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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.

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We study the propagation of rare or extreme events in a network of coupled nonlinear oscillators, where counter-rotating oscillators play the role of the malfunctioning agents. The extreme events originate from the coupled counter-oscillating pair of oscillators through a mechanism of saddle-node bifurcation. A detailed study of the propagation and the destruction of the extreme events and how these events depend on the strength of the coupling is presented. Extreme events travel only when nearby oscillators are in synchronization. The emergence of extreme events and their propagation are observed in a number of excitable systems for different network sizes and for different topologies.

Slow and fast dynamics of unsynchronized coupled nonlinear oscillators is hard to extract. In this paper, we use the concept of perpetual points to explain the short duration ordering in the unsynchronized motions of the phase oscillators. We show that the coupled unsynchronized system has ordered slow and fast dynamics when it passes through the perpetual point. Our simulations of single, two, three, and 50 coupled Kuramoto oscillators show the generic nature of perpetual points in the identification of slow and fast oscillations. We also exhibit that short-time synchronization of complex networks can be understood with the help of perpetual motion of the network.

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.

We report the appearance of strange nonchaotic attractors in a discrete FitzHugh–Nagumo neuron model with discontinuous resetting. The well-known strange nonchaotic attractors appear in quasiperiodically forced continuous-time dynamical systems as well as in a discrete map with a small intensity of noise. Interestingly, we show that a discrete FitzHugh–Nagumo neuron model with a sigmoidal recovery variable and discontinuous resetting generates strange nonchaotic attractors without external force. These strange nonchaotic attractors occur as intermittency behavior (locally unstable behavior in laminar flow) in the periodic dynamics. We use various characterization techniques to validate the existence of strange nonchaotic attractors in the considered system.

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