Chaos Solitons & Fractals最新文献_第10页

Mechanisms investigation of spiking and chaos in memristive neurons based on locally active memristor models 基于局部有源记忆电阻器模型的记忆神经元尖峰和混沌机制研究

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-27 DOI: 10.1016/j.chaos.2026.117926

Yiqing Li , Yan Liang , Zhenzhou Lu , Fang Yuan , Yujiao Dong , Guangyi Wang , Ahmet Samil Demirkol , Ronald Tetzlaff , Alon Ascoli

Locally active memristors (LAMs) exhibit small-signal amplification capability, making them suitable for use in artificial neuron circuits. Spiking oscillations and chaotic dynamics are two representative neuromorphic behaviors that have shown promise in spiking neural networks and combinatorial optimization applications. Spiking oscillations are identified using a newly proposed criterion based on the signal's rate of change and energy consumption characteristics, while chaotic dynamics are verified through Lyapunov exponent analysis. To investigate their underlying mechanisms, simple second-order and third-order memristive neuron circuits are employed to generate periodic spiking and chaotic neuromorphic behaviors, respectively. Based on nonlinear circuit and dynamics theory as well as numerical analysis methods, the impacts of model expressions and parameters on spiking oscillation and chaotic behavior are quantitatively investigated. The analysis results indicate that the emergence of these two neuromorphic behaviors mainly depends on the expression of memristance/memductance functions in the LAMs polynomial model and the characteristics of the instantaneous resistance and the differential resistance of the LAMs at the operating point. Hardware implementations of both circuits further validate the theoretical and simulation results. This insight provides valuable guidance for designing and optimizing neuron models and neuromorphic computing devices, advancing the realization of circuit-oriented neuromorphic computing systems.

局部有源忆阻器（lam）具有小信号放大能力，适用于人工神经元电路。尖峰振荡和混沌动力学是在尖峰神经网络和组合优化应用中具有代表性的两种神经形态行为。利用基于信号变化率和能量消耗特性的新准则识别尖峰振荡，并通过李雅普诺夫指数分析验证混沌动力学。为了研究其潜在的机制，我们使用简单的二阶和三阶记忆神经元回路分别产生周期尖峰和混沌神经形态行为。基于非线性电路和动力学理论以及数值分析方法，定量研究了模型表达式和参数对脉冲振荡和混沌行为的影响。分析结果表明，这两种神经形态行为的产生主要取决于LAMs多项式模型中memresistance /memductance函数的表达以及LAMs在工作点的瞬时电阻和微分电阻的特性。两种电路的硬件实现进一步验证了理论和仿真结果。这一见解为设计和优化神经元模型和神经形态计算设备，推进面向电路的神经形态计算系统的实现提供了有价值的指导。

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引用次数: 0

Spiral wave control via dynamic learning optimized photon scanning approach 基于动态学习的螺旋波控制优化光子扫描方法

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-27 DOI: 10.1016/j.chaos.2026.117977

Qianming Ding , Yipeng Hu , Tianyu Li , Ying Xie , Ya Jia

Optogenetics holds immense potential for modulating arrhythmias, yet its application is constrained by the difficulty in localizing the core of spiral waves, with inadequate optical stimulation often inducing wave breakup. The photon-scanning approach eliminates spiral waves by scanning a light stripe, anchoring the spiral wave core, and guiding the core to drift toward the medium boundary. This novel approach eliminates spiral waves without the need for accurate core localization and tissue properties, thereby overcoming the limitations of conventional approaches. This paper proposes an approach using dynamic learning to optimize photon scanning (DLOPS) through integrating photon scanning with the dynamic learning of synchronization techniques. The DLOPS approach eliminates spiral waves in various tissues by adjusting the illuminated area and intensity to reduce the number of activated LEDs. Simulation results indicate that compared to the original photon scanning approach, the DLOPS approach can reduce optical energy consumption by 50% to 85%. Additionally, we propose a “sandwich scanning approach” under challenging periodic boundary conditions, which successfully suppresses wave diffusion and reduces the energy consumption to levels comparable with those under no-flow boundary conditions. Finally, the DLOPS approach exhibits high robustness even in complex heterogeneous tissues. The DLOPS approach proposed in this paper could provide new insights for future research into arrhythmia treatment, thereby offering a novel low-energy and high-efficiency solution.

光遗传学在调节心律失常方面具有巨大的潜力，但其应用受到螺旋波核心定位困难的限制，光刺激不足往往会导致波破裂。光子扫描方法通过扫描光条，锚定螺旋波核心，并引导核心向介质边界漂移来消除螺旋波。这种新方法消除了螺旋波，而不需要精确的核心定位和组织特性，从而克服了传统方法的局限性。本文提出了一种将光子扫描与同步技术的动态学习相结合，利用动态学习优化光子扫描的方法。DLOPS方法通过调整照明面积和强度来减少激活led的数量，从而消除各种组织中的螺旋波。仿真结果表明，与原有的光子扫描方法相比，DLOPS方法可降低50% ~ 85%的光能消耗。此外，我们提出了一种具有挑战性的周期性边界条件下的“三明治扫描方法”，该方法成功地抑制了波的扩散，并将能量消耗降低到与无流边界条件下相当的水平。最后，DLOPS方法即使在复杂的异质组织中也表现出高稳健性。本文提出的DLOPS方法可以为未来心律失常治疗的研究提供新的见解，从而提供一种新的低能量、高效率的解决方案。

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引用次数: 0

Pursuit-evasion dynamics for multi-USV with heading angle limits and random noises 考虑航向角限制和随机噪声的多无人潜航器追避动力学

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-27 DOI: 10.1016/j.chaos.2026.117970

Meng Su , Wei Xu

Unmanned Surface Vehicles (USVs) have significantly advanced marine technology, offering substantial potential for various applications. This study introduces an innovative random pursuit-evasion framework for USVs, addressing critical gaps by simultaneously incorporating heading angle constraints and environmental noise. By integrating heading angle limits with Gaussian noise to model environmental uncertainties, we establish a robust analytical foundation for examining pursuit-evasion dynamics across varying group sizes. This framework is based on distinct evasion strategies, including Weighted Collective Avoidance and Nearest-Pursuer Avoidance. Our primary metric, mean capture time (CT), is used to evaluate scenarios with varying numbers of pursuers and a single evader. Through numerical simulations and theoretical analyses, we explore how noise intensities and heading limitations jointly affect CTs and evasion effectiveness. Our findings reveal that both environmental disturbances and kinematic constraints significantly impact the dynamics of pursuit-evasion interactions. This research advances the theoretical understanding of random pursuit-evasion dynamics and provides potential applications for enhancing the operational capabilities of USVs in complex and uncertain maritime environments.

无人水面车辆（usv）具有非常先进的海洋技术，为各种应用提供了巨大的潜力。该研究为usv引入了一种创新的随机追踪-逃避框架，通过同时考虑航向角约束和环境噪声来解决关键间隙。通过将航向角限制与高斯噪声相结合来模拟环境不确定性，我们建立了强大的分析基础，用于研究不同群体规模下的追捕-逃避动力学。该框架基于不同的规避策略，包括加权集体规避和最近追踪者规避。我们的主要度量是平均捕获时间（CT），用于评估具有不同数量的追踪者和单个逃避者的情况。通过数值模拟和理论分析，我们探讨了噪声强度和航向限制如何共同影响ct和规避效率。我们的研究结果表明，环境干扰和运动学约束都显著影响追逐-逃避相互作用的动力学。该研究为提高无人潜航器在复杂和不确定海洋环境中的作战能力提供了潜在的应用前景。

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引用次数: 0

Geometric and probabilistic structure of the uniform distribution on the sphere S2 球面s2上均匀分布的几何和概率结构

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-27 DOI: 10.1016/j.chaos.2025.117771

Pavjeet Singh , S.K. Katiyar , Pooja , Lakshmi Roychowdhury

This paper presents a self-contained exposition of the geometric and probabilistic structure of the uniform distribution on the unit sphere

S^{2} \subset R^{3}

. Relying only on spherical coordinates, symmetry principles and basic calculus, we derive fundamental properties of the uniform measure including the distributions of latitude, geodesic angles, spherical distances, Euclidean distances, spherical caps and dot products. The paper further develops explicit formulas for expectations of rotationally symmetric functions and provides closed-form expressions for mean geodesic quantities that arise naturally in geometric probability and quantization theory. In addition, we explain how rotational invariance simplifies spherical integration and leads to transparent interpretations of one-mean and multi-mean geodesic quantization on

S^{2}

. The presentation is designed to be accessible to students and researchers seeking an elementary yet rigorous introduction to spherical probability laying a foundation for further study in geometric analysis, directional statistics, and quantization on curved surfaces.

本文给出了单位球S2∧R3上均匀分布的几何结构和概率结构的完备说明。仅依靠球坐标、对称原理和基本微积分，我们推导出了均匀测度的基本性质，包括纬度分布、测地线角、球面距离、欧氏距离、球帽和点积。本文进一步发展了旋转对称函数期望的显式公式，并提供了几何概率论和量子化理论中自然出现的平均测地线量的封闭表达式。此外，我们解释了旋转不变性如何简化球面积分，并导致S2上的单均值和多均值测地线量化的透明解释。该报告旨在为寻求球面概率的基本而严格的介绍的学生和研究人员提供便利，为进一步研究几何分析，方向统计和曲面量化奠定基础。

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引用次数: 0

Generation of period doubled solitons from a mode-locked fluoride fiber laser 锁模氟化物光纤激光器产生双倍周期孤子

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-27 DOI: 10.1016/j.chaos.2026.117923

Hang Ren , Ying Yang , Yu Jiang , He Cao , Jiachen Wang , Fanlong Dong , Geguo Du , Junle Qu , Xueming Liu , Tengfei Wu , Shuangchen Ruan , Chunyu Guo

Period doubling bifurcation (PDB), a universal phenomenon in nonlinear systems, provides a unique perspective for understanding the properties of nonlinear systems, possessing potential important applications. Although it has been intensively investigated in the near-infrared (NIR) spectral region, there are no relevant reports in the mid-infrared (MIR) spectral region. Here, by combined use of numerical analysis and experimental demonstration, the phenomenon of PDB from a fluoride fiber oscillator mode-locked by the nonlinear polarization evolution (NPE) technique is reported for the first time, to the best of our knowledge. In the numerical simulations, the phenomenon of PDB at 2.8 μm is unveiled and analyzed by solving the extended coupled nonlinear Schrödinger equations, in which the pump strength and polarization state are found to play a vital role. A soliton regime with a pulse duration of 309 fs, a repetition rate of 67.16 MHz and an average output power of 63 mW is experimentally achieved, presenting uniform pulse intensity. Based on the simulations, through improving the pump strength, a stable soliton pulse train with the period-doubled state is obtained. This work promotes the development of mid-infrared ultrafast fiber lasers, opening up new opportunities for the MIR optical frequency comb and weak signal detection.

周期加倍分岔（PDB）是非线性系统中的一种普遍现象，为理解非线性系统的性质提供了一个独特的视角，具有潜在的重要应用价值。虽然在近红外（NIR）光谱区域已经有了大量的研究，但在中红外（MIR）光谱区域还没有相关的报道。本文采用数值分析和实验论证相结合的方法，首次报道了非线性极化演化（NPE）技术锁模氟化光纤振荡器的PDB现象。在数值模拟中，通过求解扩展耦合非线性Schrödinger方程，揭示并分析了2.8 μm处的PDB现象，发现泵浦强度和极化状态在其中起着至关重要的作用。实验得到脉冲持续时间为309 fs，重复频率为67.16 MHz，平均输出功率为63 mW，脉冲强度均匀的孤子区。仿真结果表明，通过提高泵浦强度，获得了稳定的倍周期孤子脉冲串。这项工作促进了中红外超快光纤激光器的发展，为MIR光频梳和微弱信号检测开辟了新的机遇。

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引用次数: 0

Numerical study of high-energy dissipative soliton generation in a 2.8μm mid-infrared ultrafast fiber laser 高能耗散孤子产生的数值研究。8 μ m中红外超快光纤激光器

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-27 DOI: 10.1016/j.chaos.2026.117988

Yuhe Dong , Wentao Liang , Xusheng Xiao , Yang Xiao , Wentao He , Shimin Chen , Lihe Yan , Chaoran Wang , Haitao Guo

Mid-infrared mode-locked fiber lasers are highly desirable for advanced applications but face limitations in scaling pulse energy. This work presents a theoretical demonstration of a high-energy laser design that employs an As

_{2}

S

_{3}

fiber for integrated dispersion and nonlinearity management in an Er

^{3 +}

:ZBLAN fiber laser. The exceptional properties of As

_{2}

S

_{3}

fiber, including its large normal dispersion and high nonlinearity, are leveraged for precise cavity control. Through numerical simulations and parameter exploration, a net normal dispersion cavity is engineered to support dissipative soliton operation. The proposed design enables stable dissipative soliton generation at

2.8 μ m

, delivering a calculated pulse energy of 528.49 nJ and a dechirped pulse width of 380.15 fs. Furthermore, our model predicts, for the first time, the existence of a noise-like pulse regime in the mid-infrared spectrum under net normal dispersion conditions. This theoretical study establishes the As

_{2}

S

_{3}

fiber as a versatile component for exploring high-energy ultrafast dynamics and providing insight into the dynamics of high-energy mid-infrared pulses.

中红外锁模光纤激光器在高级应用中是非常理想的，但在缩放脉冲能量方面面临限制。本文从理论上论证了在Er3+:ZBLAN光纤激光器中采用As2S3光纤进行综合色散和非线性管理的高能激光器设计。As2S3光纤的特殊特性，包括其大的正向色散和高非线性，可用于精确的腔控制。通过数值模拟和参数探索，设计了一个支持耗散孤子工作的净正交色散腔。该设计能够在2.8μm处产生稳定的耗散孤子，计算脉冲能量为528.49 nJ，解码脉冲宽度为380.15 fs。此外，我们的模型首次预测了在净正色散条件下中红外光谱中存在类噪声脉冲区。该理论研究确立了As2S3光纤作为探索高能超快动力学和深入了解高能中红外脉冲动力学的通用组件。

{"title":"Numerical study of high-energy dissipative soliton generation in a 2.8μm mid-infrared ultrafast fiber laser","authors":"Yuhe Dong , Wentao Liang , Xusheng Xiao , Yang Xiao , Wentao He , Shimin Chen , Lihe Yan , Chaoran Wang , Haitao Guo","doi":"10.1016/j.chaos.2026.117988","DOIUrl":"10.1016/j.chaos.2026.117988","url":null,"abstract":"<div><div>Mid-infrared mode-locked fiber lasers are highly desirable for advanced applications but face limitations in scaling pulse energy. This work presents a theoretical demonstration of a high-energy laser design that employs an As<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span>S<span><math><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub></math></span> fiber for integrated dispersion and nonlinearity management in an Er<span><math><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></math></span>:ZBLAN fiber laser. The exceptional properties of As<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span>S<span><math><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub></math></span> fiber, including its large normal dispersion and high nonlinearity, are leveraged for precise cavity control. Through numerical simulations and parameter exploration, a net normal dispersion cavity is engineered to support dissipative soliton operation. The proposed design enables stable dissipative soliton generation at <span><math><mrow><mn>2</mn><mo>.</mo><mn>8</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span>, delivering a calculated pulse energy of 528.49 nJ and a dechirped pulse width of 380.15 fs. Furthermore, our model predicts, for the first time, the existence of a noise-like pulse regime in the mid-infrared spectrum under net normal dispersion conditions. This theoretical study establishes the As<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span>S<span><math><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub></math></span> fiber as a versatile component for exploring high-energy ultrafast dynamics and providing insight into the dynamics of high-energy mid-infrared pulses.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117988"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Propagation dynamics and optical manipulation of perfect self-similar Bessel beams in linear and nonlinear regimes 线性和非线性条件下完美自相似贝塞尔光束的传播动力学和光学操纵

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-24 DOI: 10.1016/j.chaos.2026.117939

Nan Wang , Xiaoying Tang , Shunyu Liu , Lu Tian , Yu-Xuan Ren , Yi Liang

Non-diffracting beams are a special type of optical field that can resist diffraction and maintain a constant transverse profile during propagation. Self-similar beams, on the other hand, are a special type of optical field that maintains the shape of the transverse intensity profile but scales in size during propagation. Although they are not the same, perfect self-similar Bessel beams (PSBBs) as an intermediate mode between non-diffracting beams and self-similar beams, maintain a strictly self-similar transverse profile and constant intensity during propagation. Here, we start from the linear propagation dynamics of PSBBs, and the nonlinear self-focusing in a biased photorefractive strontium-barium niobate (SBN) crystal, and demonstrate the optical manipulation of Rayleigh particles with PSBBs. The power flow, trapping force, and torque of PSBBs all decrease with the propagation distance, while the orbital angular momentum (OAM) and corresponding angular momentum density (AMD) remain constant during propagation. In a nonlinear medium, the intensity of the beam shows an alternating multi-foci along the propagation direction, characterized by periodic local enhancement and broadening. The attenuation rate of the trapping force is fast and the propagation stability is much lower than that in the linear case. Our work not only reveals the unique properties of PSBBs but also has significant implications for in-depth understanding of the optical field control in nonlinear media and the construction of advanced photonic devices.

非衍射光束是一种特殊类型的光场，它可以抵抗衍射并在传播过程中保持恒定的横向轮廓。另一方面，自相似光束是一种特殊类型的光场，它保持横向强度轮廓的形状，但在传播过程中尺寸会缩小。完美自相似贝塞尔光束（PSBBs）作为介于非衍射光束和自相似光束之间的中间模式，在传播过程中保持严格自相似的横向轮廓和恒定的强度。本文从PSBBs的线性传播动力学和偏光折变铌酸锶钡（SBN）晶体的非线性自聚焦出发，论证了PSBBs对瑞利粒子的光学操纵。PSBBs的功率流、俘获力和转矩随传播距离的增加而减小，而轨道角动量（OAM）和相应的角动量密度（AMD）在传播过程中保持不变。在非线性介质中，光束的强度沿传播方向呈交变多焦，具有周期性局部增强和展宽的特征。捕获力衰减速度快，传播稳定性远低于线性情况。我们的工作不仅揭示了PSBBs的独特性质，而且对深入理解非线性介质中的光场控制和构建先进的光子器件具有重要意义。

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引用次数: 0

gPC-based robustness analysis of neural systems through probabilistic recurrence metrics 基于gpc的神经系统概率递归鲁棒性分析

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-24 DOI: 10.1016/j.chaos.2026.117949

Uros Sutulovic , Daniele Proverbio , Rami Katz , Giulia Giordano

Neuronal systems often preserve their characteristic functions and signalling patterns, also referred to as regimes, despite parametric uncertainties and variations. For neural models having uncertain parameters with a known probability distribution, probabilistic robustness analysis (PRA) allows us to understand and quantify under which uncertainty conditions a regime is preserved in expectation. We introduce a new computational framework for the efficient and systematic PRA of dynamical systems in neuroscience and we show its efficacy in analysing well-known neural models that exhibit multiple dynamical regimes: the Hindmarsh–Rose model for single neurons and the Jansen–Rit model for cortical columns. Given a model subject to parametric uncertainty, we employ generalised polynomial chaos to derive mean neural activity signals, which are then used to assess the amount of parametric uncertainty that the system can withstand while preserving the current regime, thereby quantifying the regime’s robustness to such uncertainty. To assess persistence of regimes, we propose new metrics, which we apply to recurrence plots obtained from the mean neural activity signals. The overall result is a novel, general computational methodology that combines recurrence plot analysis and systematic persistence analysis to assess how much the uncertain model parameters can vary, with respect to their nominal value, while preserving the nominal regimes in expectation. We summarise the PRA results through probabilistic regime preservation (PRP) plots, which capture the effect of parametric uncertainties on the robustness of dynamical regimes in the considered models.

尽管参数不确定和变化，神经系统通常保持其特征功能和信号模式，也称为体制。对于具有已知概率分布的不确定参数的神经模型，概率鲁棒性分析（PRA）使我们能够理解和量化在哪些不确定性条件下，一个状态保持在期望中。我们为神经科学中动态系统的高效和系统PRA引入了一个新的计算框架，并展示了它在分析具有多种动态机制的知名神经模型方面的有效性：单个神经元的Hindmarsh-Rose模型和皮质柱的Jansen-Rit模型。给定一个受参数不确定性影响的模型，我们采用广义多项式混沌来推导平均神经活动信号，然后使用这些信号来评估系统在保持当前状态的同时可以承受的参数不确定性的数量，从而量化该状态对这种不确定性的鲁棒性。为了评估制度的持久性，我们提出了新的指标，我们将其应用于从平均神经活动信号获得的递归图。总体结果是一种新颖的、通用的计算方法，它结合了递归图分析和系统持久性分析，以评估不确定模型参数相对于其名义值可以变化多少，同时保留期望中的名义制度。我们通过概率状态保存（PRP）图总结了PRA结果，PRP图捕获了参数不确定性对所考虑模型中动态状态鲁棒性的影响。

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引用次数: 0

The dynamics of higher-order contagion on structurally diverse networks 结构多样化网络上的高阶传染动力学

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-24 DOI: 10.1016/j.chaos.2026.117950

Yi Wang , Ying Liu , Shuguang Guan , Yi-Cheng Zhang , Ming Tang

Modern individuals typically participate in multiple distinct social groups, characterizing the structural diversity of their social environment. Empirical observations suggest that individuals are more likely to adopt new ideas when these ideas are validated by multiple distinct groups. Our work shifts the focus from traditional, individual-based higher-order interactions to a novel group-based mechanism, which is determined by the structure of the entire group surrounding a node. We define the structural diversity coefficient based on the number of connected components in the node’s neighborhood, and propose a novel social contagion model that incorporates higher-order effect based on structural diversity. We develop both homogeneous mean-field method and dynamic message passing approach to analyze key dynamical properties and extensive numerical simulations validate the accuracy of the theoretical analyses. The results demonstrate that the introduction of group-based higher-order effect converts the system’s phase transition from continuous to discontinuous. Strengthening higher-order effect leaves the forward threshold unchanged while lowering the backward threshold. Moreover, when only higher-order effect is present, the system exhibits bistability and first-order transition with respect to the higher-order interaction strength, whereas the system exhibits no forward threshold. Our work generalizes the concept of higher-order networks to propose a unified framework for understanding group-based higher-order structures and their associated dynamics.

现代个体通常参与多个不同的社会群体，这体现了其社会环境的结构多样性。经验观察表明，当新想法得到多个不同群体的验证时，个人更有可能接受这些新想法。我们的工作将焦点从传统的、基于个体的高阶交互转移到一种新的基于群体的机制，这是由节点周围的整个群体的结构决定的。我们基于节点的邻域连接组件数定义了结构多样性系数，并提出了一种基于结构多样性的高阶效应社会传染模型。采用齐次平均场法和动态消息传递法分析了系统的关键动力学特性，并进行了大量的数值模拟，验证了理论分析的准确性。结果表明，基于群的高阶效应的引入使系统的相变由连续转变为不连续。增强高阶效应后，前向阈值不变，后向阈值降低。此外，当仅存在高阶效应时，系统相对于高阶相互作用强度表现出双稳定性和一阶跃迁，而系统不表现出前向阈值。我们的工作概括了高阶网络的概念，提出了一个统一的框架来理解基于群体的高阶结构及其相关动力学。

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引用次数: 0

Soliton structures, modulational instability, and chaotic dynamics of the coupled Schrödinger–Boussinesq equation 孤子结构，调制不稳定性，以及耦合Schrödinger-Boussinesq方程的混沌动力学

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-24 DOI: 10.1016/j.chaos.2026.117969

Ahmed H. Arnous , Kamyar Hosseini , Muhammad Amin S. Murad , Sachin Kumar

We investigate the coupled Schrödinger–Boussinesq (SB) system, a nonlinear model describing resonant interactions between short- and long-wave components in optics, plasma physics, and fluid mechanics. Using a traveling-wave reduction, we transform the governing PDEs into a canonical nonlinear ODE and derive a broad family of exact solutions, including solitary and singular solitons, finite-background localized states, and Jacobi elliptic periodic waves. We analyze the modulational instability of continuous-wave states, identifying parameter regimes where uniform wave trains destabilize into localized excitations and elucidating the interplay between dispersion, coupling, and nonlinearity. Recasting the reduced dynamics in phase space, we classify equilibria, phase portraits, and connecting orbits, thereby characterizing the conditions for solitary and periodic patterns. With weak external periodic forcing, we apply the Melnikov method to derive explicit thresholds for homoclinic orbit splitting and rigorously predict the onset of chaos. Together, these results establish a unified analytical framework connecting soliton formation, modulational instability, and chaotic dynamics in the SB system, thereby advancing the broader understanding of nonlinear wave phenomena in multiscale physical media.

我们研究了耦合Schrödinger-Boussinesq （SB）系统，这是光学、等离子体物理和流体力学中描述短波和长波分量之间共振相互作用的非线性模型。利用行波约简，我们将控制偏微分方程转化为正则非线性偏微分方程，并推导出一系列精确解，包括孤孤子和奇异孤子、有限背景局域态和Jacobi椭圆周期波。我们分析了连续波状态的调制不稳定性，确定了均匀波序列不稳定为局部激励的参数制度，并阐明了色散，耦合和非线性之间的相互作用。在相空间中重铸简化动力学，我们对平衡、相肖像和连接轨道进行了分类，从而表征了孤立模式和周期模式的条件。在弱周期外强迫条件下，应用Melnikov方法导出了同斜轨道分裂的显式阈值，并对混沌的发生进行了严格的预测。总之，这些结果建立了一个统一的分析框架，将SB系统中的孤子形成、调制不稳定性和混沌动力学联系起来，从而促进了对多尺度物理介质中非线性波现象的更广泛理解。

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引用次数: 0