This work investigates the impulsive optimal control problem for second-order hybrid systems that combines discrete dynamics with continuous dynamics based on adaptive dynamic programming. An impulsive optimal control protocol is proposed, and a parallel computation method is introduced to reduce computational time. Furthermore, a specialized mechanism is developed to adjust the selection tendency of impulsive intervals. Finally, an illustrative example is provided to demonstrate the feasibility of the proposed method.

Effective regulation of information diffusion in complex social systems requires balancing containment and intervention cost, yet how network community structure interacts with targeted interventions remains unclear. We develop a community structure-regulation coupling framework (COSREF) that integrates community structure with process-level regulation of transmission and show how their interplay governs diffusion. Tuning two regulation parameters governing within- and cross-community transmission yields three regimes: no, localized, and global diffusion, separated by abrupt transitions. This structure-regulation perspective reveals a low-cost intervention region where small, targeted adjustments contain spread, unifies topology and regulation within a single theoretical setting, and provides general principles for efficiently and robustly regulating modular systems. Analyses of large cross-platform real-world social networks confirm our analytical predictions and simulation results, demonstrating COSREF's robustness across investigated topologies and its applicability to real information environments.

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.

Abstract Hypernetworks capture coupling structures where interactions extend beyond pairs to groups of three or more units, called hyperedges. They are of increasing importance for many systems such as the brain, social groups, ecosystems, and the climate. We describe here a synchronization phenomenon that is distinctive for hypernetworks. We uncover that in a system of three coupled oscillators with resonant frequencies, the coupling by a triadic hypernetwork motif, where a third node modulates the interaction between two others, can induce a stable locking of a phase triplet, while no pairwise locking is observed. Using normal form transformations and phase reduction, we derive analytically how a specific choice of the coupling functions induces this hyperlocking. We confirm our predictions with both numerical simulations and chemical experiments. Our findings uncover a new synchronization mechanism intrinsic to higher-order interactions and open new directions for controlling real-world complex dynamics beyond pairwise frameworks.

Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame, and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory dynamics in the sound and global heat release rate fluctuations. Modeling the interdependence between local interactions and the global emergence of order in such spatially extended complex systems is exacting. Here, we present a novel reduced-order model to capture the influence of the local interactions on distinct variables exhibiting global emergence of order in a turbulent reacting flow system. We represent each variable that exhibits global oscillatory instability as an oscillator with a cubic nonlinearity. The oscillator is driven by a forcing term that represents the holistic influence of the inter-subsystem interactions on the global behavior. The forcing term essentially couples the local interactions and the globally emergent dynamics in the model. Further, the influence of the inter-subsystem interactions on the behavior of each subsystem is different. Therefore, we use different forcing terms for each variable inspired by the physical interactions in the system. The nonlinear oscillators representing the acoustic and the heat release rate oscillations are hence forced using Wiener and Markov-modulated Poisson processes, respectively. Using this approach, we are able to reproduce (i) the multifractal characteristics of acoustic pressure fluctuations during chaotic dynamics, (ii) the loss of multifractality through the experimentally observed scaling law behavior during the transition from chaos to order, and (iii) the emergence of periodicity and bifurcation in heat release rate dynamics.

The task of jointly forecasting dynamical systems from unlabeled, trajectory-varying measurements is confronted by a fundamental circular dependency: identifying system parameters requires known equations, while modeling equations presupposes estimated parameters. A dual-network Joint Representation And Prediction (JoRAP) framework is proposed to resolve this interdependence, simultaneously distinguishing all trajectories and approximating their vector fields. JoRAP integrates a trajectory representation neural network (TRNN) that encodes individual trajectories into vectorial embeddings, and a vector field neural network (VFNN) that infers the derivatives at any states from each embedding. This co-design enables a fully autonomous learning, simultaneously identifying diverse trajectories and capturing the characteristics of dynamical behaviors. Evaluated on unlabeled trajectories of nonlinear dynamical systems with partial observability, JoRAP achieves accurate long-horizon predictions and learns representations that distinguish dynamical regimes such as periodic, chaotic, and multistable behaviors. Our framework establishes a data-driven paradigm that requires neither predefined equations nor known parameters, enabling joint analysis and forecast of diverse complex systems from observations alone.

occurrence of noise-induced tipping often poses a serious threat to the safety and stability of systems. Therefore, achieving early warning of noise-induced tipping is particularly important. Considering that tipping events may be difficult to recover from once they occur, this letter presents a criterion for identifying the occurrence of noise-induced tipping, as well as a method for recording its occurrence time. Taking ecological and engineering systems as examples, the distribution of occurrence time for noise-induced tipping is statistically obtained. Then, the distribution type is examined using the Kolmogorov-Smirnov test and Quantile-Quantile plot. It is found that the occurrence time of noise-induced tipping follows a Gaussian distribution. Based on these results, we can predict the time window of noise-induced tipping and calculate the probability of its occurrence within a certain interval. Our findings provide a new perspective for predicting catastrophic tipping events. Copyright (c) 2026 EPLA All rights, including for text and data mining, AI training, and similar technologies, are reserved.

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 Niño 3.4 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.

Anticipating critical transitions and identifying bifurcation types in complex systems remains a major challenge due to high dimensionality and limited labeled data. In this study, we propose spatial-to-temporal auto reservoir computing, a self-supervised approach of reservoir computing designed to detect early warning signals of critical transitions and identify the corresponding bifurcation types, including transcritical, period-doubling, and Neimark-Sacker bifurcations. Grounded on Takens' embedding theorem, it performs spatial-to-temporal information transformation via a reservoir structure, by encoding high-dimensional spatial data into the temporal dynamics of a single representative variable. This ultralow one-dimensional representation is obtained in a self-supervised and analytical manner, making it particularly suited for critical transition analyses in time-varying, high-dimensional systems. In addition, based on the Poincaré recurrence principle, the proposed method captures the structural information of the local phase space by constructing a spatial neighborhood network centered at each input state to enhance the robustness. The proposed method is validated on synthetic models and real-world datasets across multiple domains including paleoclimate, ecology and physiology, consistently achieving high accuracy and robustness under varying noise levels and parameter choices.

Hermann Haken’s synergetics provides a fundamental theoretical framework for understanding the emergence of macroscopic order from microscopic interactions in complex dynamical systems. In this paper, we explore how different ways of quantifying recurrences serve as powerful tools to analyse phase-space dynamics within this synergetic perspective. Recurrence-based methods uncover evolving patterns, transitions between regular and chaotic behaviour, and characteristic time-scale separations that govern complex dynamics. We further discuss recent advances in combining recurrence analysis with machine learning, highlighting their potential to uncover hidden dynamical patterns and inform predictive modelling. Overall, recurrence approaches can be regarded as a synergetically motivated avenue for studying the universal properties of non-linear systems across disciplines.

Facing climate change, the transformation to renewable energy poses stability challenges for power grids due to their reduced inertia and increased decentralization. Traditional dynamic stability assessments, crucial for safe grid operation with higher renewable shares, are computationally expensive and unsuitable for large-scale grids in the real world. Although multiple proofs in the network science have shown that network measures, which quantify the structural characteristics of networked dynamical systems, have the potential to facilitate basin stability prediction, no studies to date have demonstrated their ability to efficiently generalize to real-world grids. With recent breakthroughs in Graph Neural Networks (GNNs), we are surprised to find that there is still a lack of a common foundation about: Whether network measures can enhance GNNs' capability to predict dynamic stability and how they might help GNNs generalize to realistic grid topologies. In this paper, we conduct, for the first time, a comprehensive analysis of 48 network measures in GNN-based stability assessments, introducing two strategies for their integration into the GNN framework. We uncover that prioritizing measures with consistent distributions across different grids as the input or regarding measures as auxiliary supervised information improves the model's generalization ability to realistic grid topologies, even when models trained on only 20-node synthetic datasets are used. Our empirical results demonstrate a significant enhancement in model generalizability, increasing the R-2 performance from 66% to 83%. When evaluating the probabilistic stability indices on the realistic Texan grid model, GNNs reduce the time needed from 28,950 hours (Monte Carlo sampling) to just 0.06 seconds. This study could provide fundamental insights into basin stability assessments using GNNs, setting a new benchmark for future research.

We investigate stochastic resonance (SR) in an ensemble of coupled overdamped bistable oscillators driven by colored noise. The network incorporates the weighted contributions of both pairwise coupling and 2-simplex coupling. Our findings reveal a suppression effect of colored noise on SR in higher-order networks, namely, that increasing the noise correlation time monotonically reduces the resonance peak. Furthermore, for a fixed noise correlation time, increasing the weight of higher-order interactions decreases the peak amplitude. Meanwhile, as both the noise correlation time and the weight of higher-order interactions increase, the optimal noise intensity shifts progressively to larger values. To clarify the underlying mechanism, we establish a close connection between SR and the four-stage variation in network synchronization level. Specifically, the effects of higher-order coupling and colored noise on SR can be understood through their impact on network synchronization, which exhibits distinct extrema. Our analysis reveals that higher-order interactions primarily promote the spatial propagation of suppression effects due to colored noise.

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.

Synchronisation, the tendency of climatic events to occur simultaneously, can arise from small-scale and large-scale atmospheric dynamics. Climate variables can be synchronised across broad spatial and temporal scales, manifesting as regional, continental and global teleconnection patterns. In the study, we analysed spatiotemporal patterns of inland extreme precipitation events (EPEs) and extreme sea surface temperature events (ESSTEs) in the Northern Hemisphere (0 degrees N-60 degrees N) to better understand their connection. Using gridded monthly gauge- and interpolation-based datasets for precipitation and sea surface temperature from 1930 through 2020, we detected extreme events based on the 95th percentile threshold. We then quantified the synchronisation between extreme events using the event synchronisation (ES) method and compared our findings to a null model distribution to ensure that the identified links were non-random. Subsequently, we constructed EPE and ESSTE complex networks and calculated key network metrics including degree centrality , mean geographic distance (MGD) and clustering coefficient . Our results showed that the EPEs and ESSTEs exhibited non-monotonic trends over the past nine decades, with significant increasing trends after 1980. Key EPE network hubs were detected in Mexico, the African Sahel and parts of Asia, while ESSTE hubs appeared in the Atlantic Ocean near the UK and US borders, the Pacific Ocean close to East Asia and the Mediterranean and Red Seas. Analyses of MGD and revealed that the EPE network had larger MGDs and more intense local clustering in continental areas (Sahel and East Asia), indicating that EPEs experience teleconnections within these locations even though they also experience strong local associations. The findings of our EPE network contrast with those of our ESSTE network, which had lower MGD values and close clustering within specific ocean basins, as expected due to localised ocean-atmosphere coupling. Our findings suggest that the drivers for extreme climate events are complex and can lead to strong local and global connections.

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.

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.

Synchronization is a fundamental phenomenon in networked dynamical systems with applications ranging from power grids to biological networks. While much progress has been made in understanding synchronization in chaotic and periodic systems through the master stability function (MSF) framework, less attention has been given to systems exhibiting simpler attractors, such as fixed points or quasiperiodic (torus) behaviors. This paper addresses this gap by systematically analyzing the synchronization properties of coupled systems with point and torus attractors using the MSF approach. The results show that systems with point attractors can display an unexpected synchronization scenario in which stable synchrony can emerge in disjoint regions of the coupling parameter space. We propose a generalized classification scheme for synchronization types in such systems, drawing parallels to existing frameworks for chaotic and periodic oscillators. This study contributes to a more comprehensive understanding of synchronization behavior in complex networks.

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.

Brain networks have emerged as a crucial tool for exploring brain organization and aiding in brain disorder classification. Recent graph neural network (GNN)-based methods have demonstrated strong potential for brain network analysis. However, most of these methods insufficiently model lateralized heterogeneity induced by hemispheric asymmetry. Additionally, traditional message-passing schemes mainly rely on direct neighbors, which restricts their ability to capture high-order synergistic interactions among distant brain regions. To overcome these challenges, this paper proposes a Lateralization-Aware Multi-View High-Order Graph Learning (LMHGL) framework for brain disorder classification, which provides a unified scheme to model hemispheric asymmetry, supporting high-order intra-hemispheric interactions and multi-view collaboration at the decision level. Specifically, LMHGL introduces an anatomically constrained heat diffusion mechanism to model high-order intra-hemispheric interactions. By propagating information along structural connectivity, it captures biologically plausible multi-hop dependencies and enhances the representation of lateralized brain organization. Furthermore, a multi-view collaborative decision mechanism integrates global and hemispheric-specific features, enabling the joint characterization of holistic and lateralized pathological patterns. Extensive experiments on three real-world brain disorder datasets demonstrate that LMHGL consistently outperforms state-of-the-art methods, highlighting the effectiveness of jointly modeling hemispheric asymmetry and anatomically constrained high-order interactions for learning discriminative brain network representations.

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. 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. To interpret these emergent behaviors, we develop a moisture avalanche model that reproduces the observed scaling laws and links them to threshold-driven moisture transport and precipitation dissipation. These scaling properties 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, driven by thermodynamic amplification and dynamical reorganization. Our findings establish a statistical physics framework for ARs, connecting critical phenomena to the spatiotemporal structure of extreme events in a warming climate.