arXiv subjects

Jürgen Kurths

Publications and source records attributed to Jürgen Kurths.

At least 37 records · Page 2Linked to original sources

arXiv2026

Recurrence Patterns Correlation

Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific, localized structures. To address this, we introduce Recurrence Pattern Correlation (RPC), a quantifier inspired by spatial statistics that bridges the gap between qualitative RP inspection and quantitative analysis. RPC is designed to measure the correlation degree of an RP to patterns of arbitrary shape and scale. By choosing patterns with specific time lags, we visualize the unstable manifolds of periodic orbits within the Logistic map bifurcation diagram, dissect the mixed phase space of the Standard map, and track the unstable periodic orbits of the Lorenz '63 system's 3-dimensional phase space. This framework reveals how long-range correlations in recurrence patterns encode the underlying properties of nonlinear dynamics and provides a more flexible tool to analyze pattern formation in recurrent dynamical systems.

nlin.CD↗

arXiv2026

Fixed-Size Dynamic Scale-Free Networks: Modeling, Stationarity, and Resilience

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the node count remains constant, instead prioritizing node growth. In this work, we depart from the assumptions of node number variation and preferential attachment to present an innovative model that conceptualizes node degree fluctuations as a state-dependent random walk process with stasis and variable diffusion coefficient. We show that this model yields stochastic dynamic networks with stable scale-free properties. Through comprehensive theoretical and numerical analyses, we demonstrate that the degree distribution converges to a power-law distribution, provided that the lowest degree state within the network is not an absorbing state. Furthermore, we investigate the resilience of the fraction of the largest component and the average shortest path length following deliberate attacks on the network. By using three real-world networks, we confirm that the proposed model accurately replicates actual data. The proposed model thus elucidates mechanisms by which networks, devoid of growth and preferential attachment features, can still exhibit power-law distributions and be used to simulate and study the resilience of attacked fixed-size scale-free networks.

cs.SI↗

arXiv2025

Evolutionary Dynamics Based on Reputation in Networked Populations with Game Transitions

The environment undergoes perpetual changes that are influenced by a combination of endogenous and exogenous factors. Consequently, it exerts a substantial influence on an individual's physical and psychological state, directly or indirectly affecting the evolutionary dynamics of a population described by a network, which in turn can also alter the environment. Furthermore, the evolution of strategies, shaped by reputation, can diverge due to variations in multiple factors. To explore the potential consequences of the mentioned situations, this paper studies how game and reputation dynamics alter the evolution of cooperation. Concretely, game transitions are determined by individuals' behaviors and external uncontrollable factors. The cooperation level of its neighbors reflects individuals' reputation, and further, a general fitness function regarding payoff and reputation is provided. Within the context of the donation game, we investigate the relevant outcomes associated with the aforementioned evolutionary process, considering various topologies for distinct interactions. Additionally, a biased mutation is introduced to gain a deeper insight into the strategy evolution. We detect a substantial increase in the cooperation level through intensive simulations, and some important phenomena are observed, e.g., the unilateral increase of the value of prosocial behavior limits promotion in cooperative behavior in square-lattice networks.

physics.soc-ph↗

arXiv2025

Protection Degree and Migration in the Stochastic SIRS Model: A Queueing System Perspective

With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated.

cs.SI↗

arXiv2025

Evolving Network Modeling Driven by the Degree Increase and Decrease Mechanism

Ever since the Barabási-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured with a dynamic evolution including network reduction in addition to network growth. In this paper, we propose a novel mechanism for evolving networks from the perspective of vertex degree. We construct a queueing system to describe the increase and decrease of vertex degree, which drives the network evolution. In our mechanism, the degree increase rate is regarded as a function positively correlated to the degree of a vertex, ensuring the preferential attachment in a new way. Degree distributions are investigated under two expressions of the degree increase rate, one of which manifests a ``long tail'', and another one varies with different values of parameters. In simulations, we compare our theoretical distributions with simulation results and also apply them to real networks, which presents the validity and applicability of our model.

cs.SI↗

arXiv2025

A Unified Theory for Transient Synchronization Stability Analysis of Renewable Dominated Power Systems

The change of electric power generation - from synchronous generator (SG) to converter - is generally regarded as the second revolution of power system. Different from rotor swing of SG in traditional grids mainly described by the swing equation (SE), the converter dynamics plays an indispensable role in modern renewable dominated power systems (RDPS). The high complexity of the RDPS, including spatial large-scale, nonlinearity, multi-time-scale, and even sequential switching, prevents us from fully understanding its dynamics and assessing its transient stability under large disturbance. Here, a variety of transient switching mechanism models of renewable devices relying on wind or solar energies under low-voltage ride-through are established and unified, which can be perfectly described by a generalized swing equation (GSE) under parameter changes for switching dynamics. The GSE focusing on the dominant phase-locking loop dynamics is similar to the SE. Mainly relying on the mechanical equivalence and the energy conservative principle, a substantially improved equal-area criterion method is proposed. Based on this method, even for large-scale renewable fields, the calculation errors for the critical clearing time are only about 1%. This elegant nonlinear-dynamics-based approach establishes a unified theory including modelling and analysis for the RDPS transient dynamics.

eess.SY↗

arXiv2025

Tipping Points and Cascading Transitions: Methods, Principles, and Evidences

This review synthesizes recent advancements in understanding tipping points and cascading transitions within the Earth system, framing them through the lens of nonlinear dynamics and complexity science. It outlines the fundamental concepts of tipping elements, large-scale subsystems like the Atlantic Meridional Overturning Circulation and the Amazon rainforest, and classifies tipping mechanisms into bifurcation-, noise-, and rate-induced types. The article critically evaluates methods for detecting early-warning signals, particularly those based on critical slowing down, while also acknowledging their limitations and the promise of non-conventional indicators. Furthermore, we explore the significant risk of cascading failures between interacting tipping elements, often modeled using conceptual network models. This shows that such interactions can substantially increase systemic risk under global warming. The review concludes by outlining key challenges related to data limitations and methodological robustness, and emphasizes the promising role of artificial intelligence and complex network science in advancing prediction and risk assessment of Earth system tipping dynamics.

physics.ao-ph↗

arXiv2025

Synchronization transitions and spike dynamics in a higher-order Kuramoto model with Lévy noise

Synchronization in various complex networks is significantly influenced by higher-order interactions combined with non-Gaussian stochastic perturbations, yet their mechanisms remain mainly unclear. In this paper, we systematically investigate the synchronization and spike dynamics in a higher-order Kuramoto model subjected to non-Gaussian Lévy noise. Using the mean order parameter, mean first-passage time, and basin stability, we identify clear boundaries distingusihing synchronization and incoherent states under different stability indexes and scale parameters of Lévy noise. For fixed coupling parameters, synchronization weakens as the stability index decreases, and even completely disappears when the scale parameter exceeds a critical threshold. By varying coupling parameters, we find significant dynamical phenomena including bifurcations and hysteresis. Lévy noise smooths the synchronization transitions and requires stronger coupling compared to Gaussian white noise. Furthermore, we define spikes and systematically investigate their statistical and spectral characteristics. The maximum number of spikes is observed at small scale parameter. A generalized spectral analysis further reveals burst-like structure via an edit distance algorithm. Moreover, a power-law distribution is observed in the large inter-window intervals of spikes, showing great memory effects. These findings deepen the understanding of synchronization and extreme events in complex networks driven by non-Gaussian Lévy noise.

cond-mat.stat-mech↗

arXiv2025

Delayed Interactions in Active Agents: Stability and Formations

Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs) that incorporate inertial effects. In this paper, we investigate the stability of pattern formation of active agents with inertia and time delays, in both uncoupled and coupled scenarios. We derive and analyze a high-dimensional linear DDE model that characterizes the stability of such formations. Starting with the uncoupled scenario, where agents are driven only by a virtual leader, we describe the stability spectrum and provide conditions for the delay-independent (absolute) stability of the formations, as well as delay-dependent stability and unstable hyperbolic behavior. Different cases correspond to distinct universality classes of the corresponding spectrum. For the coupled scenario, where agents are driven by both the virtual leader and inter-agent interactions, we consider both symmetric and non-symmetric coupling topologies. Here we also provide an explicit spectrum classification, including the absolute stability criterion. Additionally, we investigate interactions in the large-delay limit, where delays affect inter-agent coupling, while local feedback remains instantaneous. In this limit, we prove rigorously that the stability region in the complex plane of the eigenvalues of the Laplacian matrix converges to a circle centered at the origin, a phenomenon previously observed in delay-coupled networks. Our findings provide a universal framework for understanding stable formations and motions of active agents with delayed interactions.

math.DS↗

arXiv2025

Dynamic Evolution of Complex Networks: A Reinforcement Learning Approach Applying Evolutionary Games to Community Structure

Complex networks serve as abstract models for understanding real-world complex systems and provide frameworks for studying structured dynamical systems. This article addresses limitations in current studies on the exploration of individual birth-death and the development of community structures within dynamic systems. To bridge this gap, we propose a networked evolution model that includes the birth and death of individuals, incorporating reinforcement learning through games among individuals. Each individual has a lifespan following an arbitrary distribution, engages in games with network neighbors, selects actions using Q-learning in reinforcement learning, and moves within a two-dimensional space. The developed theories are validated through extensive experiments. Besides, we observe the evolution of cooperative behaviors and community structures in systems both with and without the birth-death process. The fitting of real-world populations and networks demonstrates the practicality of our model. Furthermore, comprehensive analyses of the model reveal that exploitation rates and payoff parameters determine the emergence of communities, learning rates affect the speed of community formation, discount factors influence stability, and two-dimensional space dimensions dictate community size. Our model offers a novel perspective on real-world community development and provides a valuable framework for studying population dynamics behaviors.

cs.SI↗

arXiv2025

Bursty Switching Dynamics Promotes the Collapse of Network Topologies

Time-varying connections are crucial in understanding the structures and dynamics of complex networks. In this paper, we propose a continuous-time switching topology model for temporal networks that is driven by bursty behavior and study the effects on network structure and dynamic processes. Each edge can switch between an active and a dormant state, leading to intermittent activation patterns that are characterized by a renewal process. We analyze the stationarity of the network activation scale and emerging degree distributions by means of the Markov chain theory. We show that switching dynamics can promote the collapse of network topologies by reducing heterogeneities and forming isolated components in the underlying network. Our results indicate that switching topologies can significantly influence random walks in different networks and promote cooperation in donation games. Our research thus provides a simple quantitative framework to study network dynamics with temporal and intermittent interactions across social and technological networks.

physics.soc-ph↗

arXiv2025

Tipping in an adaptive climate network model

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.

nlin.AO↗

arXiv2025

Predicting temperatures in Brazilian states capitals via Machine Learning

Climate change refers to substantial long-term variations in weather patterns. In this work, we employ a Machine Learning (ML) technique, the Random Forest (RF) algorithm, to forecast the monthly average temperature for Brazilian's states capitals (27 cities) and the whole country, from January 1961 until December 2022. To forecast the temperature at $k$-month, we consider as features in RF: $i)$ global emissions of carbon dioxide (CO$_2$), methane (CH$_4$), and nitrous oxide (N$_2$O) at $k$-month; $ii)$ temperatures from the previous three months, i.e., $(k-1)$, $(k-2)$ and $(k-3)$-month; $iii)$ combination of $i$ and $ii$. By investigating breakpoints in the time series, we discover that 24 cities and the gases present breakpoints in the 80's and 90's. After the breakpoints, we find an increase in the temperature and the gas emission. Thereafter, we separate the cities according to their geographical position and employ the RF algorithm to forecast the temperature from 2010-08 until 2022-12. Based on $i$, $ii$, and $iii$, we find that the three inputs result in a very precise forecast, with a normalized root mean squared error (NMRSE) less than 0.083 for the considered cases. From our simulations, the better forecasted region is Northeast through $iii$ (NMRSE = 0.012). Furthermore, we also investigate the forecasting of anomalous temperature data by removing the annual component of each time series. In this case, the best forecasting is obtained with strategy $i$, with the best region being Northeast (NRMSE = 0.090).

physics.ao-ph↗

arXiv2025

Is the atmospheric river operating at a self-organized criticality state?

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.

physics.geo-ph↗

arXiv2025

Physics for the environment and sustainable development

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.

nlin.CD↗

arXiv2025

Nonlinear interactions between the Amazon River basin and the Tropical North Atlantic at interannual timescales

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. ...

physics.ao-ph↗

arXiv2025

Non-monotonic emergence of order from chaos in turbulent thermo-acoustic fluid systems

Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a non-monotonic emergence of order amidst chaos in a turbulent thermo-acoustic fluid system. Fluctuations play a vital role in determining the dynamical state and transitions in a system. In this work, we use complex networks to encode jumps in amplitude scales owing to fluctuations as links between nodes representing amplitude bins. The number of possible amplitude transitions at a fixed timescale reflects the complexity of dynamics at that timescale. The network entropy quantifies the number of and uncertainty associated with such transitions. Using network entropy, we show that the uncertainty in fluctuations first increases and then decreases as the system transitions from chaos via intermittency to order. The competition between turbulence and nonlinear interactions leads to such non-monotonic emergence of order amidst chaos in turbulent thermo-acoustic fluid systems.

physics.flu-dyn↗

arXiv2025

An Evolutionary Game With the Game Transitions Based on the Markov Process

The psychology of the individual is continuously changing in nature, which has a significant influence on the evolutionary dynamics of populations. To study the influence of the continuously changing psychology of individuals on the behavior of populations, in this paper, we consider the game transitions of individuals in evolutionary processes to capture the changing psychology of individuals in reality, where the game that individuals will play shifts as time progresses and is related to the transition rates between different games. Besides, the individual's reputation is taken into account and utilized to choose a suitable neighbor for the strategy updating of the individual. Within this model, we investigate the statistical number of individuals staying in different game states and the expected number fits well with our theoretical results. Furthermore, we explore the impact of transition rates between different game states, payoff parameters, the reputation mechanism, and different time scales of strategy updates on cooperative behavior, and our findings demonstrate that both the transition rates and reputation mechanism have a remarkable influence on the evolution of cooperation. Additionally, we examine the relationship between network size and cooperation frequency, providing valuable insights into the robustness of the model.

cs.SI↗