J urgen Kurths

Shanchao Peng, Minyu Feng, Liang-Jian Deng et al.

Understanding how information propagation affects epidemic dynamics has become an emerging topic of interest. However, the influence of interpersonal relationship heterogeneity on information acquisition and disease transmission has been largely overlooked. In this work, we introduce a hypergraph structure for Cyber-Physical Systems (CPSs) with two distinct layers. The upper layer, referred to as the cyber layer, consists of a mixed hypergraph, capturing both pairwise propagation and higher-order diffusion of epidemic-related information. The lower layer, referred to as the physical layer, employs a Susceptible-Infected-Susceptible (SIS) process to capture epidemic spreading. This work introduces an adaptive perception-protection mechanism based on Jaccard similarity, which accounts for interpersonal heterogeneity. In this mechanism, individuals receive information based on their relationships with neighbors and take protective measures accordingly. We analyze the impact of interpersonal relationships and the adoption of neighborhood-based self-protection strategies on epidemic dynamics. Furthermore, we conduct a theoretical analysis based on the Microscopic Markov Chain Approach (MMCA), analytically derive the outbreak threshold, and confirm the results with extensive Monte Carlo (MC) simulations. The results show that stronger interpersonal relationships can promote information propagation, significantly increase the threshold for epidemic outbreaks, and effectively suppress the scale of the epidemic. The study provides theoretical support for designing epidemic control strategies considering interpersonal heterogeneity and improves the understanding of epidemic spreading on hypergraphs.

Juntian Huang, Jurgen Kurths, Ying Tang

Reservoir computing offers a lightweight framework for forecasting dynamical systems but may struggle to capture long-range dependencies due to limited representational capacity. Conventional reservoir computing recurrently uses trainable reservoirs with hyperparameter sensitivity, while the next-generation reservoir computing removes recurrence at the cost of rapidly growing feature dimensions. Here, we develop Kolmogorov-Arnold Reservoir Computing (KARC), which replaces reservoirs with explicit basis-function expansions inspired by the Kolmogorov-Arnold representation theorem. We rigorously show that KARC is a lightweight design of Kolmogorov-Arnold networks (KANs), preserving the potential expressive capacity of KANs while admitting efficient closed-form training of reservoir computing. At comparable cost, KARC outperforms existing reservoir computing methods on challenging benchmarks including partial differential equations. It can also be integrated with generative diffusion models for text-to-image generation. This work thus establishes a principled bridge between reservoir computing and KANs, enabling efficient and high-fidelity dynamical system forecasting.

Nubius Brandner, Frank Hellmann, Hans Würfel et al.

Large-scale power outages are typically caused by cascading failures. These unfold dynamically through complex interactions between network dynamics and individual component failures. In contrast, the study of cascading failures in physics has focused on analyzing line overloads in the quasi-static regime. We introduce a new model that integrates the dynamics of node and line failures with a paradigmatic oscillator model for power grid synchronization. This enables us to investigate the collective cascading behavior of coupled failures for the first time. We study the impact of nodal robustness, the ability of nodes to tolerate transient disturbances, and inertia, the ability of nodes to resist frequency deviations, on cascade sizes. We discover two novel mechanisms driving system fragility: i) While low inertia is widely considered a major challenge for power grids, we find that high inertia can amplify cascade sizes unless accompanied by appropriate adjustments of other dynamical properties. ii) Further, we find that an increase in the robustness of individual nodes can paradoxically lead to larger cascades. This latter phenomenon constitutes a novel type of Braess's paradox. Understanding such counterintuitive collective effects may become central for achieving resilient future power grids.