Chaos Solitons & Fractals最新文献

英文中文

Flexible manipulation of longitudinal polarization vortices by superposed cylindrical vector optical field 利用叠加圆柱矢量光场灵活操纵纵向极化涡

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-23 DOI: 10.1016/j.chaos.2026.117952

Xu-Zhen Gao, Jia Ai, Hong-Teng Xu, Hui-Ru Liu, Jing-Rui Chen, Guo-Dong Tan, Yue Pan

Photonic orbital angular momentum (OAM) carried by optical vortex has emerged as a fundamental degree of freedom in modern optics, revolutionizing applications from high-capacity communications to quantum information processing. Recently, the manipulation of novel optical vortices has attracted widespread attention and found numerous applications. Here, we demonstrate a kind of superposed cylindrical vector optical field (SC-VOF), and achieve flexible manipulated longitudinal polarization vortices in focal plane. By selecting different parameters of the SC-VOF, the one-, two-, and three-dimensional longitudinal polarization vortices are generated, and the topological charge and photonic OAM can be flexibly manipulated. The flexible manipulation of longitudinal polarization vortices, featuring arbitrary topological charges and controllable photonic OAM, enables a wide range of cutting-edge applications, including high-resolution fluorescent imaging, enhanced Raman spectroscopy, and advanced optical tweezers in both scientific research and industrial technologies.

光学涡旋携带的光子轨道角动量（OAM）已经成为现代光学中的一个基本自由度，从大容量通信到量子信息处理的应用都发生了革命性的变化。近年来，新型光学涡旋的操纵引起了广泛的关注，并得到了广泛的应用。在这里，我们展示了一种叠加圆柱矢量光场（SC-VOF），并在焦平面上实现了柔性可操纵的纵向极化涡。通过选择不同的SC-VOF参数，可以产生一维、二维和三维纵向极化涡，并可以灵活地控制拓扑电荷和光子OAM。纵向极化涡旋的灵活操作，具有任意拓扑电荷和可控光子OAM，可以实现广泛的尖端应用，包括高分辨率荧光成像，增强拉曼光谱，以及科学研究和工业技术中的先进光镊。

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引用次数: 0

Symmetric higher-order interactions in Kuramoto oscillators with time-delayed coupling: Emergence of chimera states and multi-cluster synchronization 具有时滞耦合的Kuramoto振子中的对称高阶相互作用：嵌合体状态的出现和多簇同步

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-23 DOI: 10.1016/j.chaos.2026.117972

Dhilshath Shajahan

We investigate the dynamics of Kuramoto oscillators with symmetric higher-order interactions in the presence of time delays. Unlike previous studies focusing on asymmetric interactions, we analyze symmetric coupling terms of the form

\sum_{j, k} sin (θ_{j} + θ_{k} - 2 θ_{i} + ϕ)

, where

ϕ

represents a phase lag parameter. Using the Ott–Antonsen (OA) ansatz, we derive reduced equations for the order parameter and demonstrate that time delays can induce novel collective behaviors including chimera states, multi-cluster synchronization, and explosive desynchronization. Our analysis reveals that the interplay between symmetric higher-order interactions and time delays creates bistable regions where coherent and incoherent states coexist. We identify critical delay values that promote the emergence of partial synchronization patterns and show that the phase lag parameter

ϕ

controls the transition between different synchronization regimes. Numerical simulations with

N = 1 0^{4}

oscillators confirm our analytical predictions and reveal rich dynamics including traveling wave solutions, spatiotemporal chaos, and novel breathing chimera states. The system exhibits up to five coexisting stable states in certain parameter regions, significantly extending the multistability observed in previous higher-order Kuramoto models.

研究了具有对称高阶相互作用的Kuramoto振子在时滞存在下的动力学。与以往关注非对称相互作用的研究不同，我们分析了形式为∑j，ksin（θj+θk−2θi+ φ）的对称耦合项，其中φ表示相位滞后参数。利用Ott-Antonsen (OA) ansatz，我们推导了阶参量的简化方程，并证明了时间延迟可以诱导新的集体行为，包括嵌合体状态、多簇同步和爆炸不同步。我们的分析表明，对称高阶相互作用和时间延迟之间的相互作用产生了相干和非相干状态共存的双稳态区域。我们确定了促进部分同步模式出现的临界延迟值，并表明相位滞后参数ϕ控制不同同步制度之间的过渡。N=104振子的数值模拟证实了我们的分析预测，并揭示了丰富的动力学，包括行波解、时空混沌和新型呼吸嵌合体状态。该系统在某些参数区域显示出多达五个共存的稳定状态，大大扩展了先前高阶Kuramoto模型中观察到的多重稳定性。

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引用次数: 0

MAPPO-LCR: Multi-Agent Proximal Policy Optimization with Local Cooperation Reward in spatial public goods games MAPPO-LCR：空间公共物品博弈中具有局部合作奖励的多智能体近端策略优化

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-23 DOI: 10.1016/j.chaos.2026.117948

Zhaoqilin Yang , Axin Xiang , Kedi Yang , Tianjun Liu , Youliang Tian

Imitation learning and conventional reinforcement learning struggle to capture strategic coupling in large spatial public goods games. This work introduces Multi-Agent Proximal Policy Optimization (MAPPO) into spatial public goods games to study learning-driven cooperation. Unlike independent PPO learners, MAPPO evaluates collective outcomes through a centralized critic with decentralized policy execution. This structure stabilizes learning dynamics and reveals clearer cooperation transition thresholds. Building on this framework, we examine MAPPO with a Local Cooperation Reward (MAPPO-LCR) to incorporate neighborhood-level cooperation signals. Local cooperative feedback strengthens spatial interactions and sharpens cooperation transitions near critical regimes. Extensive simulations and statistical analyses show that MAPPO is more stable than PPO, while MAPPO-LCR further improves robustness. These results clarify how deep multi-agent learning internalizes spatial cooperation mechanisms in structured social dilemmas.

在大型空间公共物品博弈中，模仿学习和传统强化学习难以捕捉战略耦合。本文将多智能体近端策略优化（MAPPO）引入到空间公共物品博弈中，研究学习驱动型合作。与独立的PPO学习器不同，MAPPO通过集中的批评家和分散的政策执行来评估集体结果。这种结构稳定了学习动态，揭示了更清晰的合作过渡阈值。在此框架的基础上，我们研究了带有本地合作奖励（MAPPO- lcr）的MAPPO，以纳入邻居级合作信号。局部合作反馈加强了空间相互作用，并使关键机制附近的合作转变更加尖锐。大量的仿真和统计分析表明，MAPPO比PPO更稳定，而MAPPO- lcr进一步提高了鲁棒性。这些结果阐明了深度多智能体学习如何内化结构化社会困境中的空间合作机制。

引用次数: 0

The impact of financial markets uncertainty on oil price uncertainty 金融市场的不确定性对油价不确定性的影响

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-23 DOI: 10.1016/j.chaos.2026.117975

Gil Cohen

This study examines the dynamic interactions between oil-market uncertainty and financial-market volatility indices. We employed three principal statistical tools to ascertain the importance of the explanatory variable on the crude oil volatility index (OVX). As proxies for the uncertainty in the stock and bond markets, we used their respective “fear gauges” (VIX for stocks and MOVE for bonds). Our findings indicate that OVX is positively influenced by changes in the uncertainties of both the bond and stock markets, positively affected by changes in the yields of 10-year U.S. Treasury Notes, and negatively influenced by changes in the S&P 500. Granger's causality tests revealed that while oil price uncertainty is affected by uncertainties in both bond and stock markets, it only has an impact on bond market uncertainty and not on stock market uncertainty. The results from Neural Networks (NN) highlighted that bond market uncertainty is the primary predictor of oil market uncertainty, followed by the S&P 500 and the VIX.

本研究探讨石油市场不确定性与金融市场波动指数之间的动态相互作用。我们采用了三种主要的统计工具来确定解释变量对原油波动指数（OVX）的重要性。作为股票和债券市场不确定性的代理，我们使用了它们各自的“恐惧指标”（股票的VIX和债券的MOVE）。我们的研究结果表明，OVX受到债券和股票市场不确定性变化的积极影响，受到10年期美国国债收益率变化的积极影响，受到标准普尔500指数变化的消极影响。格兰杰因果检验表明，油价不确定性同时受到债券市场和股票市场不确定性的影响，但仅对债券市场不确定性有影响，对股票市场不确定性没有影响。神经网络（NN）的结果强调，债券市场的不确定性是石油市场不确定性的主要预测指标，其次是标准普尔500指数和波动率指数。

引用次数: 0

Chaos-induced soliton dynamics in a gain-assisted rubidium medium 增益辅助铷介质中混沌诱导孤子动力学

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-23 DOI: 10.1016/j.chaos.2026.117981

Muhsin Hayat , Waqar Ahmad , Mohammad Mahtab Alam , F. Maiz , Hamiden Abd El-Wahed Khalifa

This study investigates the behaviour of self-localized optical modes derived from the Rodrigue form of Legendre polynomials propagating through a gain-assisted atomic medium. The optical pulses demonstrate significant spatiotemporal changes, exhibiting patterns of localized intensity peaks and intensity dips on a continuous wave background. These unique dynamics are coherently manipulated by applied pump and coupled driving fields, which are also generated from the Rodrigue form of Legendre polynomials. The maximum localized intensity of these pulses can be precisely tuned from 0.002% to 100% with changes in position, time, and the intensity of the control field. The spatial location of the peak intensity is shown to shift depending on the decay rates and driving field parameters. The resulting modified pulse dynamics apply to areas including DNA dynamics, heartbeat modelling, and ultrasound imaging and therapy.

本文研究了由勒让德多项式的罗德里格形式导出的自定域光模在增益辅助原子介质中的传播行为。光脉冲表现出明显的时空变化，在连续波背景上表现出局部强度峰值和强度下降的模式。这些独特的动力学是由泵浦和耦合驱动场相干地操纵的，它们也是由罗德里格形式的勒让德多项式产生的。这些脉冲的最大局部强度可以随着位置、时间和控制场强度的变化而精确地从0.002%调谐到100%。峰值强度的空间位置随衰减率和驱动场参数的变化而变化。由此产生的修改脉冲动力学应用于包括DNA动力学，心跳建模，超声成像和治疗等领域。

引用次数: 0

Corrigendum to “Noise-induced resonant acceleration of a charge in an intermittent magnetic field: An exact solution for ergodic and non-ergodic fluctuations” [Chaos, Solitons & Fractals, volume 203 (2026), 117670] “间歇磁场中电荷的噪声诱导共振加速：遍历和非遍历波动的精确解”的勘误表[混沌，孤子和分形，第203卷（2026），117670]

IF 7.8 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-22 DOI: 10.1016/j.chaos.2026.117962

Gerardo Aquino, Mauro Bologna

引用次数: 0

Modeling chaotic synchronization dynamics using Koopman Physics-Informed Neural Networks 基于Koopman物理信息神经网络的混沌同步动力学建模

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-22 DOI: 10.1016/j.chaos.2026.117944

N.P. Sasikumar, P. Balasubramaniam

Modeling chaotic synchronization from data is challenging because standard approaches such as NeuralODEs and PINNs lose stability, degrade under noise, and provide little insight into the underlying dynamics. This article introduce a Koopman Physics-Informed Neural Network (Koopman-PINN) that combines Koopman operator embeddings with physics-based residual training to learn accurate and interpretable representations of coupled chaotic oscillators. The model yields clean spectral modes, robust phase-space reconstructions, and reliable separation of synchronized and desynchronized behavior. Experiments on coupled Rössler oscillators show that Koopman-PINN maintains stability over long prediction horizons, generalizes to unseen trajectories, and outperforms NeuralODEs and classical PINNs while providing quantitative spectral features unavailable in existing methods. This framework offers a data-efficient and interpretable approach for analyzing nonlinear synchronization dynamics.

从数据中建模混沌同步是具有挑战性的，因为像NeuralODEs和pinn这样的标准方法会失去稳定性，在噪声下会退化，并且无法深入了解潜在的动态。本文介绍了一种库普曼物理信息神经网络（Koopman- pinn），它将库普曼算子嵌入与基于物理的残差训练相结合，以学习耦合混沌振荡的准确和可解释的表示。该模型产生干净的光谱模式，鲁棒的相空间重建，以及可靠的同步和非同步行为分离。在耦合Rössler振子上的实验表明，Koopman-PINN在较长的预测范围内保持稳定性，可以推广到看不见的轨迹，并且在提供现有方法无法提供的定量光谱特征的同时，优于NeuralODEs和经典pinn。该框架为分析非线性同步动力学提供了一种数据高效且可解释的方法。

引用次数: 0

Corrigendum to “Bifurcations and dynamics of nonlinear excitations in twisted-bilayer optical lattices” [Chaos, Solitons and Fractals 195 (2025) 116314] “扭曲双层光学晶格中非线性激励的分岔和动力学”的勘误表[混沌，孤子和分形，195 (2025)116314]

IF 7.8 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-22 DOI: 10.1016/j.chaos.2026.117953

Pingping Fang, Chao Gao, Ji Lin

引用次数: 0

Nonlocal KdV hierarchy reduction and asymptotic solutions in the nonlocal Lakshmanan–Porsezian–Daniel equation 非局部Lakshmanan-Porsezian-Daniel方程的非局部KdV层次约简及渐近解

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-22 DOI: 10.1016/j.chaos.2026.117982

Wentao Li , Zhao Zhang , Xiangyu Yang , Biao Li

The nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with higher-order dispersion and nonlinear effects is investigated. By employing the multiple-scale method, the nonlocal Korteweg–de Vries (KdV) hierarchy, which admits only

PT

-symmetric invariant solutions, has been derived from the reverse space–time nonlocal LPD equation. The one- and two-soliton solutions of the nonlocal KdV equation accurately reproduce the corresponding soliton dynamics of the nonlocal LPD equation, while the nonlocal fifth-order KdV term provides essential higher-order dispersion corrections. The remaining discrepancies arise mainly from differences in the higher-order perturbation terms between the nonlocal LPD and KdV equations, suggesting that the fitting accuracy can be further improved by incorporating additional higher-order corrections.

研究了具有高阶色散和非线性效应的非局部Lakshmanan-Porsezian-Daniel （LPD）方程。利用多尺度方法，导出了只允许pt对称不变量解的逆时空非局域LPD方程的非局域Korteweg-de Vries （KdV）层次。非局部KdV方程的一孤子解和二孤子解精确地再现了非局部LPD方程的相应孤子动力学，而非局部五阶KdV项提供了必要的高阶色散校正。其余的差异主要来自于非局部LPD和KdV方程之间的高阶扰动项的差异，这表明通过加入额外的高阶校正可以进一步提高拟合精度。

引用次数: 0

Spatial-economic feedbacks in a diffusive predator-prey fishery: Harvest viability and Turing bifurcation 扩散性捕食者-猎物渔业中的空间经济反馈：收获活力和图灵分岔

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-22 DOI: 10.1016/j.chaos.2026.117947

Xuebing Zhang , Wenjun Liu , Ali Moussaoui , Pierre Auger

The interaction between endogenous market forces and spatial population dynamics is an important source of complex behavior in harvested ecosystems. This paper proposes a reaction–diffusion bioeconomic model that incorporates adaptive harvesting effort and price responsiveness. Mathematical analysis and numerical simulations show that the coupling between economic feedback and diffusion can induce Turing instability, transforming spatially uniform populations into stable heterogeneous patterns. Such patterns reflect a nontrivial redistribution of biomass driven by market-regulated harvesting and dispersal. Moreover, the system may exhibit bistability, allowing a high-biomass equilibrium and a low-biomass equilibrium to coexist over a range of parameters. Owing to the endogenous dependence of price on resource abundance, these alternative states can generate markedly different economic returns, and the low-biomass regime may yield higher revenue under scarcity-driven price responses. These findings illustrate how nonlinear feedbacks between market dynamics and spatial ecology can generate rich spatiotemporal structures and multiple long-term outcomes in bioeconomic systems, providing insight into the coupled ecological and economic consequences of adaptive harvesting.

内生市场力量和空间种群动态之间的相互作用是采伐生态系统复杂行为的重要来源。本文提出了一个反应-扩散生物经济模型，该模型结合了适应性收获努力和价格响应性。数学分析和数值模拟表明，经济反馈和扩散之间的耦合会引起图灵不稳定性，使空间均匀的种群转变为稳定的异质格局。这种模式反映了由市场调控的收获和分散所驱动的生物质再分配。此外，该系统可能表现出双稳定性，允许高生物量平衡和低生物量平衡在一定参数范围内共存。由于价格对资源丰度的内生依赖，这些替代状态可以产生显著不同的经济回报，在稀缺性驱动的价格响应下，低生物量制度可能产生更高的收入。这些发现说明了市场动态和空间生态之间的非线性反馈如何在生物经济系统中产生丰富的时空结构和多种长期结果，为了解适应性采伐的生态和经济耦合后果提供了见解。

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引用次数: 0

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Chaos Solitons & Fractals

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