We describe a class of extreme events emerging in systems with discontinuous boundaries that exhibit stick-slip dynamics. This kind of systems is capable of generating extreme events when the system trajectory sticks to a sliding set and slides for a relatively large distance along the discontinuous boundary to one of the system's subspaces. We present two examples of such systems, a microelectromechanical cantilever and a driven class-B laser, where this type of extreme events appear. We show that their forecasting is possible by monitoring the sliding trajectory along the discontinuous boundary. In both cases, the probability distribution of recurrence times exhibits a power-law behavior, typical for extreme events. The results of this study can be of interest for engineering applications, for example, to predict extremely large-amplitude oscillations in cantilevers, systems with friction, lasers, and other systems with discontinuous boundaries.

To face the impact of climate change in all dimensions of our society in the near future, the European Union (EU) has established an ambitious target. Until 2050, the share of renewable power shall increase up to 75% of all power injected into nowadays’ power grids. While being clean and having become significantly cheaper, renewable energy sources (RES) still present an important disadvantage compared to conventional sources. They show strong fluctuations, which introduce significant uncertainties when predicting the global power outcome and confound the causes and mechanisms underlying the phenomena in the grid, such as blackouts, extreme events, and amplitude death. To properly understand the nature of these fluctuations and model them is one of the key challenges in future energy research worldwide. This review collects some of the most important and recent approaches to model and assess the behavior of power grids driven by renewable energy sources. The goal of this survey is to draw a map to facilitate the different stakeholders and power grid researchers to navigate through some of the most recent advances in this field. We present some of the main research questions underlying power grid functioning and monitoring, as well as the main modeling approaches. These models can be classified as AI- or mathematically inspired models and include dynamical systems, Bayesian inference, stochastic differential equations, machine learning methods, deep learning, reinforcement learning, and reservoir computing. The content is aimed at the broad audience potentially interested in this topic, including academic researchers, engineers, public policy, and decision-makers. Additionally, we also provide an overview of the main repositories and open sources of power grid data and related data sets, including wind speed measurements and other geophysical data.

Unexpected catastrophic transitions are often observed in complex systems. However, the prediction of such transitions is difficult in practice. Here, we find a special kind of extreme events with a dragon-king probability distribution that occur just prior to a catastrophic transition and, hence, can serve as its precursor. To illustrate the application of dragon kings as a precursor, we consider a practical experimental thermo-fluid system and a theoretical model of coupled logistic maps with quasi-periodic forcing, both systems displaying a catastrophic transition.

We study extreme and critical events in the forced Liénard systems with charge control memristor. It has been found that the system exhibits hidden attractors either in the absence or presence of an external sinusoidal force. We give evidence that these attractors play a crucial role in the appearance of critical events. We attempt to explain the mechanism leading to the emergence of catastrophic transitions. Finally, we present that the observed critical transitions are typical for memristor based models and understanding of them gives some insight on how to avoid these types of devastating events at the time of the device fabrication process.