Early warning signals for critical transitions in complex systems

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

Early warning signals indicate a critical transition in Betelgeuse

Critical transitions occur in complex dynamical systems, when the system dynamics undergoes a regime shift. These can often occur with little change in the mean amplitude of system response prior to the actual time of transition. The recent dimming and brightening event in Betelgeuse occured as a sudden shift in the brightness and has been the subject of much debate. Internal changes or an external dust cloud have been suggested as reasons for this change in variability. We examine whether the dimming and brightening event of 2019-20 could be due to a critical transition in the pulsation dynamics of Betelgeuse, by studying the characteristics of the light curve prior to transition. We calculate the quantifiers hypothesised to rise prior to a critical transition for the light curve of Betelgeuse upto the dimming event of 2019-20. These include the autocorrelation at lag-1, variance and the spectral coefficient calculated from detrended fluctation analysis (DFA), apart from two measures that quantify the recurrence properties of the light curve. Significant rises are confirmed using the Mann-Kendall trend test. We see a significant increase in all quantifiers (p < 0.05) prior to the dimming event of 2019-20. This suggests that the event was a critical transition related to the underlying nonlinear dynamics of the star. Together with results that suggests minimal change in $T_{eff}$ and infra-red flux, a critical transition in the pulsation dynamics could be a possible reason for the unprecedented dimming of Betelgeuse. The rise in the studied quantifiers prior to the dimming event, supports this possibility.Comment: 8 pages, 8 figure

Bimodality and scaling in recurrence networks from ECG data

Human heart is a complex system that can be studied using its electrical activity recorded as Electrocardiogram (ECG). Any variations or anomalies in the ECG can indicate abnormalities in the cardiac dynamics. In this work, we present a detailed analysis of ECG data using the framework of recurrence networks (RNs). We show how the measures of the recurrence networks constructed from ECG data sets, can quantify the complexity and variability underlying the data. Our study shows for the first time that the RNs from ECG show the unique feature of bimodality in their degree distribution. We relate this to the complex dynamics underlying the cardiac system, with structures at two spatial scales. We also show that there is relevant information to be extracted from the scaling of measures with recurrence threshold ε. Thus we observe two scaling regions in the link density for ECG data which are compared with scaling in RNs from standard chaotic and hyperchaotic systems and noise. While both bimodality and scaling are common features of RNs from all types of ECG data, we find that disease specific variations in them can be quantified