IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0289031

Laura Molero González, Roy Cerqueti, Raffaele Mattera, Juan E Trinidad Segovia

{"title":"The random matrix-based informative content of correlation matrices in stock markets.","authors":"Laura Molero González, Roy Cerqueti, Raffaele Mattera, Juan E Trinidad Segovia","doi":"10.1063/5.0289031","DOIUrl":"https://doi.org/10.1063/5.0289031","url":null,"abstract":"Studying and comprehending the eigenvalue distribution of the correlation matrices of stock returns is a powerful tool to delve into the complex structure of financial markets. This paper deals with the analysis of the role of eigenvalues and their associated eigenvectors of correlation matrices within the context of financial markets. We exploit the meaningfulness of Random Matrix Theory with the specific aspect of the Marchenko-Pastur distribution law to separate noise from true signal, but with a special focus on giving an interpretation of what these signals mean in the financial context. We empirically show that the highest eigenvalue serves as a proxy of market spillover. Furthermore, based on an analysis of portfolio betas, we prove that the eigenvector associated with this eigenvalue is the market portfolio. These analyses of portfolio betas also reveal that the second- and third-highest eigenvalues, and their associated eigenvectors, result in some cases of counter-behavior that makes them suitable to be a safe haven during high-volatility periods. The analysis is performed on a set of indices coming from developed and emerging countries over a time period ranging from 2015 to 2024.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144999710","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

Predicting complex time series with deep echo state networks. 用深度回波状态网络预测复杂时间序列。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0283425

Afrouz Delshad, Elizabeth M Cherry

{"title":"Predicting complex time series with deep echo state networks.","authors":"Afrouz Delshad, Elizabeth M Cherry","doi":"10.1063/5.0283425","DOIUrl":"https://doi.org/10.1063/5.0283425","url":null,"abstract":"Although many real-world time series are complex, developing methods that can learn from their behavior effectively enough to enable reliable forecasting remains challenging. Recently, several machine-learning approaches have shown promise in addressing this problem. In particular, the echo state network (ESN) architecture, a type of recurrent neural network where neurons are randomly connected and only the read-out layer is trained, has been proposed as suitable for many-step-ahead forecasting tasks. ESNs have been shown to be effective in predicting complex time series while reducing training costs, thereby improving efficiency. Deep echo state networks, which extend the architecture of ESNs by stacking multiple reservoir layers, have also been proposed as an option to learn different features of the dynamics across the layers, but to date they have received less study. In this work, we analyzed the performance of deep ESNs for several variations in network structure, including a hybrid approach that integrated a knowledge-based model. We found that for specific network structures, deep ESNs could improve prediction accuracy over baseline ESNs with the same number of neurons by up to 65% for a chaotic data set derived from the Mackey-Glass model and 14% for an experimental data set of complex zebrafish cardiac voltage recordings. Similarly, deep hybrid ESNs could reduce error compared to same-size flat hybrid ESNs by up to 59% for the Mackey-Glass data set and 11% for the experimental data set. Our results also showed that the hybrid approach was especially beneficial for the experimental data set and that deep network structures improved prediction robustness.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145029032","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

Quasi-soliton solution to the model of two-color optical waves in PT-symmetry structures. pt对称结构中双色光波模型的拟孤子解。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0282090

Tatiana M Lysak, Irina G Zakharova, Aleksei A Kalinovich

引用次数: 0

Collective directional switches of swarming systems with higher-order interactions. 具有高阶相互作用的群体系统的集体方向开关。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0285101

Shijie Liu, Rui Xiao, Yongzheng Sun

{"title":"Collective directional switches of swarming systems with higher-order interactions.","authors":"Shijie Liu, Rui Xiao, Yongzheng Sun","doi":"10.1063/5.0285101","DOIUrl":"https://doi.org/10.1063/5.0285101","url":null,"abstract":"Sudden coherent changes in the movement direction are common in animal groups; yet, the mechanism of higher-order and delayed interactions in shaping such collective switching dynamics remains poorly understood. Here, we propose a self-propelled particle model incorporating both pairwise and higher-order social interactions to study the directional switching behaviors in swarming systems, considering scenarios with and without delay. By applying a dimensional reduction method and the Fokker-Planck equation, we obtain the theoretical stationary probability density and the mean switching time. The results reveal that, without time delay, the higher-order interactions significantly increase the mean switching time, promoting stable, ordered movement states and reducing directional switches. When the time delay is introduced, the impact of higher-order interactions becomes non-monotonic. For small delays, they continue to suppress directional switching; for large delays, they instead facilitate more frequent directional switching. This non-monotonic pattern also appears in simulations on realistic social networks, underscoring the generality of the phenomenon. Our study illustrates how higher-order structures and time delays influence collective switching dynamics, highlighting the limitations of pairwise models and the necessity of considering complex interaction networks.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145130128","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

Detecting subtle deviations in Brownian motion representations driven by a Schauder basis. 探测由邵德基驱动的布朗运动表示中的细微偏差。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0287678

Massimiliano Frezza

引用次数: 0

Topological modes of variability of the wind-driven ocean circulation. 风驱动海洋环流变率的拓扑模式。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0261968

Gisela D Charó, Denisse Sciamarella, Juan Ruiz, Stefano Pierini, Michael Ghil

引用次数: 0

Dynamical analysis of a latent HIV infection model with general incidence and multiple delays. 具有一般发病和多重延迟的HIV潜伏感染模型的动力学分析。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0276462

Yu Yang, Lan Zou

引用次数: 0

Route to chaos in multi-species ecosystems. 多物种生态系统的混乱之路。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0291485

Robin Delabays, Philippe Jacquod

{"title":"Route to chaos in multi-species ecosystems.","authors":"Robin Delabays, Philippe Jacquod","doi":"10.1063/5.0291485","DOIUrl":"https://doi.org/10.1063/5.0291485","url":null,"abstract":"We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed-points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in natural or laboratory-controlled ecosystems and in mathematical models. Here, we emphasize the emergence of limit cycles following Hopf bifurcations tuned by the variability of interspecies interaction. As this variability increases and owing to the large dimensionality of the system, limit cycles typically acquire a growing spectrum of frequencies. This often leads to the appearance of strange attractors, with a chaotic dynamics of species abundances characterized by a positive Lyapunov exponent. We observe that limit cycles and strange attractors preserve biodiversity to some extent, as they maintain dynamical stability without species extinction. We give numerical evidences that this route to chaos dominates in ecosystems with strong enough interactions and where predator-prey behavior dominates over competition and mutualism. Based on arguments from random matrix theory, we further conjecture that this scenario is generic in ecosystems with a large number of species and identify the key parameters driving it. Overall, we show that the model we consider provides a unifying framework, where a wide range of population dynamics emerge from a simple few-parameter model.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013994","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

Collective fluctuations in the finite-size Kuramoto model below the critical coupling: Shot-noise approach. 临界耦合下有限尺寸Kuramoto模型中的集体波动：短噪声方法。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0287893

S Yu Kirillov, V V Klinshov

引用次数: 0

Brownian motion with stochastic energy renewals. 具有随机能量更新的布朗运动。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0285588

Ion Santra, Kristian Stølevik Olsen

引用次数: 0

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