arXiv subjects

Jürgen Kurths

Publications and source records attributed to Jürgen Kurths.

At least 19 recordsLinked to original sources

arXiv2026

Fractional-order SIS-UAU subdiffusion model for rumor propagation

Understanding information and rumor diffusion in complex social systems is essential for risk management. Classical SIS-UAU (Susceptible-Infected-Susceptible / Unaware-Aware-Unaware) models rely on Markovian assumptions and thus fail to capture the memory effects and subdiffusive behaviors commonly observed in real social interactions. To address this limitation, we propose a fractional-order SIS-UAU model based on Caputo derivatives, embedding non-Markovian memory into a duplex awareness-rumor spreading process. Methodologically, we derive the corresponding mean-field equations and establish existence, uniqueness, positivity, boundedness, and a Matignon-type stability criterion. The basic reproduction number is obtained, revealing how awareness dynamics reshape the effective rumor threshold. Numerically, we develop a block-adaptive FFT (Fast Fourier Transform) solver to efficiently handle long-horizon fractional dynamics, enabling large-scale simulations. Our results show that fractional memory significantly slows the transient evolution of rumors without altering the steady state. Furthermore, infection-layer parameters dominate long-term rumor prevalence, awareness transmission substantially suppresses rumor levels, and multilayer network topology-especially degree heterogeneity-critically influences propagation outcomes. Collectively, these findings underscore the necessity of integrating memory effects, awareness dynamics, and network structure for realistic rumor modeling

physics.soc-ph↗

arXiv2026

Stability-Shaped Deep Graph Learning

In deep graph neural networks, increasing depth enlarges the receptive field but often leads to over-smoothing, where node representations tend to align. We develop a unified, mode-wise stability framework for deep GNN propagation that provides a principled characterization of over-smoothing. By interpreting layer depth as time and layer updates as graph-coupled dynamics, over-smoothing can be understood as an undesirable dynamical synchronization of features, for which the master stability curve provides a theoretical tool to assess the stability of synchrony. Guided by this theory, we further propose Stability-Shaped Deep Graph Learning (SDGL) to mitigate over-smoothing in deep GNNs. SDGL has two complementary instantiations: one induces controlled Turing instability to replace synchronization with spatial pattern formation, and the other maintains stable near-critical propagation. Experiments on diverse node- and graph-level benchmarks demonstrate the improved depth scaling and consistent accuracy gains over strong baselines, including graphs exhibiting long-range dependencies.

cs.LG↗

arXiv2026

WaveGSSM: Graph Wave State Space Models for Propagating Spatio-Temporal Patterns

Spatio-temporal graph models typically encode each snapshot with a GNN and then connect the resulting representations through a temporal module. This space-then-time design is effective, yet it does not explicitly represent how a pattern moves across the graph. We show empirically that, for a propagating process, the same present field can lead to different futures when its recent rate of change differs, motivating an explicit representation of motion in the predictive state. We introduce WaveGSSM, a second-order graph state-space model that maintains two coupled latent states at each node, one for the current pattern and one for its temporal rate of change. A graph-wave transition updates the motion state through graph interactions and uses it to advance the pattern state, coupling spatial propagation and temporal evolution within a single rollout. We evaluate WaveGSSM on four temporal-graph benchmarks and global weather forecasting. It consistently achieves the best mean performance across the temporal-graph benchmarks and reduces the geopotential RMSE by 20.2% on average for 1- to 5-day weather forecasts relative to a backbone-matched snapshot model, while better preserving large-scale atmospheric patterns.

cs.LG↗

arXiv2026

Frequency bursts in adaptive delay-coupled oscillators

We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.

nlin.AO↗

arXiv2026

Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning

A central question of network science is how functional properties of systems emerge from their structure. For networked dynamical systems, structure is typically captured through network measures. We investigate the relationship between these measures and stability metrics across non-linear and linear oscillators, as well as real-world power grid topologies and dynamics. We find that this relationship is highly sensitive to the underlying ensemble: minor changes in the networks considered, such as going from mean degree 6 to mean degree 8, can invert the correlation between a network measure and stability. We also investigate network measures as inputs for machine learning, as well as Graph Neural Networks (GNNs) as predictors of stability. Both GNNs and the non-linear combination of many network measures can accurately predict stability within a given ensemble, yet both can fail when the ensemble changes. We conclude that neither approach reliably identifies the underlying structural causes of instability.

nlin.AO↗

arXiv2026

Self-similarity of mobility networks

Mobility systems of people and goods are inherently multi-scale, spanning levels of organization from individual cities to regions and nations. Understanding whether mobility networks exhibit similar patterns across these scales is important. Such similarity would point to common organizing principles, enabling insights gained at one scale to inform planning and management at others. Despite growing efforts to analyze mobility at multiple scales, such cross-scale similarity remains poorly understood, and renormalization provides a natural framework for addressing this question. Here, we propose a Neighbor-Limited Box Covering method to renormalize undirected weighted mobility networks. This method iteratively selects box centers in descending order of node strength, merges each center with a fixed number of its highest-weight neighbors to form a renormalized node, and aggregates edge weights between renormalized nodes to generate the network at the next scale. We apply this technique to uncover multi-scale structures of real-world inter-city human mobility and freight trip networks in China and find that the topological structures, weighted structural features, and dynamic processes all exhibit self-similarity across these multi-scale mobility networks. Moreover, we find that the constituent nodes in most renormalized nodes show a strong spatial cohesion, and the boundaries of them closely follow existing political and socio-economic borders, even though the method does not explicitly incorporate any spatial information. Our study not only reveals the consistency of multi-scale inter-city mobility patterns, but also provides important insights into their spatial organization. Furthermore, our method is applicable to mobility networks of different sizes and has potential as a powerful tool for the multi-scale analysis of various other real-world complex systems.

physics.soc-ph↗

arXiv2026

Kolmogorov-Arnold Reservoir Computing

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 fixed 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 facilitating text-to-image generation. This work thus establishes a principled bridge between reservoir computing and KANs, yielding a unified framework for efficient dynamical forecasting and generative modeling.

cs.LG↗

arXiv2026

AI-Driven Stabilization in Power Grids through Controlling Line Admittances

The global transition from traditional power plants to renewable energy sources introduces new challenges in grid stability, primarily because inverter-based technologies provide insufficient inertia. To address this, we introduce an artificial intelligence algorithm that autonomously stabilizes power grids by adaptively tuning admittance regulators in response to disturbances. This Adaptive Admittance Controller (AAC) algorithm not only stabilizes the system in real time but also identifies the best regulator locations, thereby unifying grid planning and real time control within a single framework. When tested on a real UK power grid, the AAC markedly reduces frequency deviations and rapidly restores nominal operation. In addition, the algorithm isolates a small number of key regulators and intervenes only on these, lowering both system complexity and cost. The AAC algorithm further reduces the nonlinearity effect, quickly stabilizing the frequency and power flow. This intelligent control scheme enables power grids to reliably return to stable operating conditions under a broad spectrum of fault scenarios. The proposed framework can also be used to mitigate cascading failures by adaptively controlling critical links in a variety of networked infrastructures, such as cascades of traffic congestion on road networks or fuse failures in energy-saving systems.

physics.soc-ph↗

arXiv2026

Information-Epidemic Dynamics in Cyber-Physical Systems: A Hypergraph Framework with Interpersonal Relationships

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.

physics.soc-ph↗

arXiv2026

Nodal Braess's Paradox and Inertia Destabilization with Dynamic Node and Line Failures in Power Grids

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.

nlin.AO↗

arXiv2026

Climate and dengue synchronization in southern Brazil: a municipal analysis with cross-state validation

Dengue transmission is rapidly expanding beyond its historical tropical range, raising concerns about how climate change may alter the collective dynamics of epidemics. While most studies focus on transmission risk, much less is known about how climate affects the synchronization of outbreaks. In this work, we investigate dengue synchronization using epidemiological and climate data from 74 municipalities in the state of Paraná (southern Brazil) between 2010 and 2024. We quantify outbreak coherence using the Event Synchronization (ES) method. Our results reveal a transition from a low-transmission regime to a high-transmission regime accompanied by a marked increase in synchronization across cities. We also show that climate anomalies increase the number of permissive days for dengue transmission. Our results suggest that such days are significantly associated with outbreak synchronization. We identify a two-stage climate mechanism: conducive climatic conditions first reduce the probability of asynchronous states and coincide with the emergence of synchronized outbreaks, and subsequently sustain higher synchronization levels. Extending the analysis through comparative analyses in Ceará and Minas Gerais, we uncover that climate consistently amplifies synchronization, although its role in the onset of synchronization depends on regional climatic regimes. These findings highlight climate-driven synchronization as an emerging feature shaping dengue dynamics.

physics.soc-ph↗

arXiv2026

Phase locking and multistability in the topological Kuramoto model on cell complexes

Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension within simplicial and cell complexes. We introduce the topological nonlinear Kirchhoff conditions to characterize all phase-locked states of the topological Kuramoto model. These states are organized by winding numbers associated with generalized independent cycles, which quantify how phases wind around these cycles. Using rings, Platonic solids, and regular simplices as illustrative examples, we uncover a universal rule: boundaries must have at least five elements for multistability to arise. We further find that independent winding numbers associated with lower- and higher-dimensional boundaries generate cascades of multistability across dimensions. These results show how the topology and boundary structure of cell complexes influence phase locking and multistability, and provide a general framework for collective dynamics on cell complexes.

nlin.AO↗

arXiv2026

Digital Epidemiology with Awareness-Based Event-Triggered Migration in Networked Cyber-Physical Systems

Understanding how human mobility and information propagation influence the course of an epidemic remains a key challenge in digital epidemiology. In this work, we develop a new awareness-based, event-triggered epidemic model embedded within a networked Cyber-Physical System (CPS). In our framework, disease transmission and the dissemination of epidemic-related information evolve together on two interconnected layers. In detail, the physical layer models disease spread through human movement between two types of locations - residences and transfer stations - forming a bipartite metapopulation network. This structure captures the rendezvous effect, which reflects how gatherings in shared locations contribute to infection spread. The cyber layer represents the flow of information through digital communication networks. We introduce an event-triggered migration regulation mechanism, whereby individuals adapt their movement patterns based on local awareness thresholds, leading to a decentralized control process embedded within the network. Using a microscopic Markov chain approach (MMCA), we derive the epidemic threshold analytically and validate our results through extensive Monte Carlo simulations. Our findings show that event-triggered migration effectively suppresses the overall spread of the disease and lowers infection peaks - especially in heterogeneous populations and densely connected gathering points. These results demonstrate the potential of CPS-based epidemic models to enable real-time, awareness-driven interventions and to inform the design of decentralized control strategies that leverage digital communication dynamics.

physics.soc-ph↗

arXiv2026

Planetary climate interactions of the Qinghai-Tibetan Plateau

The Qinghai-Tibetan Plateau (QTP), Earth's "Third Pole", profoundly shapes the Asian monsoon and regional climate and exerts far-reaching influence on the global climate system. Yet its role in organizing planetary-scale climate interactions remains poorly quantified. Here we develop a climate network framework to explicitly resolve the planetary teleconnection architecture associated with the QTP across historical observations and future climate projections, with physical consistency assessed using Lagrangian trajectory diagnostics and targeted numerical experiments. We uncover a persistent and directional interaction structure linking the QTP with multiple major climate tipping elements. In particular, we identify a robust tripolar interaction mode coupling the QTP with both the Arctic and Antarctica through coherent atmospheric-oceanic pathways. Our findings establish the QTP as a critical planetary climate integrator, revealing a significant blind spot in current climate models and risk frameworks regarding cascading tipping dynamics in a warming world.

physics.ao-ph↗

arXiv2026

Epidemic Transmission Modelling on the Birth-death Evolving Network with Indirect Contacts

Epidemic modelling on complex networks has been studied intensively all the time. The majority of relative research assumes that the time scale of the underlying network evolution is much larger compared to the propagation dynamics on it, while the co-evolution of epidemics and networks needs exploring further. In this paper, we investigate how our recently proposed birth-death evolving network impacts the Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic process. Our evolving network considers the increase and the heritable deletion of nodes, which enables to depicting individual behaviors during an epidemic, e.g., population migration and indirect contacts. To model the above processes, we construct a Markovian queueing network and perform analyses for the variation of population size of different epidemic states. In simulations, we reveal how the population migration and indirect contacts caused by our network dynamic properties influence the population sizes of each epidemic state, and find that newly-created indirect contacts facilitate epidemic transmission.

physics.soc-ph↗

arXiv2026

Stochastic resonance in higher-order networks driven by colored noise

We investigate stochastic resonance (SR) in an ensemble of coupled overdamped bistable oscillators driven by colored noise. The networks incorporate the weighted contributions of both pairwise coupling and 2-simplex coupling. Our findings show that these higher-order interactions further exacerbate the suppression effect of colored noise on SR, reducing the peak of resonance curves and shifting the optimal noise intensity toward higher values. To clarify the underlying mechanism, we establish a close connection between SR and the four-stage variation in network synchronization level. Specially, the synchronization extremes explain the effect of higher-order coupling and colored noise on SR. Our analysis reveals that higher-order interactions do not reverse, but primarily promote the spatial propagation of suppression effects due to colored noise.

cond-mat.stat-mech↗

arXiv2026

Boundary-Induced Biases in Climate Networks of Extreme Precipitation and Temperature

To address spatial boundary effects in climate networks, two surrogate-based correction methods, (1) subtraction and (2) division, have been widely applied in the literature. In the subtraction method, an original network measure is adjusted by subtracting the expected value obtained from a surrogate ensemble, whereas in the division method, it is normalized by dividing by this expected value. However, to the best of our knowledge, no prior study has assessed whether these two correction approaches yield statistically different results. In this study, we constructed complex networks of extreme precipitation and temperature events (EPEs and ETEs) across the CONUS for both summer (June-August, JJA) and winter (December-February, DJF) seasons. We computed key network metrics degree centrality (DC), clustering coefficient (CC), mean geographic distance (MGD), and betweenness centrality (BC) and applied both correction methods. Although the corrected spatial patterns generally appeared visually similar, statistical analyses revealed that the network measures derived from the subtraction and division methods were significantly different at the 95 percent confidence level. Across the CONUS, network hubs of EPEs were primarily concentrated in the northwestern United States during summer and shifted toward the east during winter, reflecting seasonal differences in the dominant atmospheric drivers. In contrast, the ETE networks showed strong spatial coherence and pronounced regional teleconnections in both seasons, with higher connectivity and longer synchronization distances in winter, consistent with large-scale circulation patterns such as the Pacific-North American and North Atlantic Oscillation modes. Our results indicated that the network metrics CC and MGD were more sensitive to the correction methods than the DC and BC, particularly in the EPE networks.

stat.AP↗

arXiv2026

Long-term prediction of ENSO with physics-guided Deep Echo State Networks

The El Niño-Southern Oscillation (ENSO) is a dominant mode of interannual climate variability, yet the mechanisms limiting its long-lead predictability remain unclear. Here we develop a physics-guided Deep Echo State Network (DESN) that operates on physically interpretable climate modes selected from the extended recharge oscillator (XRO) framework. DESN achieves skillful Niño3.4 predictions up to 16-20 months ahead with minimal computational cost. Mechanistic experiments show that extended predictability arises from nonlinear coupling between warm water volume and inter-basin climate modes. Error-growth analysis further indicates a finite ENSO predictability horizon of approximately 30 months. These results demonstrate that physics-guided reservoir computing provides an efficient and interpretable framework for diagnosing and predicting ENSO at long lead times.

physics.ao-ph↗