arXiv subjects

Jurgen Kurths

Publications and source records attributed to Jurgen Kurths.

17 recordsLinked to original sources

arXiv2026

Social comparison shapes the evolution of cooperation in structured populations

Human cooperation unfolds in social environments where individuals influence each other through payoff-based learning and social comparison, the tendency to evaluate fitness relative to others. However, it is still unclear how social comparison and population structure jointly shape cooperation. Here, we incorporate social comparison theory into evolutionary dynamics on structured populations, letting fitness depend on individual and neighbour payoffs weighted by a comparison parameter. Under weak selection, we derive conditions favoring cooperation and find that the proposed comparison nonlinearly reshapes the critical benefit-to-cost ratio. Even one individual applying this protocol can affect the population, especially in heterogeneous networks. When comparison tendencies vary, the full distribution, not just the mean, determines evolutionary outcomes. Using a swarm-intelligence-based framework across typical and empirical networks, we identify cooperation-maximizing patterns: optimal states exhibit heterogeneous comparison tendencies, yet collectively align toward assimilative development. These results provide a basis for designing social incentives that harness comparison to promote collective cooperation in human groups.

physics.soc-ph↗

arXiv2026

Thermodynamic criticality of coupled oscillators

Strict thermodynamic scaling relations, such as the Rushbrooke inequality, are fundamentally established for equilibrium critical phenomena in the thermodynamic limit. In finite-size dynamical systems exhibiting synchronization, the direct application of such identities is hindered both by the finiteness of the network and the nonequilibrium nature of the spontaneous synchronization transition. To bypass this difficulty, we rigorously study the dynamical counterparts of the order parameter, susceptibility, and specific heat in finite systems of dynamical oscillators with nonlinear coupling. By measuring these quantities as a function of system size, we extract the associated critical exponents governing the transition. The validity of our thermodynamic mapping is tested by directly confirming the Rushbrooke inequality. Our results establish that standard equilibrium thermodynamic scaling architectures can be systematically applied to the finite-size scaling of nonequilibrium synchronization dynamics.

nlin.AO↗

arXiv2026

Synchronization of topological signals in higher-order adaptive multilayer network

The study of synchronization in complex systems has recently been revolutionized by incorporating higher-order interactions through simplicial complexes. Building in particular upon the higher-order Kuramoto model, which considers oscillators on nodes, links, and higher-dimensional simplices. This work extends the monolayer framework of the higher-order Kuramoto model to multilayer networks where the layers are adaptively coupled through order parameters of the oscillators placed on the simplices. We propose two multilayer architectures: one that allows interactions between signals of the same dimension across layers and the other that permits cross-dimensional interactions. We observe that a higher coupling strength is required for synchronization transitions of the node signals and the projected uplink and downlink signals during adaptation. For example, incorporating node dynamics into link evolution delays the onset of synchronization. This study opens an avenue for understanding complex dynamical processes within interconnected higher-order structures. Finally, we present a comprehensive theoretical framework, first for a bilayer network where layers are random networks treated under the annealed approximation, and then extend the analysis to the case of fully connected layers. The theoretical predictions align remarkably well with numerical simulations, accurately capturing the dynamics of the original model in a globally coupled scenario.

nlin.CD↗

arXiv2025

Mining higher-order triadic interactions

Complex systems often involve higher-order interactions which require us to go beyond their description in terms of pairwise networks. Triadic interactions are a fundamental type of higher-order interaction that occurs when one node regulates the interaction between two other nodes. Triadic interactions are found in a large variety of biological systems, from neuron-glia interactions to gene-regulation and ecosystems. However, triadic interactions have so far been mostly neglected. In this article, we propose {the Triadic Perceptron Model (TPM)} that demonstrates that triadic interactions can modulate the mutual information between the dynamical state of two linked nodes. Leveraging this result, we formulate the Triadic Interaction Mining (TRIM) algorithm to extract triadic interactions from node metadata, and we apply this framework to gene expression data, finding new candidates for triadic interactions relevant for Acute Myeloid Leukemia. Our work reveals important aspects of higher-order triadic interactions that are often ignored, yet can transform our understanding of complex systems and be applied to a large variety of systems ranging from biology to climate.

nlin.AO↗

arXiv2025

Complex Network Modelling with Power-law Activating Patterns and Its Evolutionary Dynamics

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce a complex network model that considers the stochastic switching of individuals between activated and quiescent states at power-law rates and the corresponding evolutionary dynamics. By using the Markov chain and renewal theory, we discover a homogeneous stationary distribution of activated sizes in the network with power-law activating patterns and infer some statistical characteristics. To better understand the effect of power-law activating patterns, we study the two-person-two-strategy evolutionary game dynamics, demonstrate the absorbability of strategies, and obtain the critical cooperation conditions for prisoner's dilemmas in homogeneous networks without mutation. The evolutionary dynamics in real networks are also discussed. Our results provide a new perspective to analyze and understand social physics in time-evolving network systems.

cs.SI↗

arXiv2025

Transitions to synchronization in adaptive multilayer networks with higher-order interactions

Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate the dynamics of an adaptive multilayer network of Kuramoto oscillators with higher-order interactions. The dynamics of the nodes within the layers are adaptively controlled through the global synchronization order parameter with the adaptations present alongside both pairwise and higher-order interactions. We first explore the dynamics with a linear form of the adaptation function and discover a tiered transition to synchronization, along with continuous and abrupt routes to synchronization. Multiple routes to synchronization are also observed due to the presence of multiple stable states. We investigate the bifurcations behind these routes and illustrate the basin of attraction to attain a deeper understanding of the multistability, that is born as a consequence of the adaptive interactions. When nonlinear adaptation is infused in the system, we observe three different kinds of tiered transition to synchronization, viz., continuous tiered, discontinuous tiered, and tiered transition with a hysteretic region. Our study provides an overview of how inducting order parameter adaptations in higher-order multilayer networks can influence dynamics and alter the route to synchronization in dynamical systems.

nlin.AO↗

arXiv2020

Statistical physics approaches to the complex Earth system

Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge for a better understanding of the Earth system, including climate extreme events, earthquakes and Earth geometric relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as, critical phenomena, network theory, percolation, tipping points analysis, as well as entropy can be applied to complex Earth systems (climate, earthquakes, etc.). Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics approaches can be useful in the field of Earth system science.

physics.soc-ph↗

arXiv2019

A machine learning approach to predicting dynamical observables from network structure

Estimating the outcome of a given dynamical process from structural features is a key unsolved challenge in network science. The goal is hindered by difficulties associated to nonlinearities, correlations and feedbacks between the structure and dynamics of complex systems. In this work, we develop an approach based on machine learning algorithms that is shown to provide an answer to the previous challenge. Specifically, we show that it is possible to estimate the outbreak size of a disease starting from a single node as well as the degree of synchronicity of a system made up of Kuramoto oscillators. In doing so, we show which topological features of the network are key for this estimation, and provide a rank of the importance of network metrics with higher accuracy than previously done. Our approach is general and can be applied to any dynamical process running on top of complex networks. Likewise, our work constitutes an important step towards the application of machine learning methods to unravel dynamical patterns emerging in complex networked systems.

physics.soc-ph↗

arXiv2019

Complexity based approach for El Nino magnitude forecasting before the "spring predictability barrier"

The El Nino Southern Oscillation (ENSO) is one of the most prominent interannual climate phenomena. An early and reliable ENSO forecasting remains a crucial goal, due to its serious implications for economy, society, and ecosystem. Despite the development of various dynamical and statistical prediction models in the recent decades, the ``spring predictability barrier'' (SPB) remains a great challenge for long (over 6-month) lead-time forecasting. To overcome this barrier, here we develop an analysis tool, the System Sample Entropy (SysSampEn), to measure the complexity (disorder) of the system composed of temperature anomaly time series in the Nino 3.4 region. When applying this tool to several near surface air-temperature and sea surface temperature datasets, we find that in all datasets a strong positive correlation exists between the magnitude of El Nino and the previous calendar year's SysSampEn (complexity). We show that this correlation allows to forecast the magnitude of an El Nino with a prediction horizon of 1 year and high accuracy (i.e., Root Mean Square Error $=0.23^\circ C$ for the average of the individual datasets forecasts). For the on-going 2018 El Nino event, our method forecasts a weak El Nino with a magnitude of $1.11\pm 0.23^\circ C$. Our framework presented here not only facilitates a long--term forecasting of the El Nino magnitude but can potentially also be used as a measure for the complexity of other natural or engineering complex systems.

physics.ao-ph↗

arXiv2019

Parameter-free quantification of stochastic and chaotic signals

Recurrence entropy $(\cal S)$ is a novel time series complexity quantifier based on recurrence microstates. Here we show that $\mathsf{max}(\cal S)$ is a \textit{parameter-free} quantifier of time correlation of stochastic and chaotic signals, at the same time that it evaluates property changes of the probability distribution function (PDF) of the entire data set. $\mathsf{max}(\cal S)$ can distinguish distinct temporal correlations of stochastic signals following a power-law spectrum, $\displaystyle P(f) \propto 1/f^α$ even when shuffled versions of the signals are used. Such behavior is related to its ability to quantify distinct subsets embedded in a time series. Applied to a deterministic system, the method brings new evidence about attractor properties and the degree of chaoticity. The development of a new parameter-free quantifier of stochastic and chaotic time series opens new perspectives to stochastic data and deterministic time series analyses and may find applications in many areas of science.

physics.data-an↗

arXiv2017

Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several studies have uncovered optimal topologies for synchronization by making purposeful alterations to a network. Yet, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. This co-evolution - and the extent to which the dynamics of the individual units can shape the organization of the network itself - is not well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. The system employs a co-evolutionary rewiring strategy that depends only on instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple regulatory rule - which preserves connections between more out-of-phase oscillators while rewiring connections between more in-phase oscillators - can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding both a dependence on the intrinsic frequencies of the oscillators and the global coupling. For large enough coupling and after sufficient adaptation, the resulting networks exhibit degree - frequency and frequency - neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions. By considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena can arise in complex systems utilizing local rules.

nlin.AO↗

arXiv2016

Assessing the impact of costly punishment and group size in collective-risk climate dilemmas

The mitigation of the effects of climate change on humankind is one of the most pressing and important collective governance problems nowadays$^{1-4}$. To explore different solutions and scenarios, previous works have framed this problem into a Public Goods Game (PGG), where a dilemma between short-term interests and long-term sustainability arises$^{5-9}$. In such a context, subjects are placed in groups and play a PGG with the aim of avoiding dangerous climate change impact. Here we report on a lab experiment designed to explore two important ingredients: costly punishment to free-riders and group size. Our results show that for high punishment risk, more groups succeed in achieving the global target, this finding being robust against group size. Interestingly enough, we also find a non-trivial effect of the size of the groups: the larger the size of the groups facing the dilemmas, the higher the punishment risk should be to achieve the desired goal. Overall, the results of the present study shed more light into possible deterrent effects of plausible measures that can be put in place when negotiating climate treaties and provide more hints regarding climate-related policies and strategies.

physics.soc-ph↗

arXiv2013

Noise-aided Logic in an Electronic Analog of Synthetic Genetic Networks

We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.

physics.bio-ph↗

arXiv2008

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.

physics.soc-ph↗

arXiv2006

Universality in the synchronization of weighted random networks

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of few parameters.

cond-mat.dis-nn↗

arXiv2006

Synchronized bursts following instability of synchronous spiking in chaotic neuronal networks

We report on the origin of synchronized bursting dynamics in various networks of neural spiking oscillators, when a certain threshold in coupling strength is exceeded. These ensembles synchronize at relatively low coupling strength and lose synchronization at stronger coupling via spatio-temporal intermittency. The latter transition triggers multiple-timescale dynamics, which results in synchronized bursting with a fractal-like spatio-temporal pattern of spiking. Implementation of an appropriate technique of separating oscillations on different time-scales allows for quantitative analysis of this phenomenon. We show, that this phenomenon is generic for various network topologies from regular to small-world and scale-free ones and for different types of coupling.

nlin.CD↗

arXiv2004

Decaying of Phase Synchronization - A Physiological Tool

We describe the effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method. We develop a modified method that overcomes these effects and apply this method to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.

cond-mat.stat-mech↗