Chaos Solitons & Fractals最新文献

英文中文

Co-evolution mechanism of peer effect and dynamic networks in multi-agent systems from a dual-game perspective 双博弈视角下多智能体系统同伴效应与动态网络的协同进化机制

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-02 DOI: 10.1016/j.chaos.2025.117631

Fengzhen Jiang , Yanfei Yang

This research develops a multi-agent evolutionary game model that integrates dynamic networks, the peer effect strategy update rule, and a dual-game framework including the Prisoner's Dilemma Game (PDG) and the Snowdrift Game (SDG). Unlike previous research that analyzes these elements separately, we systematically examine their synergistic effect on the evolution of cooperation. Through simulations on the Newman–Watts (NW) small-world network and the Barabási–Albert (BA) scale-free network, we reveal a novel cooperation-emergence mechanism: the synergy between network structural adaptation and peer effect substantially accelerates the diffusion of cooperation and stabilizes network evolution. The results reveal that the adjustment of network topology exerts a more significant impact on improving system stability compared with the strategy update, while peer effect provides necessary social reinforcement for cooperative clustering. After stabilization, residual defectors are predominantly isolated nodes, and SDG participants exhibit a higher survival rate. These findings enrich the theoretical understanding of cooperative dynamics in complex systems and offer guidance for promoting cooperation in real-world multi-agent environments.

本研究建立了一个整合动态网络、同伴效应策略更新规则和囚徒困境博弈（PDG）和雪堆博弈（SDG）双重博弈框架的多智能体进化博弈模型。不同于以往的研究分别分析这些因素，我们系统地考察了它们对合作演化的协同效应。通过对Newman-Watts （NW）小世界网络和Barabási-Albert （BA）无标度网络的模拟，揭示了一种新的合作-涌现机制：网络结构适应和同伴效应的协同作用显著加速了合作扩散，稳定了网络演化。结果表明，网络拓扑调整对提高系统稳定性的影响比策略更新更显著，而对等效应为协同聚类提供了必要的社会强化。稳定后，剩余的叛逃者主要是孤立的节点，可持续发展目标参与者表现出更高的存活率。这些发现丰富了复杂系统中合作动力学的理论认识，并为促进现实多智能体环境中的合作提供了指导。

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引用次数: 0

μ-Stability of (η1,η2)-pseudo almost periodic solution for octonion-valued fuzzy BAM cellular neural networks with mixed delays 混合时滞八元数模糊BAM细胞神经网络(η 1, η 2) -伪概周期解的μ -稳定性

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-02 DOI: 10.1016/j.chaos.2025.117665

Manel Amdouni

Complex-valued and quaternion-valued neural networks often struggle with inherently complex, high-dimensional data, such as hyperspectral images, volumetric data, or physical systems with seven degrees of freedom. To tackle these challenges, researchers have looked for a more advanced and expressive model: octonion-valued neural networks. Octonions extend quaternions and are represented as an eight-dimensional number system, providing a rich algebraic structure that enables the modeling and processing of highly multidimensional signals while capturing intricate relationships between components.

In this paper, we propose a class of fuzzy BAM cellular neural networks with mixed delays, where the inputs, outputs, weights, and biases are all octonions. Firstly, we will demonstrate the existence and uniqueness of a

(η_{1}, η_{2})

-pseudo almost periodic solution using the exponential dichotomy of linear equations, related inequalities, new sufficient conditions, and the contraction mapping fixed point theorem. Secondly, we will establish the

μ

-stability of octonion-valued fuzzy BAM cellular neural networks by constructing new Lyapunov functions. Finally, we will provide an example to illustrate the feasibility and effectiveness of our main results. Notably, we will employ the non-decomposition method to obtain the existence, uniqueness, and

μ

-stability of octonion-valued fuzzy BAM cellular neural networks.

复值和四元数值神经网络经常与固有的复杂高维数据作斗争，例如高光谱图像、体积数据或具有七个自由度的物理系统。为了应对这些挑战，研究人员寻找了一种更先进、更有表现力的模型：八元数值神经网络。八元数扩展四元数，并表示为一个八维数字系统，提供了丰富的代数结构，使建模和处理高度多维信号，同时捕获组件之间的复杂关系。在本文中，我们提出了一类具有混合延迟的模糊BAM细胞神经网络，其中输入、输出、权重和偏差都是八元数。首先，我们将利用线性方程的指数二分法、相关不等式、新的充分条件和收缩映射不动点定理证明(η1,η2)-伪概周期解的存在唯一性。其次，我们将通过构造新的Lyapunov函数来建立八元数值模糊BAM细胞神经网络的μ稳定性。最后，我们将提供一个实例来说明我们的主要结果的可行性和有效性。值得注意的是，我们将采用非分解方法来获得八元数值模糊BAM细胞神经网络的存在性、唯一性和μ稳定性。

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引用次数: 0

Corrigendum to “quantum vortices in entanglement: A novel idea for large vortex filaments” [Chaos Soliton. Fract. volume 202, January 2026, 117582] “纠缠中的量子涡旋：大涡旋细丝的新想法”[混沌孤子]的更正。打破。2026年1月，202卷，117582]

IF 7.8 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-02 DOI: 10.1016/j.chaos.2025.117721

S.V. Talalov

引用次数: 0

Impact of generalized growth dynamics and spatial dispersal on maximum sustainable yield in harvested populations 广义生长动态和空间分散对收获种群最大可持续产量的影响

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-02 DOI: 10.1016/j.chaos.2025.117659

Bilel Elbetch , Ali Moussaoui

This study explores the influence of generalized growth rates on the Maximum Sustainable Yield (MSY) in harvested populations. By employing generalized logistic models, such as the Richards and Gompertz formulations, we analytically derive the conditions under which MSY is attained in single-species systems. The analysis is then extended to multi-patch environments with inter-patch dispersal to examine the impact of migration on total MSY. Our key findings show that the MSY in a connected system is always less than or equal to the sum of the MSYs of isolated patches. Moreover, under biologically realistic assumptions, we demonstrate that increasing migration rates between patches leads to a strictly decreasing total MSY. Numerical simulations support the theoretical results, emphasizing that species-specific growth dynamics and spatial connectivity must be jointly considered for effective resource management. These results reveal a fundamental trade-off between ecological connectivity and harvesting potential in spatially structured populations.

本研究探讨了广义生长率对收获群体最高可持续产量的影响。通过采用广义逻辑模型，如Richards和Gompertz公式，我们解析地推导了单物种系统中获得MSY的条件。然后将分析扩展到具有斑块间分散的多斑块环境中，以检查迁移对总MSY的影响。我们的主要发现表明，连接系统中的MSY总是小于或等于孤立补丁的MSYs之和。此外，在生物学现实的假设下，我们证明了斑块间迁移率的增加导致总MSY的严格减少。数值模拟结果支持理论结果，强调物种特定生长动态和空间连通性必须共同考虑有效的资源管理。这些结果揭示了在空间结构种群中生态连通性和收获潜力之间的基本权衡。

引用次数: 0

The impact of high-order multi-source information verification mechanisms on propagation dynamics in multilayer high-order networks 高阶多源信息验证机制对多层高阶网络传播动态的影响

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-01 DOI: 10.1016/j.chaos.2025.117715

Yihan Liu , Ming Tang , Yinzuo Zhou

In epidemic dynamics, the coupling between information diffusion and disease transmission is profoundly influenced by higher-order interactions. To capture this effect, we propose a higher-order multi-source information confirmation mechanism, which accounts for individuals’ reliance on multiple, mutually reinforcing sources of information when adopting protective behaviors. By employing a Markov chain framework, we derive an analytical description of the coupled dynamics, and validate our theoretical predictions through numerical simulations. Our results reveal that when perceptive nodes strongly attenuate higher-order transmission in the physical layer, the density of perceptive nodes exhibits a nonlinear response to the disease transmission rate—first increasing and then decreasing. Furthermore, higher-order information in the physical layer (layer B) exerts a stronger regulatory effect on disease spreading than that in the information layer (layer A). This cross-layer confirmation of neighbors’ perception and infection states, mediated by higher-order interactions, leads to a lower steady-state infection density in the physical layer and a higher perception density in the information layer compared with a scenario without such multi-source confirmation.

在流行动力学中，信息扩散与疾病传播之间的耦合受到高阶相互作用的深刻影响。为了捕捉这种效应，我们提出了一种高阶多源信息确认机制，该机制解释了个体在采取保护行为时对多个相互增强的信息来源的依赖。采用马尔可夫链框架，推导了耦合动力学的解析描述，并通过数值模拟验证了理论预测。我们的研究结果表明，当感知节点强烈衰减物理层的高阶传播时，感知节点的密度对疾病传播率表现出先增加后降低的非线性响应。此外，物理层（B层）的高阶信息对疾病传播的调节作用强于信息层（a层）。这种由高阶相互作用介导的对邻居感知和感染状态的跨层确认，导致与没有这种多源确认的场景相比，物理层的稳态感染密度较低，信息层的感知密度较高。

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引用次数: 0

Engineering optical quartic solitons embedded on a nonvanishing continuous-wave background in weakly birefringent fibers 工程光学四次孤子嵌入在弱双折射光纤中不消失的连续波背景上

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-01 DOI: 10.1016/j.chaos.2025.117718

Emmanuel Kengne

We demonstrate that the balancing self- and cross-phase modulation, four-wave-mixing, and both quadratic, cubic and quartic dispersive effects induces propagating optical vector quartic solitons embedded on a nonzero continuous wave background in weakly birefringent fiber media governed by two-component coherently coupled nonlinear Schrödinger equations with higher-order dispersions. Parameter domains are delineated in which these optical solitons exist. The classes of found quartic solitons include bright solitons, dark solitons, bright breathers, W-shaped solitons, bright-dark solitons, bright-dark breathers, combined bright-soliton-W-shaped solitons, and combined bright-breather-W-shaped solitons with nonvanishing amplitudes at infinity. Also, fractional-transform solitons are explored for the model under consideration. Regimes for the modulation instability of a continuous-wave signal propagating inside weakly birefringent fiber media are investigated and an analytic expression for the gain spectrum is obtained and shown to be dependent on the three dispersion orders and nonlinear effects. We further show how the continuous wave background impacts the structure of optical vector quartic solitons in weakly birefringent fiber media. We hope our findings may offer new applications in long-distance telecommunication networks involving higher-order dispersion of the fiber.

我们证明了平衡自相位调制和交叉相位调制，四波混频，以及二次、三次和四次色散效应，在具有高阶色散的双分量相干耦合非线性Schrödinger方程控制的弱双折射光纤介质中，可以诱导嵌入在非零连续波背景上的传播光矢量四次孤子。描述了这些光孤子存在的参数域。被发现的四次孤子的种类包括明亮孤子、暗孤子、明亮呼吸者、w形孤子、亮-暗孤子、亮-暗呼吸者、明亮孤子- w形孤子的组合，以及在无穷远处振幅不消失的明亮呼吸者- w形孤子的组合。此外，还对模型的分数变换孤子进行了探讨。研究了连续波信号在弱双折射光纤介质中传输时的调制不稳定性，得到了增益谱的解析表达式，并证明了增益谱依赖于三阶色散和非线性效应。我们进一步展示了连续波背景如何影响弱双折射光纤介质中光矢量四次孤子的结构。我们希望我们的发现可以为涉及光纤高阶色散的长途电信网络提供新的应用。

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引用次数: 0

Assessing discrete time series irreversibility through detailed balance analysis 通过详细的平衡分析评估离散时间序列的不可逆性

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-01 DOI: 10.1016/j.chaos.2025.117717

Massimiliano Zanin

The analysis of the time irreversibility of time series has received increasing attention in the last decade, thanks to its potential for understanding the dynamics of normal and altered complex systems. While many metrics and tests have been proposed, these have mostly been focused on real-valued time series, in detriment of the analysis of symbolic sequences. We here present a simple test to assess the time irreversibility of the latter ones, based on a detailed balance evaluation; able to handle individual sequences or collections thereof; and that can further be conditioned to past symbols to extend the time scale of the evaluation. We test the proposed approach on symbolic sequences extracted from synthetic dynamical systems, written texts, and air transport operations. We further provide an open-source version of the test in a Python package.

时间序列的时间不可逆性分析在过去十年中受到越来越多的关注，这是因为它有可能理解正常和改变的复杂系统的动力学。虽然已经提出了许多度量和测试，但这些大都集中在实值时间序列上，不利于对符号序列的分析。我们在此提出一个简单的测试来评估后一种时间不可逆性，基于详细的平衡评估；能够处理单个序列或其集合；这可以进一步限制过去的符号来延长评估的时间尺度。我们对从综合动力系统、书面文本和航空运输操作中提取的符号序列进行了测试。我们进一步在Python包中提供了该测试的开源版本。

引用次数: 0

Phase transition in heterogeneous traffic streams integrating current optimal flux difference under human-driven and connected autonomous vehicles scenario 人驾驶与网联自动驾驶场景下整合当前最优流量差的异构交通流相变

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-01 DOI: 10.1016/j.chaos.2025.117680

Shuhong Yang , Dongxue Xia , Yuangui Liu , Guanghan Peng

The persistent existence of mixed traffic flows—consisting of human-driven vehicles (HDVs) and connected autonomous vehicles (CAVs)—poses a significant challenge for future transportation systems. A fundamental but understudied dimension of this heterogeneity resides in the different capacities of CAVs and HDVs to estimate and respond to real-time traffic flux. Therefore, we in this study propose the current optimal flux difference effect (COFDE) as an innovative parameter, incorporating it into a new lattice hydrodynamic model designed for mixed traffic flows. Through rigorous theoretical analysis—including the derivation of linear stability criteria and the mKdV equation—the influence of COFDE on traffic phase transitions is clarified. Supplementary numerical simulations, utilizing density profiles, limit cycles, and spectral analysis, further confirm these theoretical predictions. The findings reveal that COFDE markedly improves the stability and smoothness of heterogeneous traffic flow, effectively alleviating density oscillations and facilitating the achievement of equilibrium states. Notably, the COFDE associated with CAVs possesses a stronger ability to enhance vehicle stability compared to that of HDVs; Additionally, higher CAV penetration rates further boost the overall stability of the traffic system. This work highlights the vital role of information estimation in future traffic management, providing essential insights into the dynamics of mixed-vehicle scenarios and laying a theoretical foundation for advanced control strategies in intelligent transportation systems.

混合交通流的持续存在——由人类驾驶车辆（HDVs）和联网自动驾驶车辆（cav）组成——对未来的交通系统构成了重大挑战。这种异质性的一个基本但尚未得到充分研究的方面在于自动驾驶汽车和自动驾驶汽车估计和响应实时交通流量的能力不同。因此，我们在本研究中提出当前最优通量差效应（COFDE）作为创新参数，并将其纳入为混合交通流设计的新晶格水动力模型中。通过严格的理论分析，包括线性稳定性判据和mKdV方程的推导，阐明了COFDE对交通相变的影响。利用密度分布、极限环和光谱分析的辅助数值模拟进一步证实了这些理论预测。研究结果表明，COFDE显著提高了异构交通流的稳定性和平滑性，有效缓解了密度振荡，促进了均衡状态的实现。值得注意的是，与hdv相比，与cav相关的COFDE具有更强的增强车辆稳定性的能力；此外，更高的自动驾驶汽车渗透率进一步提高了交通系统的整体稳定性。这项工作强调了信息估计在未来交通管理中的重要作用，为混合车辆场景的动态提供了重要的见解，并为智能交通系统中的先进控制策略奠定了理论基础。

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引用次数: 0

Event-triggered fuzzy learning control for uncertain robotic manipulators via gradient descent approach 基于梯度下降法的不确定机器人事件触发模糊学习控制

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-01 DOI: 10.1016/j.chaos.2025.117672

Min Ma , Zefeng Lin , Zhihong Zhao , Tong Wang , Shuai Sui

This paper develops an event-triggered fuzzy learning control scheme for robotic manipulators subject to uncertain dynamics and unknown control gains. A novel gradient descent strategy is put forward to balance the trade-off between the event-triggered updating of motor driving signals and tracking performance, by which the control design dependence on prior knowledge from manipulator dynamics is simultaneously alleviated. The constructed gradient descent-based fuzzy learning mechanism improves the approximation accuracy of fuzzy logic systems (FLSs) to uncertain manipulator dynamics. And an error compensating-based command filter design technique is introduced to reduce the computation burden. Lyapunov analysis theory rigorously proves the semi-global uniform ultimate boundedness (SUUB) of the closed-loop system. In the end, a simulation case and some comparison results are illustrated to demonstrate the efficacy of the proposed gradient descent-based event-triggered control scheme.

针对具有不确定动力学和未知控制增益的机械臂，提出了一种事件触发模糊学习控制方案。提出了一种新的梯度下降策略，以平衡事件触发的电机驱动信号更新和跟踪性能之间的权衡，同时减轻了控制设计对机械臂动力学先验知识的依赖。所构建的基于梯度下降的模糊学习机制提高了模糊逻辑系统对不确定机械臂动力学的逼近精度。为了减少计算量，提出了一种基于误差补偿的命令滤波器设计方法。Lyapunov分析理论严密地证明了闭环系统的半全局一致极限有界性。最后，给出了一个仿真实例和一些比较结果，以验证所提出的基于梯度下降的事件触发控制方案的有效性。

引用次数: 0

Dynamics analysis, integrated circuit implementation, and prescribed performance backstepping control of a coupled network of 5-DOF Duffing-type MEMS resonators 五自由度duffing型MEMS谐振器耦合网络的动力学分析、集成电路实现和规定性能反步控制

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-12-01 DOI: 10.1016/j.chaos.2025.117613

Wenliang Qi , Shaohua Luo , Zan Ding , Shuyun Lin , Hassen M. Ouakad

This paper investigates the nonlinear dynamics of a coupled network of 5-DOF (Degree of Freedom) Duffing-type micro-electro-mechanical systems (MEMS) resonators, develops an integrated circuit-based equivalent circuit system, and proposes a prescribed-performance adaptive neural network backstepping controller. Initially, to improve the modal frequency and dynamic range of traditional single or multiple resonators (up to four DOFs), we propose a coupled network consisting of 5 MEMS resonators which mutually couples in a specified layout, and accurately establish the relevant mathematical model. The dynamic analysis reveals how coupling stiffness and excitation amplitude influence the system transitions be-tween periodic and chaotic states. Subsequently, to mitigate risks in the fabrication-stage development of the MEMS chips, a PCB-based platform is constructed to validate the model and define the design boundaries. Furthermore, a prescribed-performance adaptive backstepping control scheme is proposed to simultaneously suppress chaos, guarantee fast preset performance convergence, and achieve high-precision tracking under constraints. In this scheme, an accelerated tracking differentiator not only mitigates the complexity explosion of conventional backstepping but also enhances convergence speed, while an interval type-2 fuzzy neural network (IT2FNN) and an improved cubic prescribed performance function (CPPF) are adopted to approximate unknown nonlinearities and constrain tracking errors within predefined bounds, respectively. Finally, comprehensive simulation results demonstrate the scheme's feasibility, robustness, and superior performance.

研究了五自由度duffing型微机电系统（MEMS）谐振器耦合网络的非线性动力学特性，开发了基于集成电路的等效电路系统，提出了一种规定性能的自适应神经网络反步控制器。首先，为了提高传统单腔或多腔谐振器（最多4个dof）的模态频率和动态范围，我们提出了一个由5个MEMS谐振器组成的耦合网络，这些谐振器在指定的布局中相互耦合，并准确建立了相关的数学模型。动力学分析揭示了耦合刚度和激励幅值如何影响系统在周期和混沌状态之间的转换。随后，为了降低MEMS芯片制造阶段开发的风险，构建了基于pcb的平台来验证模型并定义设计边界。在此基础上，提出了一种规定性能的自适应反演控制方案，在抑制混沌的同时，保证预置性能快速收敛，并在约束条件下实现高精度跟踪。在该方案中，加速跟踪微分器不仅减轻了传统反演的复杂度爆炸，而且提高了收敛速度，同时采用区间2型模糊神经网络（IT2FNN）和改进的三次规定性能函数（CPPF）分别逼近未知非线性和将跟踪误差约束在预定义范围内。最后，综合仿真结果验证了该方案的可行性、鲁棒性和优越的性能。

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