Chaos Solitons & Fractals最新文献

英文中文

A non-singleton type-3 neuro-fuzzy fixed-time synchronizing method 一种非梭子型-3 神经模糊定时同步法

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-28 DOI: 10.1016/j.chaos.2024.115671

Hamid Taghavifar , Ardashir Mohammadzadeh , Chunwei Zhang

This paper presents a synchronizing approach to chaotic systems with unknown nonlinear dynamics using a Gaussian non-singleton type-3 (NT3) fuzzy logic system (T3-FLS). The proposed method effectively addresses the challenges of parameter uncertainties and external disturbances by utilizing higher-order fuzzy approximations, thereby enhancing robustness and adaptability. By incorporating a projection operator, the control scenario ensures stability. The design includes a fixed-time adaptive synchronization technique that guarantees convergence in a predetermined time frame, independent of the initial values. The presented theoretical analysis proves the superiority of the designed synchronization approach, while simulations demonstrate significant improvements in synchronization performance and resilience against uncertainties. Specifically, the proposed method achieves root mean square errors of 0.1990 and 0.2754 for the tracking errors, representing improvements over 30% compared to the other benchmarking methods. These outcomes demonstrate the robustness of our proposed controller in handling chaotic systems under various operating conditions.

本文提出了一种利用高斯非鞘锥型-3（NT3）模糊逻辑系统（T3-FLS）对具有未知非线性动力学的混沌系统进行同步的方法。所提出的方法通过利用高阶模糊近似，有效地解决了参数不确定性和外部干扰的难题，从而增强了鲁棒性和适应性。通过加入投影算子，控制方案确保了稳定性。该设计包括一种固定时间自适应同步技术，可确保在预定时间框架内收敛，与初始值无关。所提出的理论分析证明了所设计的同步方法的优越性，而模拟则证明了同步性能和对不确定性的适应能力的显著提高。具体来说，与其他基准方法相比，拟议方法的跟踪误差均方根误差分别为 0.1990 和 0.2754，改进幅度超过 30%。这些结果证明了我们提出的控制器在各种运行条件下处理混沌系统的鲁棒性。

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引用次数: 0

Adaptive practical prescribed-time control for uncertain nonlinear systems with time-varying parameters 具有时变参数的不确定非线性系统的自适应实用规定时间控制

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-28 DOI: 10.1016/j.chaos.2024.115677

Tianping Zhang , Wei Zhang

In this paper, adaptive practical prescribed-time (PPT) control is proposed for a class of uncertain nonlinear systems with time-varying parameters and unmodeled dynamics. By constructing a novel time-varying scaling function and utilizing nonlinear mapping, the PPT control is successfully resolved. The dynamical uncertainties resulting from unmodeled dynamics are estimated by employing an auxiliary available signal, and the unknown continuous terms are handled by the aid of radial basis function neural networks (RBFNNs). A novel adaptive control method is developed by introducing the compensating signals and dynamic surface control as well as practical prescribed-time control. All the signals involved are proved to be semi-globally uniformly ultimately bounded, and the tracking error could enter the pre-specified convergence region within a pre-specified time. The robotic manipulator system is used to demonstrate the effectiveness of the proposed control approach.

本文针对一类具有时变参数和未建模动态的不确定非线性系统，提出了自适应实用规定时间（PPT）控制。通过构建新颖的时变缩放函数和利用非线性映射，PPT 控制得以成功解决。通过使用辅助可用信号来估计未建模动态所产生的动态不确定性，并借助径向基函数神经网络（RBFNN）来处理未知连续项。通过引入补偿信号和动态表面控制以及实用的规定时间控制，开发了一种新型自适应控制方法。所有涉及的信号都被证明是半全局均匀终极约束的，并且跟踪误差可以在预先指定的时间内进入预先指定的收敛区域。机器人机械手系统被用来证明所提出的控制方法的有效性。

引用次数: 0

Fostering cooperative evolution through probabilistic punishment and environmental feedback in public goods game 在公共产品博弈中通过概率惩罚和环境反馈促进合作进化

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-28 DOI: 10.1016/j.chaos.2024.115693

Jiaqi Liu, Qianwei Zhang, Rui Tang

Punishing selfish individuals is regarded as an effective method to maintain social cooperation. In reality, the corresponding punishment probability should vary with different game environments. However, most current research treats this probability as a constant or exogenously given. In this paper, based on the public goods game, we design an environmental feedback mechanism and establish a feedback evolutionary game model. The model assumes that the probability of punishing defectors will change with the proportion of cooperators, ultimately influencing individual decision-making. Through theoretical analysis and numerical simulations, we obtain three stable states of the system under different parameter conditions: a state of complete defection with low punishment probability, a state of complete cooperation with high punishment probability, and a bistable state. Our research results indicate that the environmental feedback mechanism plays a crucial role in promoting long-term social stability and sustainable development.

惩罚自私的个体被认为是维持社会合作的有效方法。实际上，相应的惩罚概率应随不同的博弈环境而变化。然而，目前大多数研究都将这种概率视为常数或外生给定。本文以公共物品博弈为基础，设计了一种环境反馈机制，并建立了一个反馈演化博弈模型。该模型假设惩罚叛逃者的概率会随着合作者比例的变化而变化，最终影响个体决策。通过理论分析和数值模拟，我们得到了系统在不同参数条件下的三种稳定状态：低惩罚概率的完全叛逃状态、高惩罚概率的完全合作状态和双稳态。我们的研究结果表明，环境反馈机制在促进社会长期稳定和可持续发展方面发挥着至关重要的作用。

引用次数: 0

Design of key term separated identification model for fractional input nonlinear output error systems: Auxiliary model based Runge Kutta optimization algorithm 设计分数输入非线性输出误差系统的关键项分离识别模型基于辅助模型的 Runge Kutta 优化算法

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-28 DOI: 10.1016/j.chaos.2024.115696

Muhammad Aown Ali , Naveed Ishtiaq Chaudhary , Taimoor Ali Khan , Wei-Lung Mao , Chien-Chou Lin , Muhammad Asif Zahoor Raja

Fractional calculus generalizes the conventional calculus to real order and become a popular tool for efficient modeling of complex engineering problems by providing better insight to the system through involving historical information. In this study, fractional calculus concepts are incorporated into input nonlinear output error (INOE) system and is generalized to fractional INOE (FINOE) model through Grunwald-Letnikov differential operator. The key-term-separation based identification model is presented to estimate the parameters of FINOE system that avoids the burden of identifying extra parameters due to cross product terms. The parameter estimation of systems modeled by Hammerstein output error structure is a challenging task, especially with incorporation of fractional concepts. An auxiliary model based Runge Kutta (RUN) optimization methodology is proposed for viable estimation of FINOE parameters by using the estimate for unmeasurable terms of information vector. The mean-square-error based fitness function is developed that minimizes the difference between the actual and estimated responses of the FINOE system. The efficacy of the proposed scheme is investigated in terms of convergence speed, computational cost, resilience, stability and correctness in approximation of accurate weights of the FINOE system for multiple noise variations. The superiority of the RUN for FINOE is endorsed via comparative analysis with 8 states of the arts in noisy environments.

分数微积分将传统微积分推广到实阶，并通过历史信息为系统提供更好的洞察力，成为复杂工程问题高效建模的常用工具。在本研究中，分数微积分概念被纳入输入非线性输出误差（INOE）系统，并通过格伦沃尔德-列特尼科夫微分算子被推广到分数 INOE（FINOE）模型。本文提出了基于关键项分离的辨识模型，用于估算 FINOE 系统的参数，从而避免了由于交叉积项造成的额外参数辨识负担。以哈默斯坦输出误差结构建模的系统的参数估计是一项具有挑战性的任务，尤其是在包含分数概念的情况下。本文提出了一种基于辅助模型的 Runge Kutta (RUN) 优化方法，利用对信息矢量中不可测量项的估计，对 FINOE 参数进行可行的估计。开发了基于均方误差的拟合函数，使 FINOE 系统的实际响应与估计响应之间的差异最小化。从收敛速度、计算成本、恢复能力、稳定性和在多种噪声变化情况下近似 FINOE 系统精确权重的正确性等方面，对所提方案的功效进行了研究。通过与噪声环境中 8 种艺术状态的比较分析，证明了 RUN 在 FINOE 中的优越性。

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引用次数: 0

Self-triggered consensus resilient control for multi-agent systems against sensor deception attacks based on a single parameter learning method 基于单一参数学习方法的多机器人系统自触发共识弹性控制，对抗传感器欺骗攻击

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-25 DOI: 10.1016/j.chaos.2024.115649

Junwen Xiao, Yongchao Liu

This paper presents a self-triggered consensus resilient control method for nonlinear multi-agent systems (MASs) under sensor deception attacks. A single parameter learning method is integrated into backstepping technique to simplify design procedure. The neural networks are utilized to compensate for unknown dynamics of the MASs. Moreover, a self-triggered mechanism is presented for MASs to refrain from continuously monitoring triggering conditions and conserve communication resources. The designed controller can resist sensor deception attacks and guarantee that all signals of the MASs are uniformly bounded. An expository simulation example reveals the virtue of the presented method.

本文针对传感器欺骗攻击下的非线性多代理系统（MAS）提出了一种自触发共识弹性控制方法。为了简化设计程序，本文将单参数学习方法集成到反步进技术中。利用神经网络对 MAS 的未知动态进行补偿。此外，还为 MAS 提出了一种自触发机制，以避免持续监控触发条件并节省通信资源。所设计的控制器可以抵御传感器欺骗攻击，并保证 MAS 的所有信号都是均匀有界的。一个说明性仿真实例揭示了所提出方法的优点。

引用次数: 0

Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model 非线性动态振动行为模型的积分谐振负导数反馈抑制控制策略

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-25 DOI: 10.1016/j.chaos.2024.115686

H.S. Bauomy , A.T. EL-Sayed , F.T. El-Bahrawy

One of the major problems in robotics research has been developing an actuator system for extremely dynamic-legged robots. High torque density and the capacity to control dynamic physical interactions are two design requirements for high-speed locomotion that are challenging for conventional actuators used in manufacturing applications to meet. To address this system and apply the desired control to reach the best stability position, the robot's foot was simulated with the Van der Pol equations, applied the required control, and studied that application. This work describes the actions of a new novel control mechanism known as the Integral Resonant Negative Derivative Feedback (IRNDF) controller, which reduces the vibration response of a double Van der Pol oscillator subjected to external excitations. This unique controller combines integral resonant control (IRC) and negative derivative feedback (NDF) controllers to provide a new controller effect for double Van der Pol oscillators. The multiple scale perturbation technique (MSPT) has been applied to solve the controlled system analytically. The MATLAB and MAPLE programs have been used to complete and clarify all of the numerical talks. The frequency response curves have been used to study the impact that altering the parameter values had on the amplitude. The controlled system vibration amplitude is governed by frequency-response equations (FREs), which have been constructed. In the vibration system, the IRC, NDF, and IRNDF controllers were compared to see which one was the best. Numerical results show that the unique IRNDF controller is the best at reducing oscillations and decreasing amplitude values. The effects of the effective parameters on the controlled system have been identified. The frequency-response equation that was derived has been used to plot the various response curves for the framework that show the stable and unstable zones when the controller is off and on. Lastly, excellent agreement between the derived numerical findings and the analytical ones was observed. Lastly, utilizing time histories and response curves to compare analytical and numerical solutions was fascinating and significant.

机器人研究中的一个主要问题是为极动态的足式机器人开发致动器系统。高扭矩密度和控制动态物理交互的能力是高速运动的两个设计要求，而制造应用中使用的传统致动器很难满足这两个要求。为了解决这一系统问题，并应用所需的控制来达到最佳稳定位置，我们用范德尔波尔方程对机器人的脚进行了模拟，应用了所需的控制，并对该应用进行了研究。这项工作描述了一种称为积分谐振负偏差反馈（IRNDF）控制器的新型控制机制的作用，它可以降低双范德波尔振荡器在外部激励下的振动响应。这种独特的控制器结合了积分谐振控制（IRC）和负导数反馈（NDF）控制器，为双范德波尔振荡器提供了一种新的控制器效应。多尺度扰动技术（MSPT）被用于对控制系统进行分析求解。MATLAB 和 MAPLE 程序用于完成和阐明所有的数值讨论。频率响应曲线用于研究改变参数值对振幅的影响。受控系统的振动振幅受频率响应方程（FRE）控制，该方程已经构建。在振动系统中，对 IRC、NDF 和 IRNDF 控制器进行了比较，以确定哪种控制器最好。数值结果表明，独特的 IRNDF 控制器在减少振荡和降低振幅值方面效果最佳。有效参数对控制系统的影响已经确定。得出的频率响应方程用于绘制框架的各种响应曲线，显示控制器关闭和开启时的稳定区和不稳定区。最后，观察到推导出的数值结果与分析结果非常一致。最后，利用时间历程和响应曲线来比较分析和数值解决方案是非常有意义的。

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引用次数: 0

Data driven cost-sensitive boosted tree for interpretable banking systemic risk prediction 数据驱动的成本敏感提升树，用于可解释的银行系统性风险预测

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-25 DOI: 10.1016/j.chaos.2024.115664

Meng Xia , Zhijie Wang , Wanan Liu

Systemic risk (SR) in the banking sector poses a significant threat to both the financial system and the real economy. Its inherent characteristics of nonlinearity, non-equilibrium, and interconnectedness make it challenging to analyze using conventional statistical methods. In this paper, a cost-sensitive gradient boosting tree algorithm, FLXGBoost, is proposed for predicting SR. FLXGBoost considers the boosted tree, XGBoost as the base framework, boosting trees as the fundamental framework, guaranteeing the robustness of SR prediction. Additionally, to tackle the challenge of extreme data imbalance prevalent in SR prediction tasks, a cost-aware loss function, focal loss, is embedded into the boosted tree to enable FLXGBoost a risk-aware fashion. Moreover, a tree-derived interpretable algorithm SHAP is incorporated into this cost-sensitive solution, making FLXGBoost an accurate and interpretable risk-aware model. Experimental results on a financial risk prediction dataset pertaining to banking SR evince the capacity of FLXGBoost to significantly reduce the misclassification rate of risk banks, thereby mitigating substantial losses attributed to erroneous predictions of risky scenarios. Moreover, compared with classical imbalanced machine learning-based SR prediction approaches, the diverse evaluation metrics of FLXGBoost show that it is a competitive solution for accurate SR prediction. Besides, the explanatory analysis further demonstrates that FLXGBoost is a promising solution to address the issue of biased predictions in imbalanced banking SR in the interpretation perspective.

银行业的系统性风险（SR）对金融体系和实体经济都构成了重大威胁。其固有的非线性、非平衡性和相互关联性等特点使其很难用传统的统计方法进行分析。本文提出了一种成本敏感梯度提升树算法 FLXGBoost，用于预测 SR。FLXGBoost 以提升树 XGBoost 为基础框架，以提升树为基本框架，保证了 SR 预测的鲁棒性。此外，为了应对 SR 预测任务中普遍存在的数据极度不平衡的挑战，在助推树中嵌入了成本感知损失函数--焦点损失，使 FLXGBoost 成为一种风险感知方式。此外，这种成本敏感型解决方案中还包含了一种由树衍生的可解释算法 SHAP，从而使 FLXGBoost 成为一种准确且可解释的风险感知模型。在银行 SR 金融风险预测数据集上的实验结果表明，FLXGBoost 能够显著降低风险银行的误分类率，从而减少因错误预测风险情况而造成的重大损失。此外，与基于不平衡机器学习的传统 SR 预测方法相比，FLXGBoost 的各种评价指标表明，它是一种具有竞争力的准确 SR 预测解决方案。此外，解释性分析进一步表明，从解释角度来看，FLXGBoost 是解决不平衡银行 SR 中偏差预测问题的一种有前途的解决方案。

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引用次数: 0

Dynamic characteristics and conversion process of solitons in a Mamyshev oscillator 马迈雪夫振荡器中孤子的动态特性和转换过程

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-24 DOI: 10.1016/j.chaos.2024.115667

Yuhe Dong, Xingliang Li, Mengmeng Han, Shumin Zhang, Chaoran Wang

The Mamyshev oscillator (MO) can produce not only a single pulse (SP) but also multi-pulses (MPs). However, most of the research focuses on increasing the output pulse energy and reducing the pulse width, and only some studies reveal the characteristics of MPs output. More research is needed on achieving the conversion from MPs to SP by adjusting the oscillator parameters and determining what intermediate states will be experienced in the conversion process. Here, we study the dynamic characteristics of soliton and the conversion process between different output states of ultrafast MO. By adjusting the gain saturation energy and filter interval, we obtain the relationship between the number of MPs outputs and the oscillator parameters and observe the intermediate process from MPs pulsation to SP. The research results reveal the dynamic characteristics of non-equilibrium optical solitons, assisting in optimizing MO design.

马梅雪夫振荡器（MO）不仅能产生单脉冲（SP），还能产生多脉冲（MP）。然而，大多数研究都集中在增加输出脉冲能量和减小脉冲宽度上，只有一些研究揭示了 MPs 输出的特性。在通过调整振荡器参数实现从 MP 到 SP 的转换以及确定转换过程中会出现哪些中间状态方面，还需要进行更多的研究。在此，我们研究了孤子的动态特性以及超快 MO 不同输出状态之间的转换过程。通过调整增益饱和能量和滤波器间隔，我们得到了 MPs 输出数量与振荡器参数之间的关系，并观察了从 MPs 脉动到 SP 的中间过程。研究成果揭示了非平衡光孤子的动态特性，有助于优化 MO 的设计。

引用次数: 0

Study on a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions 研究非线性物理学中的（3+1）维 B 型 Kadomtsev-Petviashvili 方程：多重孤子解、块解和呼吸波解

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115668

Abdul-Majid Wazwaz

In this work, we study an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equations that appear in many nonlinear physics applications. We show that this extended equation retains its complete integrability via Painlevé analysis. We explore multiple soliton solutions by using the Hirota bilinear method. Moreover, we derive lump solutions where two numerical examples are tested. Breather wave solutions were also explored by using a variety of distinct schemes. We also determine other traveling wave solutions, rational solutions, periodic solutions, exponential solutions, ratio of trigonometric or hyperbolic functions, and others.

在这项工作中，我们研究了在许多非线性物理应用中出现的扩展 (3+1)-dimensional B 型 Kadomtsev-Petviashvili (BKP) 方程。我们通过 Painlevé 分析表明，这个扩展方程保持了其完全的可整性。我们利用 Hirota 双线性方法探索了多重孤子解。此外，我们还推导出了块解，并对两个数值实例进行了测试。我们还使用各种不同的方案探索了呼吸波解决方案。我们还确定了其他行波解、有理解、周期解、指数解、三角函数或双曲函数的比值等。

引用次数: 0

Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations 基于对称组的域分解，增强物理信息神经网络求解偏微分方程的能力

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-23 DOI: 10.1016/j.chaos.2024.115658

Ye Liu , Jie-Ying Li , Li-Sheng Zhang , Lei-Lei Guo , Zhi-Yong Zhang

Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain, but the lack of efficient tools for dealing with the interfaces between two adjacent sub-domains heavily hinders the training effects, even leads to the discontinuity of the learned solutions. In this paper, we propose a symmetry group based domain decomposition strategy to enhance the PINN for solving the forward and inverse problems of the PDEs possessing a Lie symmetry group. Specifically, for the forward problem, we first deploy the symmetry group to generate the dividing-lines having known solution information which can be adjusted flexibly and are used to divide the whole training domain into a finite number of non-overlapping sub-domains, then utilize the PINN and the symmetry-enhanced PINN methods to learn the solutions in each sub-domain and finally stitch them to the overall solution of PDEs. For the inverse problem, we first utilize the symmetry group acting on the data of the initial and boundary conditions to generate labeled data in the interior domain of PDEs and then find the undetermined parameters as well as the solution by only training the neural networks in a sub-domain. Consequently, the proposed method can predict high-accuracy solutions of PDEs which are failed by the vanilla PINN in the whole domain and the extended PINN in the same sub-domain. Numerical results of the Korteweg–de Vries equation with a translation symmetry and the nonlinear viscous fluid equation with a scaling symmetry show that the accuracies of the learned solutions are improved largely.

物理信息神经网络（PINN）难以准确高效地求解整个域中的偏微分方程（PDE），但由于缺乏有效工具来处理相邻两个子域之间的界面，严重影响了训练效果，甚至导致所学解的不连续性，域分解为解决这一困境提供了有效途径。本文提出了一种基于对称组的域分解策略，以增强 PINN 解决具有 Lie 对称组的 PDE 正演和反演问题的能力。具体来说，对于正向问题，我们首先利用对称组生成具有已知解信息的分割线，这些分割线可以灵活调整，用于将整个训练域划分为有限个不重叠的子域，然后利用 PINN 和对称增强 PINN 方法学习每个子域中的解，最后将其拼接到 PDE 的整体解中。对于逆问题，我们首先利用对称组对初始条件和边界条件数据的作用，在 PDE 的内部域生成标注数据，然后仅在一个子域中训练神经网络，就能找到未确定的参数和解。因此，所提出的方法可以高精度地预测虚PINN在整个域和扩展PINN在同一子域中失效的PDE解。具有平移对称性的 Korteweg-de Vries 方程和具有缩放对称性的非线性粘性流体方程的数值结果表明，学习到的解的精确度有了很大提高。

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