IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0247397

C Tyler Diggans, Abd AlRahman R AlMomani

{"title":"Generalizing geometric partition entropy for the estimation of mutual information in the presence of informative outliers.","authors":"C Tyler Diggans, Abd AlRahman R AlMomani","doi":"10.1063/5.0247397","DOIUrl":"https://doi.org/10.1063/5.0247397","url":null,"abstract":"The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a one-dimensional state space. A generalized definition of geometric partition entropy is now provided for samples within a bounded (finite measure) region of a d-dimensional vector space. The basic definition invokes the concept of a Voronoi diagram, but the computational complexity and reliability of Voronoi diagrams in high dimension make estimation by direct theoretical computation unreasonable. This leads to the development of approximation schemes that enable estimation that is faster than the current methods by orders of magnitude. The partition intersection (π) approximation, in particular, enables direct estimates of marginal entropy in any context resulting in an efficient and versatile mutual information estimator. This new measure-based paradigm for data-driven information theory allows flexibility in the incorporation of geometry to vary the representation of outlier impact, which leads to a significant broadening in the applicability of the established entropy-based concepts. The incorporation of informative outliers is illustrated through analysis of transient dynamics in the synchronization of coupled chaotic dynamical systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143662972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Beyond the bifurcation scenarios in vertical-cavity surface-emitting lasers with optical injection. 光注入垂直腔面发射激光器的分岔情况。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0239988

Gonzalo Marcelo Ramírez-Ávila, Timoteo Carletti

{"title":"Beyond the bifurcation scenarios in vertical-cavity surface-emitting lasers with optical injection.","authors":"Gonzalo Marcelo Ramírez-Ávila, Timoteo Carletti","doi":"10.1063/5.0239988","DOIUrl":"https://doi.org/10.1063/5.0239988","url":null,"abstract":"We study the dynamic behavior in a vertical-cavity surface-emitting laser subject to orthogonal optical injection through the computation of Lyapunov exponents and isospikes for a wide range of intervals in the plane of the injection parameters, i.e., the frequency detuning vs injection strength plane. Our thorough numerical experiments on this plane constitute a deep quantitative analysis of the different bifurcation scenarios leading to polarization switching (PS). First, we obtain similar results for the linearly polarized intensities for the different PS scenarios, especially when the injection strength is increased. It allows us to determine the parameter values that will be used for further analysis of the bifurcation scenarios in the parameter space. Analysis of different phase diagrams enables us to show multistability in the system and identify in the parameter planes several regions such as the predominantly chaotic lobe ones inside them are embedded some mainly regular structures such as spirals, rings, tricorns, shrimp networks, \"eye(s) of chaos,\" and chiral and nonchiral distribution of periodicities characterized by sequences of quint points. We emphasize two routes to chaos, namely, period-doubling and quint-point-based bifurcations.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143669180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Chaos in a class of piecewise nonlinear systems with homoclinic cycles. 一类具有同斜周期的分段非线性系统的混沌。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0246243

Kai Lu, Wenjing Xu

引用次数: 0

Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry breaking. 具有高阶相互作用和旋转对称破缺的Kuramoto振子的分岔和集体态。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0239017

Antonio Mihara, Célia M Kuwana, Roberto C Budzinski, Lyle E Muller, Rene O Medrano-T

引用次数: 0

Inferring kernel ϵ-machines: Discovering structure in complex systems. 推断核ϵ-machines：发现复杂系统中的结构。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0242981

Alexandra M Jurgens, Nicolas Brodu

{"title":"Inferring kernel ϵ-machines: Discovering structure in complex systems.","authors":"Alexandra M Jurgens, Nicolas Brodu","doi":"10.1063/5.0242981","DOIUrl":"https://doi.org/10.1063/5.0242981","url":null,"abstract":"Previously, we showed that computational mechanic's causal states-predictively equivalent trajectory classes for a stochastic dynamical system-can be cast into a reproducing kernel Hilbert space. The result is a widely applicable method that infers causal structure directly from very different kinds of observations and systems. Here, we expand this method to explicitly introduce the causal diffusion components it produces. These encode the kernel causal state estimates as a set of coordinates in a reduced dimension space. We show how each component extracts predictive features from data and demonstrate their application on four examples: first, a simple pendulum-an exactly solvable system; second, a molecular-dynamic trajectory of n-butane-a high-dimensional system with a well-studied energy landscape; third, the monthly sunspot sequence-the longest-running available time series of direct observations; and fourth, multi-year observations of an active crop field-a set of heterogeneous observations of the same ecosystem taken for over a decade. In this way, we demonstrate that the empirical kernel causal state algorithm robustly discovers predictive structures for systems with widely varying dimensionality and stochasticity.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143751458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analyzing deterministic and stochastic influences on the power grid frequency dynamics with explainable artificial intelligence. 用可解释的人工智能分析电网频率动态的确定性和随机影响。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0239371

Tim Drewnick, Xinyi Wen, Ulrich Oberhofer, Leonardo Rydin Gorjão, Christian Beck, Veit Hagenmeyer, Benjamin Schäfer

{"title":"Analyzing deterministic and stochastic influences on the power grid frequency dynamics with explainable artificial intelligence.","authors":"Tim Drewnick, Xinyi Wen, Ulrich Oberhofer, Leonardo Rydin Gorjão, Christian Beck, Veit Hagenmeyer, Benjamin Schäfer","doi":"10.1063/5.0239371","DOIUrl":"https://doi.org/10.1063/5.0239371","url":null,"abstract":"Power grids are essential for our society, connecting consumers and generators. Their frequency stability is impacted by supply and demand changes, including deterministic and stochastic dynamics, e.g., from market activities or fluctuating renewables. The first two Kramers-Moyal coefficients allow for a description of both the deterministic (via drift) and stochastic (via diffusion) aspects of these dynamics. Such a description and understanding could be critical to stabilizing power systems. However, how drift and diffusion differ between synchronous areas, how they vary over time, and how the generation mix influences them, remains unclear. Analyzing temporal patterns in drift and diffusion for frequency data from Australia (AUS) and Continental Europe (CE), we reveal a positive correlation between drift and diffusion. In addition, we utilize both gradient-boosted trees and neural network models to train drift and diffusion models for AUS and CE. Shapley additive explanations make these black-box models transparent and allow us to identify the total generation and load to influence the drift, while calendar features seem critical for the diffusion coefficient estimates.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143699749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Cantor subsystems on the Gehman dendrite. 格曼树突上的康托子系统。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0249144

Piotr Oprocha, Jakub Tomaszewski

引用次数: 0

The origin of localized patterns with a spatiotemporal oscillatory background state. 具有时空振荡背景状态的局域模式的起源。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0249873

Zhi-Chao Xue, Li Li

引用次数: 0

The role of solar heat in earthquake activity. 太阳热在地震活动中的作用。