Chaos最新文献

There are numerous indicators used to characterize the degree of synchronization for a non-identical system consisting of heterogeneous phase oscillators, such as the critical coupling of phase synchronization and the critical coupling of frequency synchronization and order parameter. Is it possible to predict these indicators simultaneously given the realistic situations of unknown system dynamics, including network structure, local dynamics, and coupling functions? This process, known as multi-task learning, can be achieved through the model-free technique of a feed-forward neural network in machine learning. To elaborate, we can measure the synchronization indicators of a limited number of allocation schemes and utilize these data to train the machine model. Once trained, the model can be employed to predict these indicators simultaneously for any novel allocation scheme. More importantly, the trained machine can also identify the optimal allocation for synchronization from a large pool of candidates. This method solves an outstanding question, which is how to allocate a given set of heterogeneous oscillators on a complex network in order to improve the synchronization performance. Leveraging multi-task learning's ability to predict multiple synchronization indicators, we can ensure that the system with the optimal performs well throughout the entire synchronization transition. Additionally, we test the scalability of the machine; one approach is to predict the indicators for a system composed of a new set of oscillators, and the other is to simultaneously predict the indicators of different systems.

Inferring the dynamics of a network of oscillators becomes a significant challenge in the absence of explicit system equations. We present a data-driven machine learning technique to predict different dynamical states of a network, specifically a star-structured one. The proposed method exploits a parameter-aware reservoir computing scheme based on the echo-state network (ESN) framework. Our method employs a minimal setup to learn the parameter-dependent dynamics of a large network, using only two ESN units. We utilize the topological symmetry of the network to reduce the training cost. We validate the performance of our scheme in both scenarios where the central node oscillator of the star network is identical and non-identical to the peripheral node oscillators. In both cases, the proposed scheme is able to efficiently predict various emergent multi-stable dynamics of the network with varied coupling strengths. Despite exposure to limited data during training, it shows notable performance in predicting unseen attractors, including chimera, coherent, incoherent, and cluster synchronization states present in the network dynamics. Thus, this study provides an efficient reservoir computing framework for learning the dynamics of large-scale oscillator networks.

Vincent van Gogh's late paintings are renowned for their distinctive motion-like textures, where swirling patterns and luminous contrasts evoke the dynamics of turbulent flow. While previous studies have identified turbulence-like statistics in individual works, such as The Starry Night, a systematic quantification of visual complexity across his oeuvre has remained unexplored. Here, we apply two-dimensional multifractal detrended fluctuation analysis to four major paintings produced during the artist's final 15 months to examine how scale-dependent organization evolves across this creative period. The analysis reveals clear differences in multifractal behavior among the paintings, reflecting systematic variations in the organization of luminance fluctuations. Paintings produced during periods historically documented as psychologically unstable for the artist exhibit broader multifractal spectra and stronger deviations from monofractality, whereas those created during intervals of relative calm display more homogeneous scaling patterns. To summarize this variability, we introduce the Fractal Turbulence Index, a composite metric integrating heterogeneity and roughness, which consistently differentiates the paintings according to their degree of structural complexity. Beyond the artistic context, the study demonstrates how methods originally developed for turbulence and scale-invariant phenomena can be extended to human-generated imagery, providing a quantitative framework for understanding how order, variability, and intermittency emerge in aesthetic expression.

Driven particle transport in crowded and confining environments is fundamental to diverse phenomena across physics, chemistry, and biology. A main objective in studying such systems is to identify novel emergent states and phases of collective dynamics. Here, we report on a nonequilibrium phase transition occurring in periodic structures at high particle densities. This transition separates a weak-current phase of thermally activated transport from a high-current phase of solitary wave propagation. It is reflected also in a change of universality classes characterizing correlations of particle current fluctuations. Our findings demonstrate that sudden changes to high-current states can occur when increasing particle densities beyond critical values.

Cooperation is crucial for social progress but is often undermined by free-riding behavior. This study explores how biased allocation mechanisms affect the evolution of cooperation in public goods games. By incorporating group attributes into a game-theoretic model and designing unequal payoff allocation rules based on majority group status, we simulated evolutionary dynamics on random networks. Results indicate that moderate bias strength and lower majority thresholds significantly promote cooperation, particularly when the public goods enhancement factor is moderate. These findings advance collective action theory by demonstrating the role of structural incentives in fostering cooperation and suggest directions for future empirical research and exploration of diverse network structures.

We consider a mortal random walker evolving with discrete time on a network, where transitions follow a degree-biased Markovian navigation strategy. The walker starts with a random initial budget T1∈N and must maintain a strictly positive budget to remain alive. Each step incurs a unit cost, decrementing the budget by one; the walker perishes (is ruined) upon depletion of the budget. However, when the walker reaches designated target nodes, the budget is renewed by an independent and identically distributed (IID) copy of its initial value. The degree bias is tuned to either favor or disfavor visits to these target nodes. Our model exhibits connections with stochastic resetting. The evolution of the budget can be interpreted as a deterministic drift on the integer line toward negative values, where the walker is intermittently reset to positive IID random positions and dies at the first hit of the origin. The first part of the paper focuses on the target-hitting statistics of an immortal Markovian walker. We analyze the target-hitting counting process (THCP) for an arbitrary set of target nodes. In the special case where a single target node coincides with the starting node, the THCP reduces to a renewal counting process. We establish connections with classical results from the literature. Within this framework, the second part of the paper addresses the dynamics of the evanescent walker. We derive analytical results for arbitrary configurations of target nodes, including the evanescent propagator matrix, the survival probability, the mean residence time on a set of nodes during the walker's lifetime, and the expected lifetime itself. Additionally, we compute the expected number of target hits (i.e., budget renewals) in a lifetime of the walker and related distributions. We explore both analytically and numerically a set of characteristic scenarios, including a forager scenario, in which frequent encounters with target nodes extend the walker's lifetime, and a detrimental scenario, where such encounters instead reduce it. Finally, we identify a neutral scenario in which frequent visits to target nodes have no effect on the walker's lifetime. Our analytical results are validated through random walk simulations.

We develop a minimal whole-heart model that describes cardiac electrical conduction and simulate a basic three-lead electrocardiogram (ECG). We compare our three-lead ECG model with clinical data from a Norwegian athlete database. The results demonstrate a strong correlation with the ECGs recorded for these athletes. We simulate various pathologies of the heart's electrical conduction system, including ventricular tachycardia, atrioventricular nodal reentrant tachycardia, accessory pathways, and ischemia-related arrhythmias, showing that the three-lead ECGs align with the clinical data. This minimal model serves as a computationally efficient digital twin of the heart.

Next Generation Reservoir Computing (NGRC) is a low-cost machine learning method for forecasting chaotic time series from data. Computational efficiency is crucial for scalable reservoir computing, requiring better strategies to reduce training cost. In this work, we uncover a connection between the numerical conditioning of the NGRC feature matrix-formed by polynomial evaluations on time-delay coordinates-and the long-term NGRC dynamics. We show that NGRC can be trained without regularization, reducing computational time. Our contributions are twofold. First, merging tools from numerical linear algebra and ergodic theory of dynamical systems, we systematically study how the feature matrix conditioning varies across hyperparameters. We demonstrate that the NGRC feature matrix tends to be ill-conditioned for short time lags, high-degree polynomials, and short length of training data. Second, we evaluate the impact of different numerical algorithms [Cholesky, singular value decomposition (SVD), and lower-upper decomposition] for solving the regularized least squares problem. Our results reveal that SVD-based training achieves accurate forecasts without regularization, being preferable when compared against the other algorithms.

We present a investigation of solar active regions using a complexity-based framework that combines solar observations with methods from complex network theory. Building on the historical foundation that active regions constitute buoyantly emerging magnetic flux bundles, we leverage continuous multi-wavelength data, particularly synoptic magnetograms from SOHO, to track the morphological evolution and connectivity of these magnetically intense structures in the solar photosphere and low corona. We first identify active regions as topologically coherent features in the photospheric magnetic field, and subsequently construct graphs in which nodes represent individual or recurrent flux elements, while edges capture temporal adjacency. The resulting networks exhibit scale-free degree distributions, non-trivial clustering, and signatures of dynamic reconfiguration reminiscent of self-organized criticality. These emergent properties clarify how local flux emergence, reconnection processes, and coronal loop expansions collectively shape the global magnetic topology. In particular, we find that longer-lived active regions act as network "hubs," playing a critical role in the redistribution of magnetic energy. Our analysis reinforces the notion that solar magnetic fields evolve through multi-scale interactions, bridging global dynamo action with localized eruptions and shedding new light on the triggers of flares and coronal mass ejections. By uniting data-driven detection techniques with complexity-science tools, this work highlights how network representations can strengthen models of solar activity and refine our understanding of magnetic-field behavior across the solar interior and atmosphere.

The dynamics of a test particle in the field of a model galaxy proposed by Serge Aubry is studied by a combination of theory and numerical computation. Regimes of near-integrable behavior and almost perfect chaos are found. A proposed explanation for the latter is sketched. Thoughts are presented on the implications of the analysis for galaxies.