Chaos最新文献 - Book学术

A novel approach for estimating largest Lyapunov exponents in one-dimensional chaotic time series using machine learning. 一种利用机器学习估计一维混沌时间序列中最大Lyapunov指数的新方法。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0289352

Andrei Velichko, Maksim Belyaev, Petr Boriskov

{"title":"A novel approach for estimating largest Lyapunov exponents in one-dimensional chaotic time series using machine learning.","authors":"Andrei Velichko, Maksim Belyaev, Petr Boriskov","doi":"10.1063/5.0289352","DOIUrl":"https://doi.org/10.1063/5.0289352","url":null,"abstract":"Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to produce out-of-sample, multi-horizon forecasts; the LLE is then inferred from the exponential growth of the geometrically averaged forecast error across the horizon, which serves as a proxy for trajectory divergence. We validate the approach on four canonical 1D maps-logistic, sine, cubic, and Chebyshev-achieving Rpos2 > 0.99 against reference LLE curves with series as short as M = 450. Among baselines, k-nearest neighbor (KNN) yields the closest fits (KNN-R comparable; random forest larger deviations). By design the estimator targets positive exponents: in periodic/stable regimes, it returns values indistinguishable from zero. Noise robustness is assessed by adding zero-mean white measurement noise and summarizing performance vs the average signal-to-noise ratio (SNR) over parameter sweeps: accuracy saturates for SNRm ≳ 30 dB and collapses below ≈27 dB, a conservative sensor-level benchmark. The method is simple, computationally efficient, and model-agnostic, requiring only stationarity and the presence of a dominant positive exponent. It offers a practical route to LLE estimation in experimental settings where only scalar time-series measurements are available, with extensions to higher-dimensional and irregularly sampled data left for future work.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 10","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145198548","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

Higher-order interactions, adaptivity, and phase transitions in a novel reservoir computing model. 一种新型油藏计算模型中的高阶相互作用、自适应和相变。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0278312

Anastasiia A Emelianova, Oleg V Maslennikov, Vladimir I Nekorkin

引用次数: 0

Structure-function coupling reveals the excitation-inhibition imbalance in autism spectrum disorder: A perspective from large-scale whole-brain network modeling. 结构-功能耦合揭示自闭症谱系障碍的兴奋-抑制失衡：基于大尺度全脑网络模型的视角。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0294575

Youyou Si, Honghui Zhang

{"title":"Structure-function coupling reveals the excitation-inhibition imbalance in autism spectrum disorder: A perspective from large-scale whole-brain network modeling.","authors":"Youyou Si, Honghui Zhang","doi":"10.1063/5.0294575","DOIUrl":"https://doi.org/10.1063/5.0294575","url":null,"abstract":"Excitation-inhibition (E-I) imbalance is a core pathological mechanism in autism spectrum disorder (ASD). However, current research on how E-I balance changes in ASD remains highly controversial. In this study, we integrate structural and functional magnetic resonance imaging data from the UCLA Multimodal Connectivity Database to construct a large-scale whole-brain network model, aiming to investigate the potential neural mechanism of E-I imbalance in ASD. We find that compared with healthy controls, patients with ASD exhibit stronger structural-functional connectivity (SC-FC) coupling, suggesting impaired cognitive flexibility. Model analysis demonstrates altered network dynamics in ASD, characterized by reduced optimal coupling strength between empirical and simulated FC and a lower small-world index in simulated functional networks. Furthermore, a marked shift in neural oscillations is observed in ASD, including increased activity in the δ band and decreased activity in the α band, consistent with clinical findings. More importantly, our study reveals heterogeneous reductions of the E-I ratio in ASD across multiple spatial scales, spanning from local brain regions to large-scale networks, particularly highlighting a significant negative correlation between E-I ratio and SC-FC coupling. These findings establish a direct link between E-I dysregulation and abnormal structure-function integration in brain networks, providing novel insights into the complex pathogenesis underlying ASD.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 10","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145249910","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

Dynamical analysis and near-optimal control strategy of a stochastic carbon emissions model. 随机碳排放模型的动力学分析及近最优控制策略。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0292883

Xinxin Wang, Tonghua Zhang, Sanling Yuan

{"title":"Dynamical analysis and near-optimal control strategy of a stochastic carbon emissions model.","authors":"Xinxin Wang, Tonghua Zhang, Sanling Yuan","doi":"10.1063/5.0292883","DOIUrl":"https://doi.org/10.1063/5.0292883","url":null,"abstract":"Mitigating carbon dioxide (CO2) emissions associated with energy generation is crucial for addressing the climate crisis. To better understand the dynamic relationship between CO2 concentration, human population, and energy consumption in a stochastic environment, we propose and investigate a stochastic carbon emissions model and further consider its near-optimal control (NOC) problem. We first focus on the natural evolution scenario without intervention measures to analyze the dynamic behavior of the carbon emissions system under environmental fluctuations. The results suggest that when environment noise is sufficiently large (such that ϕ<0), it will lead the population to collapse, thereby reducing energy consumption to zero, and eventually returning CO2 concentration to pre-industrial level. This is an unsustainable scenario ecologically for the model. When environment noise is not too large (such that ϖ>0), there exists a unique ergodic stationary distribution. To effectively reduce the CO2 concentration while ensuring a reasonable population size, we then develop a NOC system that incorporates two intervention strategies. Using the Pontryagin stochastic maximum principle, we establish necessary and sufficient conditions for the existence of the near-optimality. Theoretical and numerical results demonstrate that effective CO2 mitigation strategies must consider both ecological sustainability and economic feasibility. From the perspective of policymakers, this study emphasizes the importance of dynamically adjusting emission reduction strategies across different development stages. Such adaptive decision-making can effectively alleviate atmospheric CO2 concentration while ensuring economic and ecological sustainability.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 10","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145198630","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

Multi-mechanism driven geometric control of discrete memristive dual-neuron HNN: Modulation analysis and hardware implementation. 离散记忆双神经元HNN的多机制驱动几何控制：调制分析与硬件实现。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0288853

Yuke Tang, Tingkai Zhao, Xiaosheng Feng, Baoxiang Du

{"title":"Multi-mechanism driven geometric control of discrete memristive dual-neuron HNN: Modulation analysis and hardware implementation.","authors":"Yuke Tang, Tingkai Zhao, Xiaosheng Feng, Baoxiang Du","doi":"10.1063/5.0288853","DOIUrl":"https://doi.org/10.1063/5.0288853","url":null,"abstract":"In recent years, the dynamical modulation mechanisms of discrete memristive Hopfield neural networks (HNNs) have received much attention. In this paper, a four-dimensional discrete Hopfield neural network model (4DMCHNN) based on the crosstalk effect of memristive synapses is proposed. This work systematically investigates the complex dynamical regulatory behaviors emerging in neural network architectures with synaptic crosstalk, revealing how different regulatory mechanisms influence the system's chaotic properties. Analysis indicates that the system exhibits a rich variety of chaotic phenomena: amplitude control primarily depends on synaptic crosstalk intensity and internal memristor parameters; periodic dynamic modulation is dominated by memristor parameters, while the regulatory capability of the self-coupling weight on attractor offset has been improved. Furthermore, the system exhibits initial-value-induced shifts and the numerically verified coexistence of homogeneous attractors. Finally, the 4DMCHNN is implemented on a digital circuit platform, and a pseudo-random number generator constructed from its output successfully passes the NIST statistical tests. Low-cost hardware implementations drive neuromorphism toward practical applications. The investigation of predictably modulated chaotic behaviors in neural network systems, thus, offers new tools for modeling neurological diseases and implementing chaos control.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 10","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145205694","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

From homogeneity to heterogeneity: Topologically reconfigurable multi-cavity attractors in memristive chaotic maps. 从均匀性到非均匀性：忆忆混沌映射中拓扑可重构的多腔吸引子。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0283700

Jin Liu, Kehui Sun, Huihai Wang

{"title":"From homogeneity to heterogeneity: Topologically reconfigurable multi-cavity attractors in memristive chaotic maps.","authors":"Jin Liu, Kehui Sun, Huihai Wang","doi":"10.1063/5.0283700","DOIUrl":"https://doi.org/10.1063/5.0283700","url":null,"abstract":"In recent years, multi-cavity attractors have emerged as a focal point in chaotic dynamics research. However, previous studies have predominantly focused on homogeneous multi-cavity attractors, where all cavities share identical topological structures. While topologically interesting, this homogeneity leads to highly similar statistical characteristics across cavities, potentially posing a threat to its cryptographic applications. To address this limitation, this study proposes a concise chaotic map construction scheme based on discrete memristors. Mathematical analysis reveals that this map exhibits no fixed points and can stably generate hidden attractors. Crucially, by selecting periodic or aperiodic memristive functions, it is possible to construct both homogeneous and heterogeneous multistability or multi-cavity attractors. Furthermore, we demonstrate that the heterogeneous structure breaks the periodic redundancy inherent in its homogeneous counterpart, resulting in a significantly larger and scalable effective key space. This finding quantitatively validates the enhanced security potential of the proposed map in fields, such as information encryption. This research not only expands the conceptual boundaries of multi-cavity attractors in chaotic systems but also presents a promising novel framework for diverse engineering applications.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 10","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145238244","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

Control of chimera states via adaptive higher-order interactions. 通过自适应高阶相互作用控制嵌合体状态。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0296464

Andrey V Andreev, Artem A Badarin, Dibakar Ghosh, Elena N Pitsik, Alexander E Hramov

引用次数: 0

Stochastic bifurcation and safety basin study of nonlinear vibration systems in Li-doped graphene nanoplates with time delays. 掺锂石墨烯纳米板非线性振动系统的随机分岔与安全盆研究。

IF 3.2 2区数学

Chaos Pub Date : 2025-10-01 DOI: 10.1063/5.0285335

Lu Cheng, Zhouchao Wei, Zaitang Huang, Tomasz Kapitaniak

引用次数: 0

Intermittent synchronization in non-weakly coupled piecewise-linear expanding map lattice: A geometric-combinatorial approach. 非弱耦合分段线性扩展映射格中的间歇同步：一种几何组合方法。