], and higher requirements are also put forward for system reliability. For complex mechanical equipment, whether in its design and manufacturing stages [2], or in its operation and maintenance stages, equipment reliability is a key performance indicator that designers and users are concerned about.…”