Chaos最新文献

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear partial differential equation (PDE) that exhibits spatiotemporal chaos. Our research focuses on predicting changes in long-term statistical patterns of the gKS model that result from varying the dispersion relation or the length of the spatial domain. We use transfer learning to adapt ESNs to different parameter settings and successfully capture changes in the underlying chaotic attractor. Previous work has shown that transfer learning can be used effectively with ESNs for a single-orbit prediction. The novelty of our paper lies in our use of this pairing to predict the long-term statistical properties of spatiotemporally chaotic PDEs. Nevertheless, we also show that transfer learning nontrivially improves the length of time that predictions of individual gKS trajectories remain accurate.

Noise-induced critical transitions (NICTs) from one stable state to another contrasting one are widespread in ecosystems. Its occurrence may cause changes in the function and structure of an ecosystem and even bring irreparable damage to humans and nature. Therefore, it is crucial to predict the occurrence of NICTs in ecosystems. Since a single state variable evolving over time is difficult to characterize a real system, a two-dimensional lake eutrophication model with two coupled variables is used as a paradigmatic example here. The prediction of a Gaussian white noise-induced CT from a desirable state to an undesirable one is carried out. First, our results of the dynamical evolution show that the NICT occurs before the bifurcation point corresponding to the two variables, and this phenomenon becomes earlier with increasing noise intensity. Subsequently, the joint escape probability from the desirable state to the undesirable one is calculated by a finite difference scheme. To quantify the possibility of NICT in different variables, the idea that transforms the joint escape probability into the marginal escape probability by using integral summation is introduced. Then, the concept of parameter dependent basin of the unsafe regime established in one-dimensional (1D) systems is extended to achieve early warning of NICTs in two-dimensional (2D) ecosystems. This study provides a theoretical basis for predicting catastrophic CTs even in high-dimensional complex systems.

This paper proposes a novel opinion dynamics model based on two key psychological factors, namely, stubbornness and trust, that govern how agents update their opinions. By comparing the evolution of multiple configurations on hypergraphs, which capture group-based, higher-order interactions instead of pairwise ones, we find that heterogeneity leads to opinion fragmentation, whereas homogeneity drives the system toward consensus. This finding offers a plausible explanation for the persistence of opinion diversity in social networks. Through an analysis of opinion exchange between two opposing communities, we identify a group reinforcement effect driven by internal consistency, which effectively steers the direction of opinion flow. However, this reinforcement effect breaks down abruptly when a cluster's initial opinion strength falls below a critical point. This phase transition implies that achieving a critical opinion strength is a necessary condition for a weaker community to dominate a stronger one.

This article investigates how a uniform high-frequency (HF) drive applied to each site of a weakly coupled discrete nonlinear resonator array can modulate the onsite natural stiffness and damping and thereby facilitate the active tunability of the nonlinear response and the phonon dispersion relation externally. Starting from a canonical model of parametrically excited van der Pol-Duffing chain of oscillators with nearest-neighbor coupling, a systematic two-widely separated time scale expansion (Direct Partition of Motion) has been employed, in the backdrop of Blekhman's perturbation scheme. This procedure eliminates the fast scale and yields the effective collective dynamics of the array with renormalized stiffness and damping, modified by the high-frequency drive. The resulting dispersion shift controls which normal modes enter the parametric resonance window, allowing highly selective activation of specific bulk modes through external HF tuning. The collective resonant response to the parametric excitation and mode selection by the HF drive has been analyzed and validated by detailed numerical simulations. The results offer a straightforward, experimentally tractable route to active control of response and channelize energy through selective mode activation in microelectromechanical system/nano electro-mechanical system arrays and related resonator platforms.

This study introduces a deformation framework applied to the classical Gaussian map, yielding a q-deformed Gaussian map with enhanced dynamical properties. The analysis focuses on the nonlinear characteristics, bifurcation patterns, and topological entropy of the deformed system. Through analytical methods and visual tools like Lyapunov exponents and bifurcation diagrams, the q-deformed map demonstrates an expanded stability compared to its classical counterpart. Furthermore, to control chaotic dynamics in both classical and deformed Gaussian maps, a two-step feedback control mechanism is implemented. This approach stabilizes unstable periodic orbits and suppresses chaos effectively, as validated through numerical simulations.

This paper focuses on a fundamental inquiry in a coupled-oscillator model framework. It specifically addresses the direction of net information flow in mutually coupled non-identical chaotic oscillators. Adopting a specific form of conditional mutual information as a model-free and asymmetric index, we establish that if the magnitude of the maximum Lyapunov exponent can be defined as the "degree of chaos" of a given isolated chaotic system, a predominant net information transfer exists from the oscillator exhibiting a higher degree of chaos to the other while they are coupled. Subsequently, the calculation of projected Kolmogorov-Sinai entropy for variables associated with the interacting oscillators reveals that the oscillator exhibiting a higher degree of chaos is also characterized by a higher projected Kolmogorov-Sinai entropy value and transfers more information to the other oscillator. We incorporate two distinct categories of coupled "non-identical" oscillators to strengthen our claim. In the first category, both oscillators share identical functional forms, differing solely in one parameter value. We also adopt another measure, the Liang-Kleeman information flow, to support the generality of our results. The functional forms of the interacting oscillators are entirely different in the second category. We further extend our study to the coupled-oscillator models, where the interacting oscillators possess different dimensions in phase space. These comprehensive analyses support the broad applicability of our results.

A reduced-order modeling framework is developed to address the high-dimensional challenges of parameterized partial differential equations by integrating tensor-train decomposition (TTD), Gaussian process regression (GPR), and Gaussian process dynamical models (GPDMs). TTD furnishes a low-rank approximation of the solution snapshots, while GPR learns the nonlinear mapping from the input parameter space to the tensor-train format. GPDM then models the temporal dynamics, enabling accurate time evolution prediction and uncertainty quantification. The method is validated on several benchmark problems, including Burgers' equations and the incompressible Navier-Stokes equations. Comparative experiments against traditional methods such as proper orthogonal decomposition-Gaussian process regression and dynamic mode decomposition based on tensor-train decomposition-Gaussian process regression demonstrate that the proposed approach achieves superior accuracy in modeling nonlinear temporal dynamics, conducting time-domain interpolation, and quantifying prediction uncertainty.

We describe the real-time forecasting of September 2024 Arctic sea ice extent using a theory-guided machine learning method based on data-adaptive harmonic decomposition and frequency-based nonlinear stochastic modeling, as part of the Sea Ice Outlook. Compared to standard statistical and machine learning models, this method adeptly accounts for non-linear behavior, effectively incorporates memory effects, and handles a wide range of time scale variations, from synoptic (stochastic-like) weather effects to low-frequency (red-noise like) variability, significantly enhancing the accuracy and reliability of sea ice prediction.

Walking droplets-millimetric oil droplets that self-propel across the surface of a vibrating fluid bath-exhibit striking emergent statistics that remain only partially understood. In particular, in a variety of experiments, a robust correspondence has been observed between the droplet's statistical distribution and the time-average of the wave field that guides it. Durey et al. [Chaos 28, 096108 (2018)] rigorously established such a correspondence for single-droplet systems with a single, instantaneous droplet-bath impact during each vibration period, but numerical and experimental evidence suggests that the correspondence should hold far more broadly. Laboratory droplet systems, for instance, often exhibit complex bouncing modes that do not adhere to these hypotheses. We attempt to complete this program in the present work, rigorously extending this statistical correspondence to account for arbitrary droplet-bath impact models, multi-droplet interactions, and non-resonant bouncing. We investigate this correspondence numerically in systems of one and two droplets in 1D geometries, and we highlight how the time-averaged wave field can distinguish between correlated and uncorrelated pairs of droplets.

Understanding how people perceive and value landscapes is essential for sustainable planning and conservation; yet, traditional methods remain limited in scale and scope. This study introduces artificial intelligence (AI)-Perceptual Landscape Mapping (AI-PLM), an integrated analytical framework that combines geospatial intelligence, machine learning, and natural-language processing (NLP) to model collective human perception from social-media data. Using nearly 29 000 geotagged Flickr photographs and 148 000 user comments from Romania, AI-PLM operationalizes perception through three components: (1) Data collection and processing (systematic collection and normalization of multilingual, multimodal content), (2) AI-Spatial Cognition (identification of perception hotspots via Head/Tail Breaks and DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering combined with viewshed analysis), and (3) Affective-Semantic Intelligence (sentiment and topic modeling using transformer-based NLP). Results reveal strong spatial hierarchies of landscape appreciation, with intensity peaks in the Carpathians, Braşov, Bucharest, Maramureş, and the Black Sea coast. Sentiment analysis shows predominantly positive emotions associated with nature-oriented regions, while topic modeling highlights the prevalence of themes related to photography, heritage, and recreation. Together, these multimodal insights demonstrate a clear relationship between visibility, spatial clustering, and affective tone. The AI-PLM framework, thus, bridges physical geography and emotional expression, providing a scalable and transferable methodology for assessing cultural ecosystem services. By translating unstructured digital traces into structured spatial and semantic indicators, it advances the understanding of human-landscape interactions and offers practical tools for data-driven landscape management, conservation, and tourism planning in Romania and beyond.