Chaos Solitons & Fractals最新文献

英文中文

Information-theoretic quantification of high-order feature effects in classification problems 分类问题中高阶特征效应的信息论量化

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-07 DOI: 10.1016/j.chaos.2025.117724

Ivan Lazic , Chiara Barà , Marta Iovino , Sebastiano Stramaglia , Karolina Kasas-Lazetic , Nikša Jakovljević , Luca Faes

Understanding the contribution of individual features in predictive models remains a central goal in interpretable machine learning, and while many model-agnostic methods exist to estimate feature importance, they often fall short in capturing high-order interactions and disentangling overlapping contributions. In this work, we present an information-theoretic extension of the High-order interactions for Feature importance (Hi-Fi) method, leveraging Conditional Mutual Information (CMI) estimated via a k-Nearest Neighbor (kNN) approach working on mixed discrete and continuous random variables. Our framework decomposes feature contributions into unique, synergistic, and redundant components, offering a richer, model-free understanding of their predictive roles. We validate the method using synthetic datasets with known Gaussian structures, where ground truth interaction patterns are numerically derived, and further test it on non-Gaussian and real-world gene expression data from TCGA-BRCA. Results indicate that the proposed estimator accurately recovers theoretical and expected findings, providing a potential use case for developing feature selection algorithms or model development based on the interaction analysis.

理解预测模型中单个特征的贡献仍然是可解释机器学习的中心目标，虽然存在许多模型不可知的方法来估计特征的重要性，但它们在捕获高阶交互和解纠缠重叠贡献方面往往不足。在这项工作中，我们提出了特征重要性（Hi-Fi）方法的高阶相互作用的信息理论扩展，利用通过k-最近邻（kNN）方法估计的条件互信息（CMI），用于混合离散和连续随机变量。我们的框架将功能贡献分解为独特的、协同的和冗余的组件，提供了对其预测角色的更丰富的、无模型的理解。我们使用具有已知高斯结构的合成数据集验证了该方法，其中基真相互作用模式是数值推导的，并在TCGA-BRCA的非高斯和真实基因表达数据上进一步测试了该方法。结果表明，所提出的估计器准确地恢复了理论和预期的发现，为基于交互分析开发特征选择算法或模型开发提供了潜在的用例。

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引用次数: 0

The stability of group synchronization in multi-layer networks of coupled oscillators 耦合振荡器多层网络中群同步的稳定性

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-06 DOI: 10.1016/j.chaos.2025.117707

Yiran Li , Lijia Chen , Alexander Grin , Peng Ji

The synchronization of complex networks is a widespread phenomenon in both natural and engineering systems. However, the underlying mechanism of group synchronization in multi-layer networks remains unclear. In this paper, we establish a multi-layer coupled oscillator model to investigate group synchronization. By employing group representation theory, we perform a dimensionality reduction analysis and establish stability criteria. Our analysis reveals that the stability of group synchronization is governed by the relative strength of intra-layer and inter-layer coupling. We demonstrate how stability depends on coupling strength under cooperative, competitive, inter-mixing, intra-mixing inter-layer dynamics, and discover the different influence of inter-layer connectivity in stability. Then we use eigenvalue analysis to validate the proposed approach by comparing system dynamics before and after network reduction, which reserves the essential dynamical features. The model is further extended to large-scale Erdős–Rényi networks to examine the impact of systemic perturbations. We find that small structural disturbation can enhance the stability because of the decrease of the shortest path in networks. Our study enhances the understanding of synchronization in multi-layer networks and provides a theoretical foundation for controlling neural networks and other complex systems.

复杂网络的同步是自然系统和工程系统中普遍存在的现象。然而，在多层网络中，群同步的潜在机制尚不清楚。本文建立了一个多层耦合振荡器模型来研究群同步。利用群表示理论，进行了降维分析，建立了稳定性判据。我们的分析表明，群同步的稳定性是由层内和层间耦合的相对强度决定的。我们论证了在合作、竞争、混合和混合层间动力学下，稳定性取决于耦合强度，并发现了层间连通性对稳定性的不同影响。然后，通过比较网络约简前后的系统动力学特性，利用特征值分析方法验证了该方法的有效性，该方法保留了基本的动力学特征。该模型进一步扩展到大规模Erdős-Rényi网络，以检查系统扰动的影响。我们发现，由于网络中最短路径的减少，较小的结构扰动可以增强网络的稳定性。我们的研究增强了对多层网络同步的理解，为控制神经网络和其他复杂系统提供了理论基础。

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引用次数: 0

Extending Opinion Changing Rate model to world of higher order interactions 将意见变化率模型扩展到高阶交互世界

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-06 DOI: 10.1016/j.chaos.2025.117654

Aarya Jha , Anurag Singh , Ankur Kumar Singhal , Pradumn Kumar Pandey

Kuramoto models have emerged as a versatile and fascinating class of oscillator dynamics models. These models can also be adapted to social contexts, enabling the study of opinion propagation dynamics and synchronization, as exemplified by the Opinion Changing Rate (OCR) model. The original OCR model, however, only accounted for point-to-point interactions between nodes, limiting its ability to capture various real-world phenomena. In the paper, the OCR model is extended to incorporate higher-order interactions, achieved by utilizing simplicial complexes as the underlying mathematical framework. Two scenarios were examined: first, where an individual’s opinion within a complex is influenced by the aggregate opinions of the simplices to which they belong, and second, where the opinion of an

n

-order simplex depends on its adjacent

(n + 1)

- and

(n - 1)

-order simplices. Further, analyze the synchronization within systems defined by proposed approaches, exploring the implications of incorporating the higher-order interactions.

Kuramoto模型已经成为一种多用途和迷人的振荡器动力学模型。这些模型还可以适应社会环境，使研究意见传播动态和同步成为可能，如意见变化率（OCR）模型。然而，最初的OCR模型只考虑节点之间的点对点交互，限制了它捕捉各种现实世界现象的能力。在本文中，将OCR模型扩展到包含高阶相互作用，通过利用简单复形作为底层数学框架来实现。研究了两种情况：首先，复合体内的个人意见受到其所属简单体的总体意见的影响，其次，n阶简单体的意见取决于其相邻的(n+1)-和（n−1）阶简单体。进一步，分析由提议的方法定义的系统内的同步，探索合并高阶交互的含义。

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引用次数: 0

Tunable optomechanically induced transparency and Fano resonances in a hybrid whispering gallery mode-magnon system 在窃窃廊模式-磁振子混合系统中可调谐光机械诱导的透明度和法诺共振

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-06 DOI: 10.1016/j.chaos.2025.117738

Muhib Ullah , Akhtar Munir , Li-Gang Wang

The optomechanically induced transparency (OMIT) phenomenon is the optomechanical analogue of electromagnetically induced transparency that offers unique insights into light–matter interactions. We propose a hybrid setup consisting of a whispering gallery mode (WGM) microresonator and a yttrium iron garnet sphere that are uniquely in physical contact via the phonons of both materials. Utilizing the system parameters of both microspheres, we investigate the tunable single as well as multiple OMIT due to the quantum interference between the fields interacting within the WGM microresonator. By modifying the resonance conditions, the setup also exhibits Fano resonances that result from the asymmetric interference effects and can dramatically enhance system sensitivity and selectivity. To investigate the phase dynamics associated with the OMIT phenomenon and to see how it influences the system’s response to incident light, we analyze the group delay of the output probe field by tuning the detuning parameters of the optical microcavity and magnon modes. The coupling elements associated with photons, phonons, and magnons are essential and influence the quantity and behavior of the OMIT windows. Careful investigation of these phenomena offers new opportunities for manipulating and detecting quantum states, as well as developing adjustable optical filters, tunable light-speed devices, optical switches, and highly precise sensors by enabling meticulous modulation of light transmission and speed.

光力学诱导透明（OMIT）现象是电磁诱导透明的光力学模拟，为光-物质相互作用提供了独特的见解。我们提出了一种混合装置，包括一个窃窃私语廊模式（WGM）微谐振器和一个钇铁石榴石球，它们通过两种材料的声子进行独特的物理接触。利用这两种微球的系统参数，我们研究了由于WGM微谐振腔内相互作用的场之间的量子干涉而产生的可调谐单和多个省略。通过改变共振条件，该装置也表现出由不对称干涉效应引起的法诺共振，可以显著提高系统的灵敏度和选择性。为了研究与忽略现象相关的相位动力学以及它如何影响系统对入射光的响应，我们通过调整光学微腔和磁振子模式的失谐参数来分析输出探头场的群延迟。与光子、声子和磁振子相关的耦合元件是必不可少的，它们影响着省略窗口的数量和行为。对这些现象的仔细研究为操纵和探测量子态提供了新的机会，也为开发可调光学滤光片、可调光速器件、光开关和高精度传感器提供了新的机会，从而可以对光的传输和速度进行细致的调制。

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引用次数: 0

Nonlinear differential equation with non-local coupling for a helical optical waveguide 螺旋光波导非局部耦合非线性微分方程

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-05 DOI: 10.1016/j.chaos.2025.117712

Andrey A. Bocharov

A helical optical waveguide with small values of the transverse size of the waveguide and the helical pitch relative to its radius is considered. There is a Kerr-type nonlinearity in the system. Such a system results in a differential equation with the positive and negative shifts in evolutionary argument. The paper presents solutions to the evolutionary problem for such an equation. The fundamental difficulties in obtaining such solutions in the highly nonlinear case are discussed. Breather solutions are presented for time-localized initial data.

考虑了波导横向尺寸和相对于其半径的螺旋节距较小的螺旋光波导。系统中存在克尔型非线性。这样的一个系统产生了一个微分方程，在进化论证中有正的和负的变化。本文给出了这类方程演化问题的解法。讨论了在高度非线性情况下获得此类解的基本困难。给出了时间局部化初始数据的呼吸解法。

引用次数: 0

Universal nonlinear scaling of quantum tunneling with isotope mass 同位素质量量子隧穿的普遍非线性标度

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-05 DOI: 10.1016/j.chaos.2025.117737

Krishna Kingkar Pathak

Nonlinear scaling laws provide powerful unifying principles across complex systems in physics, chemistry, and biology. Here we identify and formalize a nonlinear quantum scaling law that governs tunneling isotope effects. Using an analytical confinement-inspired wavefunction ansatz and direct numerical solutions of one- and two-dimensional Schrödinger equations, we demonstrate that tunneling splittings universally obey (1)

ln Δ E \propto - \sqrt{μ},

where

μ

is the isotope mass. This exponential suppression upon isotope substitution is robust across potential details, dimensionality, and cooperative multi-proton pathways. Benchmark comparisons with malonaldehyde, the formic acid dimer, and coupled proton transfers confirm the predictive power of this law.

Beyond molecular spectroscopy, the result constitutes a general nonlinear principle of quantum transport, with implications for proton dynamics in clusters, enzymatic catalysis, and nucleic acid stability. The work thus extends the reach of nonlinear scaling concepts — traditionally applied in chaos, solitons, and fractals — into the quantum domain, establishing a universal framework for isotope-dependent tunneling phenomena.

非线性标度定律在物理、化学和生物学的复杂系统中提供了强大的统一原则。在这里，我们确定并形式化了一个非线性量子标度定律，控制隧道同位素效应。利用解析约束波函数ansatz和一维和二维Schrödinger方程的直接数值解，我们证明了隧道分裂普遍服从(1)lnΔE∝−μ，其中μ是同位素质量。这种对同位素取代的指数抑制在潜在的细节、维度和合作的多质子途径上是稳健的。与丙二醛、甲酸二聚体和偶联质子转移的基准比较证实了这一定律的预测能力。在分子光谱之外，结果构成了量子输运的一般非线性原理，对团簇中的质子动力学、酶催化和核酸稳定性具有影响。因此，这项工作将非线性标度概念的范围——传统上应用于混沌、孤子和分形——扩展到量子领域，为同位素依赖的隧道现象建立了一个通用框架。

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引用次数: 0

Congestion transition in a heterogeneous ring road car-following model incorporating visual angle defect and speed limit effects 考虑视角缺陷和限速效应的异质环城道路车辆跟随模型中的拥堵过渡

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-05 DOI: 10.1016/j.chaos.2025.117710

Guanghan Peng , Kunning Wu , Wenjing Jiao , Shuhong Yang , Zhuangsong Wu , Longzhang Xu , Chenchen Lu , Huili Tan , Dongxue Xia

Under ring-road driving conditions, autonomous vehicles (AVs) are more disproportionately affected by sight-distance deficits although applying adaptive cruise control (ACC) than human-driven vehicles (HDVs). This discrepancy accentuates the behavioral heterogeneity between AVs and HDVs. To address this issue, we develop a heterogeneous ring-road car-following model (HRR-CFM) that augments the optimal velocity model (OVM) by explicitly incorporating constrained sight-distance deficits and variable speed-limit effects. We derive the stability criteria of the HRR-CFM using control theory and validate the theoretical results through numerical simulations. Results show that HRR-CFM progressively stabilizes the traffic stream, reduces energy consumption, and markedly enhances network efficiency by increasing the AV penetration rate and introducing speed-limit control. Conversely, as the curve radius increases, sight-distance deficits become more severe, which means that vehicles are deprived of complete roadway information, intensifying traffic pressure, undermining system stability, and consequently raising energy consumption.

在环形道路行驶条件下，自动驾驶汽车（AVs）虽然采用了自适应巡航控制（ACC），但视距缺陷对其的影响比人类驾驶汽车（HDVs）更大。这种差异凸显了自动驾驶汽车和高驾驶汽车之间的行为异质性。为了解决这一问题，我们开发了一个异构环线车辆跟随模型（HRR-CFM），该模型通过明确地纳入受限视距缺陷和可变限速效应来增强最优速度模型（OVM）。利用控制理论推导了HRR-CFM的稳定性判据，并通过数值模拟验证了理论结果。结果表明，HRR-CFM通过提高自动驾驶汽车普及率和引入限速控制，逐步稳定流量流，降低能耗，显著提高网络效率。相反，随着弯道半径的增大，视距缺陷越来越严重，这意味着车辆无法获得完整的道路信息，增加了交通压力，破坏了系统的稳定性，从而提高了能耗。

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引用次数: 0

The impact of adaptive trust reinforcement in a multi-state Public Goods Game 多状态公共物品博弈中自适应信任强化的影响

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-05 DOI: 10.1016/j.chaos.2025.117725

Fatima Zahra Moussa , Khalid Zine-Dine

The Public Goods Game (PGG) is a foundational framework for studying the emergence and sustainability of cooperation among self-interested agents. However, its conventional binary structure – where individuals either contribute their full endowment or nothing – oversimplifies the range of cooperative behaviors observed in real-world settings, where partial contributions are common. In this study, we introduce a multi-state extension of the PGG, denoted

P G G_{M}

, in which agents choose from

M

discrete contribution levels, allowing for a more nuanced representation of cooperative strategies.

To promote and sustain cooperation, we propose an Adaptive Trust Reinforcement Mechanism (ATRM) in which agents adjust their trust toward peers based on observed contribution levels. Specifically, agents who contribute more gain increased trust and consequently attract greater contribution from their neighbors, while low-contributing agents experience a loss of trust, leading to reduced contribution from others. We formally define this mechanism and employ extensive agent-based simulations to analyze both the temporal evolution and the steady-state behavior of cooperation under a range of conditions.

Our results demonstrate that ATRM effectively promotes cooperation, consistently steering the system toward higher average contribution across a wide range of parameter settings. Furthermore, the incorporation of discrete contribution states enriches the strategic landscape, enabling the emergence of complex evolutionary dynamics that are absent in the traditional binary framework. These findings highlight the critical role of graded contribution and adaptive social feedback in order to more accurately capture the dynamics of collective behavior.

公共物品博弈（Public Goods Game， PGG）是研究自利主体间合作的产生和可持续性的基本框架。然而，其传统的二元结构——个人要么贡献全部禀赋，要么不贡献——过度简化了在现实环境中观察到的合作行为的范围，在现实环境中，部分贡献是常见的。在本研究中，我们引入了PGG的多状态扩展，称为PGGM，其中智能体从M个离散贡献水平中进行选择，从而允许更细致入微的合作策略表示。为了促进和维持合作，我们提出了一种自适应信任强化机制（ATRM），在该机制中，代理人根据观察到的贡献水平调整对同伴的信任。具体来说，贡献更多的代理获得了更多的信任，从而从邻居那里吸引了更多的贡献，而低贡献的代理则失去了信任，导致其他代理的贡献减少。我们正式定义了这一机制，并采用广泛的基于智能体的模拟来分析一系列条件下合作的时间演化和稳态行为。我们的研究结果表明，ATRM有效地促进了合作，在广泛的参数设置范围内始终将系统导向更高的平均贡献。此外，离散贡献状态的结合丰富了战略格局，使传统二元框架中缺乏的复杂进化动态得以出现。这些发现强调了分级贡献和适应性社会反馈的关键作用，以便更准确地捕捉集体行为的动态。

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引用次数: 0

Wave packet dynamics in rotating fluids within the Benjamin–Ono–Ostrovsky equation Benjamin-Ono-Ostrovsky方程中旋转流体中的波包动力学

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-05 DOI: 10.1016/j.chaos.2025.117731

Marcelo V. Flamarion , Efim Pelinovsky

We investigate the evolution of algebraic solitons of the Benjamin–Ono (BO) equation and wave packets within the framework of the Benjamin–Ono–Ostrovsky (BOO) equation by combining asymptotic analysis with direct numerical simulations. The BOO model incorporates a low-frequency dispersive term that accounts for the effects of background rotation in a fluid. Through asymptotic expansion, we derive a cubic nonlinear Schrödinger (NLS) equation that governs the evolution of modulated wave trains and compare its predictions with numerical simulations of the full BOO equation. Theoretical and numerical results show good agreement for small-amplitude wave packets. Furthermore, near the boundary separating the modulationally stable and unstable regimes, the wave packets display pronounced broadening accompanied by enhanced amplitude attenuation. Finally, the evolution of BO algebraic solitons within the BOO framework is analyzed, revealing their gradual transformation into modulated wave packets.

本文采用渐近分析和直接数值模拟相结合的方法，研究了Benjamin-Ono （BO）方程的代数孤子和BOO方程框架内的波包的演化。BOO模型包含一个低频色散项，用于解释流体中背景旋转的影响。通过渐近展开，我们推导了一个三次非线性Schrödinger （NLS）方程，该方程控制调制波列的演化，并将其预测与全BOO方程的数值模拟进行了比较。理论和数值结果表明，对小振幅波包具有较好的一致性。此外，在调制稳定和不稳定状态的边界附近，波包显示出明显的展宽，并伴有增强的幅度衰减。最后，分析了BO代数孤子在BOO框架下的演化过程，揭示了它们逐渐转变为调制波包的过程。

引用次数: 0

t-relational generalized iterated function systems T关系广义迭代函数系统

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-04 DOI: 10.1016/j.chaos.2025.117709

Izabella Abraham , Radu Miculescu , Alexandru Mihail

This paper introduces a new wider class of generalized iterated function systems, called

t

-relational generalized iterated function systems. An equivalence relation is used to weaken the contractivity condition on the functions defined on product spaces and the introduction of an additional function

t

allows us to use the classical Hutchinson operator. It turns out that each non-empty and compact subset of the underlying metric space generates a unique attractor for the system. Furthermore, two results pointing out the connections between the attractors and the generating compact sets are provided. Finally, we present two examples that complement our results.

本文介绍了一类新的广义迭代函数系统，称为t关系广义迭代函数系统。利用等价关系弱化了积空间上定义的函数的可缩性条件，并引入了一个附加函数t，使我们可以使用经典的Hutchinson算子。事实证明，底层度量空间的每个非空紧子集都会为系统生成一个唯一的吸引子。进一步给出了两个结果，指出了吸引子与生成紧集之间的联系。最后，我们给出了两个例子来补充我们的结果。

引用次数: 0

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