In this review, we present the different measures of early warning signals
that can indicate the occurrence of critical transitions in complex systems. We
start with the mechanisms that trigger critical transitions, how they relate to
warning signals and the methods used to detect early warning signals (EWS) for
sudden transitions or tipping. We discuss briefly a few applications in real
systems in this context, like transitions in ecology, climate and environment,
medicine, epidemics, finance and engineering. Towards the end, we mention the
issues in detecting EWS in specific applications and our perspective on future
trends in this area, especially related to sudden transitions in the dynamics
of connected systems on complex networks.Comment: 35 pages, 11 figure

Ambika, G.

George, Sandip V.

Kachhara, Sneha

English

arXiv

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.</p

Early warning signals for critical transitions in complex systems

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