Context. 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 the system response prior to the actual time of transition. The recent dimming and brightening event in Betelgeuse occurred 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. Aims. 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. Methods. We calculated the quantifiers hypothesized to rise prior to a critical transition for the light curve of Betelgeuse up to the dimming event of 2019–20. These included the autocorrelation at lag-1, variance, and the spectral coefficient calculated from detrended fluctuation analysis, in addition to two measures that quantify the recurrence properties of the light curve. Significant rises are confirmed using the Mann-Kendall trend test. Results. 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. Conclusions. Together with results that suggest a minimal change in Teff and IR flux, a critical transition in the pulsation dynamics might be a reason for the unprecedented dimming of Betelgeuse. The rise in the quantifiers we studied prior to the dimming event supports this possibility.

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&#xD;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.&#xD;

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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 network (RN). 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 RN 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 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 is 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 disease specific variations in them can be quantified.

Higher Order Spectral (HOS) analysis is often applied effectively to analyze many bio-medical signals to detect nonlinear and non-Gaussian processes. One of the most basic HOS methods is the bispectral estimation, which extracts the degree of quadratic phase coupling between individual frequency components of a nonlinear signal. Most of the studies in this direction as applied to ECG signals are on the conventional, long duration (up to 24 hours) Heart Rate Variability (HRV) data. We report results of our studies on short duration ECG data of 60 seconds using power spectral and bispectral parameters. We analyze 60 healthy cases and 60 cases of patients diagnosed with four different heart diseases, Bundle Branch Block, Cardiomyopathy, Dysrhythmia and Myocardial Infarction. From the power spectra of these data sets we observe that the pulse frequency around 1 Hz has maximum power for all normal ECG data while in all disease cases, the power in the pulse frequency is suppressed and gets distributed among higher frequencies. The bicoherence indices computed show that the pulse frequency has strong quadratic phase coupling with a large number of higher frequencies in healthy cases indicating nonlinearity in the underlying dynamical processes. The loss or decrease of the phase coupling with pulse frequency is a clear indicator of abnormal conditions. In specific cases, bicoherence studies coupled with spectral filter, suggest ECG for Myocardial Infarction has noisy components while in Dysrhythmia, power is mostly at high frequencies with strong quadratic coupling indicating much more irregularity and complexity than normal ECG signals. In addition to serving as indicators suggestive of abnormal conditions of the heart, the detailed analysis presented can lead to a wholistic understanding of normal heart dynamics and its variations during onset of diseases.