Jürgen Kurths’s research while affiliated with Humboldt-Universität zu Berlin and other places

With rising global temperatures Earth's tipping elements are becoming increasingly more vulnerable to crossing their critical thresholds. The reaching of such tipping points does not only impact other tipping elements through their connections, but can also have further effect on the global mean surface temperature (GMT) itself, either increasing or decreasing the probability of further tipping points being reached. Recently, a numerical study analyzing the risk of tipping cascades has been conducted, using a conceptual model describing the dynamics of a tipping element with its interactions with other tipping elements taken into account [1]. Here, we extend the model substantially by including adaptation, so that the GMT-feedback induced by the crossing of a tipping point is incorporated as well. We find that although the adaptive mechanism does not impact the risk for the occurrence of tipping events, large tipping cascades are less probable due to the negative GMT-feedback of the ocean circulation systems. Furthermore, several tipping elements can play a different role in cascades in the adaptive model. In particular, the Amazon rainforest could be a trigger in a tipping cascade. Overall, the adaptation mechanism tends to slightly stabilize the network.

In 2018 and 2019, Kerala, the southernmost state in India, experienced extreme precipitation, leading to appallingly devastating floods that damaged life and property. Kerala is vulnerable to flooding due to its topography, geographical location, and meteorology. Several phenomena have been attributed to these extreme precipitations; however, no single explanation suffices to explain such complex climate phenomena. We view the occurrence of extreme precipitation that leads to floods, such as an emerging phenomenon through the lens of complex system theory. We analyze the patterns of synchrony of extreme fluctuations in precipitation, outgoing longwave radiation, and water vapor transport. We construct time-varying functional climate networks, in which the statistical similarity between the time series of extreme precipitation at different spatial locations is estimated using event synchronization. The network topology reveals that excessive precipitation during the Kerala floods was associated with a coherent pattern of synchronized extreme rainfall. In the coherent phenomena discovered, the extreme rainfall was synchronized across a wide range of length scales spanning 100–1000 km. Furthermore, it traverses a synoptic scale path. After originating in the equatorial Indian Ocean, the coherent pattern moves eastward across the Bay of Bengal. The pattern stops over the Maritime Continent and changes its direction. It moves westward toward the Indian peninsula and accumulates over southwest India. We find that the extreme precipitation was driven by enhanced convective activity, leading to cloudiness and high-vapor transport in the atmosphere. Our findings improve the understanding of intraseasonal variability in the Indian monsoon and extreme precipitation events.

Recurrence analysis is a powerful tool for nonlinear time series analysis deeply rooted in the theory of dynamical systems, finding applications across many areas of science. It works by mapping recurrences of a time series or phase space trajectory into a logical matrix. Recurrence quantification analyses (RQAs) are computed from its internal structures, such as recurrence density and the distribution of diagonal and vertical lines. Here, we link the density-based recurrence measures such as determinism and laminarity to the concept of microstates. We present a way to obtain the histogram of both diagonal and vertical lines from recurrence microstates, which are small square submatrices of the recurrence matrix. This approach opens up a line of research by reframing traditional RQAs in terms of microstates. Therefore, we establish a bridge between concepts of traditional lines-based RQA and recurrence microstates, and illustrate this for various paradigmatic systems. Published by the American Physical Society 2025

Cascading failures pose a significant threat to the stability and functionality of complex systems, making their mitigation a crucial area of research. While existing strategies aim to enhance network robustness, identifying an optimal set of critical nodes that mediates the cascade for protection remains a challenging task. Here, we present a robust and pragmatic framework that effectively mitigates the cascading failures by strategically identifying and securing critical nodes within the network. Our approach leverages a graph coloring technique to identify the critical nodes using the local network topology, and results in a minimal set of critical nodes to be protected yet maximally effective in mitigating the cascade thereby retaining a large fraction of the network intact. Our method outperforms existing mitigation strategies across diverse network configurations and failure scenarios. An extensive empirical validation using real-world networks highlights the practical utility of our framework, offering a promising tool for enhancing network robustness in complex systems.

Atmospheric rivers (ARs) are essential components of the global hydrological cycle, with profound implications for water resources, extreme weather events, and climate dynamics. Yet, the statistical organization and underlying physical mechanisms of AR intensity and evolution remain poorly understood. Here we apply methods from statistical physics to analyze the full life cycle of ARs and identify universal signatures of self-organized criticality (SOC). We demonstrate that AR morphology exhibits nontrivial fractal geometry, while AR event sizes, quantified via integrated water vapor transport, follow robust power-law distributions, displaying finite-size scaling. These scaling behaviors persist under warming scenarios, suggesting that ARs operate near a critical state as emergent, self-regulating systems. Concurrently, we observe a systematic poleward migration and intensification of ARs, linked to thermodynamic amplification and dynamical reorganization. Our findings establish a statistical physics framework for ARs, linking critical phenomena to the spatiotemporal structure of extreme events in a warming climate.

A reliable understanding of the Earth system is essential for the life quality of modern society. Natural hazards are the cause of most life and resource losses. The ability to define the conditions for a sustainable development of humankind, to keep the Earth system within the boundaries of habitable states, or to predict critical transitions and events in the dynamics of the Earth system are crucial to mitigate and adapt to Earth system related events and changes (e.g., volcanic eruptions, earthquakes, climate change) and to avert the disastrous consequences of natural hazards. In this chapter, we discuss key concepts from nonlinear physics and show that they enable us to treat challenging problems of Earth sciences which cannot be solved by classic methods. In particular, the concepts of multi-scaling, recurrence, synchronization, and complex networks have become crucial in the very last decades for a substantially more profound understanding of the dynamics of earthquakes, landslides, or (palaeo-)climate. They can even provide a significantly improved prediction of several high-impact extreme events. Additionally, crucial open challenges in the realm of methodological nature and applications to Earth sciences are given.

We study the physical processes involved in the potential influence of Amazon (AM) hydroclimatology over the Tropical North Atlantic (TNA) Sea Surface Temperatures (SST) at interannual timescales, by analyzing time series of the precipitation index (P-E) over AM, as well as the surface atmospheric pressure gradient between both regions, and TNA SSTs. We use a recurrence joint probability based analysis that accounts for the lagged nonlinear dependency between time series, which also allows quantifying the statistical significance, based on a twin surrogates technique of the recurrence analysis. By means of such nonlinear dependence analysis we find that at interannual timescales AM hydrology influences future states of the TNA SSTs from 0 to 2 months later with a 90% to 95% statistical confidence. It also unveils the existence of two-way feedback mechanisms between the variables involved in the processes: (i) precipitation over AM leads the atmospheric pressure gradient between TNA and AM from 0 and 2 month lags, (ii) the pressure gradient leads the trade zonal winds over the TNA from 0 to 3 months and from 7 to 12 months, (iii) the zonal winds lead the SSTs from 0 to 3 months, and (iv) the SSTs lead precipitation over AM by 1 month lag. The analyses were made for time series spanning from 1979 to 2008, and for extreme precipitation events in the AM during the years 1999, 2005, 2009 and 2010. We also evaluated the monthly mean conditions of the relevant variables during the extreme AM droughts of 1963, 1980, 1983, 1997, 1998, 2005, and 2010, and also during the floods of 1989, 1999, and 2009. Our results confirm that the Amazon River basin acts as a land surface-atmosphere bridge that links the Tropical Pacific and TNA SSTs at interannual timescales. ...

Rate-dependent tipping that concerns the effects of the rate of parameter change on the sudden transitions has been revealed in thermoacoustic systems. However, the conventional models cannot accurately portray the intermittent oscillations observed in experiments. This study explores the tipping behaviors in a thermoacoustic system with a secondary bifurcation, simultaneously accounting for the coupling effects of rate and colored noise. Particularly, the model contains higher-order nonlinearities, which lead to the emergence of both supercritical and subcritical bifurcations. It can qualitatively reproduce the intermittent dynamics of the system. We perform a transient analysis for the system via a stochastic averaging method and explore the influence mechanisms of colored noise and rate on the tipping phenomenon. The results show that the system exhibits a tipping phenomenon from the desired state to thermoacoustic instability through the state of intermittency. Interestingly, the rate causes the delay of tipping, while its increase enlarges the amplitude of intermittent oscillations. In addition, the system changes from an abrupt tipping to a smooth tipping for large noise intensities.