Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

Pattern formation and spatiotemporal chaos in relativistic degenerate plasmas 相对论性简并等离子体中的模式形成和时空混沌

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-24 DOI: 10.1016/j.cnsns.2026.109768

S. Das Adhikary, A.P. Misra

We numerically study the nonlinear interactions of high-frequency circularly polarized electromagnetic (EM) waves and low-frequency electron-acoustic (EA) density perturbations driven by the EM wave ponderomotive force in relativistic plasmas (moderate, strong, and ultra-relativistic) with two groups of electrons–the population of relativistic degenerate dense electrons (bulk plasma) and the sparse relativistic nondegenerate (classical) electrons, and immobile singly charged positive ions. By pattern selection, we show that many solitary patterns can be generated and drenched through modulational instability of EM waves at different spatial length scales and that the EM wave radiation spectra emanating from compact astrophysical objects may not settle into stable envelope solitons but into different incoherent states, including the emergence of temporal and spatiotemporal chaos due to collisions and fusions among the patterns with strong EA wave emission. The appearance of these states is confirmed by analyzing the Lyapunov exponent spectra, correlation function, and mutual information as quantitative evidence. As a result, the redistribution of wave energy from initially exciting many solitary patterns at large scales to a few new incoherent patterns with small wavelengths in the system occurs, leading to the onset of turbulence in astrophysical plasmas.

我们在数值上研究了高频圆极化电磁（EM）波和低频电子声（EA）密度微扰的非线性相互作用，这些微扰是由相对论性等离子体（中度、强和超相对论性）中的电磁波质动势驱动的，它们具有两组电子——相对论性简并密集电子（体等离子体）和稀疏相对论性非简并电子（经典）和不移动的单电荷正离子。通过模式选择，我们发现在不同的空间长度尺度下，电磁波的调制不稳定性可以产生许多孤立模式，并且紧凑天体发出的电磁波辐射谱可能不会进入稳定的包络孤子，而是进入不同的非相干状态，包括由于强EA波发射模式之间的碰撞和融合而产生的时间和时空混沌。通过分析李雅普诺夫指数谱、相关函数和互信息作为定量证据，证实了这些态的出现。结果，波能量从最初在大尺度上激发许多孤立模式到系统中一些新的小波长非相干模式的重新分配发生了，导致天体物理等离子体中湍流的开始。

{"title":"Pattern formation and spatiotemporal chaos in relativistic degenerate plasmas","authors":"S. Das Adhikary, A.P. Misra","doi":"10.1016/j.cnsns.2026.109768","DOIUrl":"10.1016/j.cnsns.2026.109768","url":null,"abstract":"<div><div>We numerically study the nonlinear interactions of high-frequency circularly polarized electromagnetic (EM) waves and low-frequency electron-acoustic (EA) density perturbations driven by the EM wave ponderomotive force in relativistic plasmas (moderate, strong, and ultra-relativistic) with two groups of electrons–the population of relativistic degenerate dense electrons (bulk plasma) and the sparse relativistic nondegenerate (classical) electrons, and immobile singly charged positive ions. By pattern selection, we show that many solitary patterns can be generated and drenched through modulational instability of EM waves at different spatial length scales and that the EM wave radiation spectra emanating from compact astrophysical objects may not settle into stable envelope solitons but into different incoherent states, including the emergence of temporal and spatiotemporal chaos due to collisions and fusions among the patterns with strong EA wave emission. The appearance of these states is confirmed by analyzing the Lyapunov exponent spectra, correlation function, and mutual information as quantitative evidence. As a result, the redistribution of wave energy from initially exciting many solitary patterns at large scales to a few new incoherent patterns with small wavelengths in the system occurs, leading to the onset of turbulence in astrophysical plasmas.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109768"},"PeriodicalIF":3.8,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Contrast independent partially explicit splitting scheme for semi-linear multiscale wave equations with damping term 具有阻尼项的半线性多尺度波动方程的对比独立部分显式分裂格式

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-24 DOI: 10.1016/j.cnsns.2026.109784

Zhengya Yang, Yating Wang

In this paper, we propose an efficient temporal splitting scheme for semi-linear wave equations with multiscale high contrast coefficient. We employed the central difference scheme to handle the first- and second-order temporal derivatives. Additionally, the nonlinear term is treated explicitly to avoid iterative solving at each time step. To address the multiscale high contrast features, we further introduce a partially explicit temporal splitting scheme. This scheme utilizes the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to construct two multiscale spaces, effectively separating the high contrast component from the background medium. Then the scheme treats implicitly the subspace containing the high contrast and explicitly the other, such that the time step size is independent of the high contrast. We proved energy decrease and stability, providing explicit stability conditions. Finally, serval numerical experiments demonstrated that our proposed algorithm achieves robust performance across varying multiscale parameters.

本文针对多尺度高对比度系数半线性波动方程，提出了一种有效的时间分裂方法。我们采用中心差分格式来处理一阶和二阶时间导数。此外，对非线性项进行了明确处理，避免了每个时间步的迭代求解。为了解决多尺度高对比度的特点，我们进一步引入了一种部分显式的时间分裂方案。该方案利用约束能量最小化广义多尺度有限元法（CEM-GMsFEM）构造两个多尺度空间，有效地将高对比度分量与背景介质分离。然后，该方案隐式处理包含高对比度的子空间，显式处理包含高对比度的子空间，使得时间步长与高对比度无关。我们证明了能量减少和稳定性，给出了明确的稳定性条件。最后，通过数值实验验证了该算法在不同多尺度参数下的鲁棒性。

{"title":"Contrast independent partially explicit splitting scheme for semi-linear multiscale wave equations with damping term","authors":"Zhengya Yang, Yating Wang","doi":"10.1016/j.cnsns.2026.109784","DOIUrl":"10.1016/j.cnsns.2026.109784","url":null,"abstract":"<div><div>In this paper, we propose an efficient temporal splitting scheme for semi-linear wave equations with multiscale high contrast coefficient. We employed the central difference scheme to handle the first- and second-order temporal derivatives. Additionally, the nonlinear term is treated explicitly to avoid iterative solving at each time step. To address the multiscale high contrast features, we further introduce a partially explicit temporal splitting scheme. This scheme utilizes the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to construct two multiscale spaces, effectively separating the high contrast component from the background medium. Then the scheme treats implicitly the subspace containing the high contrast and explicitly the other, such that the time step size is independent of the high contrast. We proved energy decrease and stability, providing explicit stability conditions. Finally, serval numerical experiments demonstrated that our proposed algorithm achieves robust performance across varying multiscale parameters.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109784"},"PeriodicalIF":3.8,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Enhanced vibration suppression of structures using an optimized serial single-sided vibro-impact bistable NES 利用优化的单面振动冲击双稳NES增强结构的振动抑制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-23 DOI: 10.1016/j.cnsns.2026.109763

Jiang Li, Gui-Lan Yu

The effectiveness of a nonlinear energy sink (NES) is highly dependent on the initial energy level. Its vibration suppression efficiency rapidly diminishes if the initial energy deviates from a certain range. To address this issue, the present paper combines the advantages of bistability with single-sided vibro-impact, and proposes a serially connected single-sided vibro-impact bistable NES (SSSVI-BNES) designed for targeted energy transfer (TET). Compared with bistable NES (BNES) and single-sided vibro-impact NES (SSVI-NES), the SSSVI-BNES effectively resolves the energy sensitivity and energy reflux problems without increasing total mass by connecting the oscillators in series. It broadens the effective energy range and greatly reduces the root mean square (RMS) displacement and maximum displacement of the primary structure, and demonstrates robust control over structural stiffness variations. The parameters of the SSSVI-BNES are optimized using an improved adaptive genetic algorithm (IAGA), significantly improving the vibration suppression effect. The complete source code is available at our github repository: https://github.com/LJ384.

非线性能量汇（NES）的有效性高度依赖于初始能级。当初始能量偏离一定范围时，其抑振效率迅速降低。为了解决这一问题，本文结合双稳定性与单面振动冲击的优点，提出了一种用于定向能量传递（TET）的串行连接单面振动冲击双稳态NES （SSSVI-BNES）。与双稳态振动冲击系统（BNES）和单侧振动冲击系统（SSVI-NES）相比，ssvi -BNES通过串联振荡器，在不增加总质量的前提下，有效地解决了能量敏感性和能量回流问题。该方法拓宽了有效能量范围，大大降低了主结构的均方根位移和最大位移，对结构刚度变化具有较强的控制能力。采用改进的自适应遗传算法（IAGA）对SSSVI-BNES的参数进行优化，显著提高了振动抑制效果。完整的源代码可在我们的github存储库：。

{"title":"Enhanced vibration suppression of structures using an optimized serial single-sided vibro-impact bistable NES","authors":"Jiang Li, Gui-Lan Yu","doi":"10.1016/j.cnsns.2026.109763","DOIUrl":"10.1016/j.cnsns.2026.109763","url":null,"abstract":"<div><div>The effectiveness of a nonlinear energy sink (NES) is highly dependent on the initial energy level. Its vibration suppression efficiency rapidly diminishes if the initial energy deviates from a certain range. To address this issue, the present paper combines the advantages of bistability with single-sided vibro-impact, and proposes a serially connected single-sided vibro-impact bistable NES (SSSVI-BNES) designed for targeted energy transfer (TET). Compared with bistable NES (BNES) and single-sided vibro-impact NES (SSVI-NES), the SSSVI-BNES effectively resolves the energy sensitivity and energy reflux problems without increasing total mass by connecting the oscillators in series. It broadens the effective energy range and greatly reduces the root mean square (RMS) displacement and maximum displacement of the primary structure, and demonstrates robust control over structural stiffness variations. The parameters of the SSSVI-BNES are optimized using an improved adaptive genetic algorithm (IAGA), significantly improving the vibration suppression effect. The complete source code is available at our github repository: <span><span>https://github.com/LJ384</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109763"},"PeriodicalIF":3.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm 变阶分数波动方程：分析、数值近似和快速算法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-23 DOI: 10.1016/j.cnsns.2026.109786

Jinhong Jia , Chuanting Jiang , Yiqun Li , Mengmeng Liu , Wenlin Qiu

We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the well-posedness of the model as well as its high order regularity estimates. To accommodate the convolution term in the reformulated model, we adopt the Ritz-Volterra finite element projection and then derive the rigorous error estimate for the fully-discretized finite element scheme. To circumvent the high computational cost from the temporal integral term, we exploit the translational invariance of the discrete coefficients associated with the convolution structure and construct a fast divide-and-conquer algorithm which reduces the computational complexity from O(MN²) to O(MNln ²N). Numerical experiments are provided to verify the theoretical results and to demonstrate the accuracy and efficiency of the proposed method.

研究了描述扩散波在具有演化物性的粘弹性介质中传播的变阶分数阶波动方程的局部修正。我们加入了一个等价的公式来证明模型的适定性及其高阶正则性估计。为了适应重构模型中的卷积项，我们采用了Ritz-Volterra有限元投影，然后推导了完全离散有限元格式的严格误差估计。为了避免时间积分项的高计算成本，我们利用与卷积结构相关的离散系数的平移不变性，构造了一个快速的分治算法，将计算复杂度从O（MN2）降低到O（mnln2n）。数值实验验证了理论结果，验证了所提方法的准确性和有效性。

{"title":"Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm","authors":"Jinhong Jia , Chuanting Jiang , Yiqun Li , Mengmeng Liu , Wenlin Qiu","doi":"10.1016/j.cnsns.2026.109786","DOIUrl":"10.1016/j.cnsns.2026.109786","url":null,"abstract":"<div><div>We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the well-posedness of the model as well as its high order regularity estimates. To accommodate the convolution term in the reformulated model, we adopt the Ritz-Volterra finite element projection and then derive the rigorous error estimate for the fully-discretized finite element scheme. To circumvent the high computational cost from the temporal integral term, we exploit the translational invariance of the discrete coefficients associated with the convolution structure and construct a fast divide-and-conquer algorithm which reduces the computational complexity from <em>O</em>(<em>MN</em><sup>2</sup>) to <em>O</em>(<em>MN</em>ln <sup>2</sup><em>N</em>). Numerical experiments are provided to verify the theoretical results and to demonstrate the accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109786"},"PeriodicalIF":3.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Energy-decreasing parametric finite element method for geodesic Willmore flow 测地线Willmore流的降能参数有限元法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-23 DOI: 10.1016/j.cnsns.2026.109783

Cuiling Ma, Xufeng Xiao, Xiaoling Zhang, Xinlong Feng

We propose an energy-decreasing numerical scheme for the geodesic Willmore flow of closed curves on curved surfaces. This geometric flow characterizes the evolution of curves toward the minimization of the geodesic Willmore energy. Our main contributions are the derivation of novel evolution equations governing both the curve parameterization and geodesic curvature, the development of a stable fully discrete approximation combining the linear parametric finite elements in space with the implicit Euler in time, and a rigorous proof of discrete energy decay for the proposed scheme. The method effectively captures curve evolution on implicit surfaces. In addition, we generalize the energy-decreasing framework to the anisotropic geodesic Willmore flow and propose a BDF2 scheme. Through numerical experiments, we demonstrate the convergence and energy-decreasing property of the proposed approach, validating its effectiveness.

我们提出了曲面上闭曲线测地线Willmore流的能量递减数值格式。这种几何流的特征是曲线向测地线威尔莫尔能量最小化的演变。我们的主要贡献是推导了控制曲线参数化和测地线曲率的新型演化方程，开发了一个稳定的全离散近似，将空间中的线性参数有限元与时间中的隐式欧拉结合起来，并严格证明了所提出方案的离散能量衰减。该方法有效地捕捉了隐式曲面上的曲线演化过程。此外，我们将能量递减框架推广到各向异性测地线Willmore流中，并提出了BDF2格式。通过数值实验证明了该方法的收敛性和降能性，验证了该方法的有效性。

引用次数: 0

A novel deep neural network with the dynamical moving window data for nonlinear system identification 一种新的具有动态移动窗口数据的非线性系统辨识深度神经网络

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-22 DOI: 10.1016/j.cnsns.2026.109670

Yanjiao Wang, Zhaogui Cai, Muqing Deng

Deep neural networks (DNNs) have the capability to describe complex nonlinear dynamics, which have aroused wide concerns. However, the existing parameter optimization methods in DNNs based on gradient suffer from the limitations of easily falling into local minima and the poor modeling results. To overcome these problems, this paper proposes a mini-batch gradient descent algorithm with dynamical moving window data and constructs a novel deep neural network architecture by using the simpler deep learning network instead of selecting weights through regulation and optimizing its parameters through the dynamical moving window based algorithm. The results of simulation experiments show that the proposed methods have better performance in accuracy and convergence rate compared with the existing methods for identifying nonlinear systems.

深度神经网络（Deep neural network, dnn）具有描述复杂非线性动力学的能力，引起了人们的广泛关注。然而，现有的基于梯度的深度神经网络参数优化方法存在容易陷入局部极小值和建模效果差的局限性。为了克服这些问题，本文提出了一种基于动态移动窗口数据的小批量梯度下降算法，并利用更简单的深度学习网络构建了一种新的深度神经网络架构，而不是通过调节选择权值，并通过基于动态移动窗口的算法优化其参数。仿真实验结果表明，与现有的非线性系统识别方法相比，所提出的方法在精度和收敛速度方面具有更好的性能。

引用次数: 0

Novel subgradient extragradient methods for equilibrium problems in Hilbert spaces 希尔伯特空间平衡问题的新次梯度外聚方法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-22 DOI: 10.1016/j.cnsns.2026.109777

Pham Ky Anh , Ngo Thi Thuong , Nguyen The Vinh

In this paper, by combining the inertial technique and subgradient extragradient method with a new strategy of stepsize selection, we propose a novel extragradient-type method to solve pseudomonotone equilibrium problems in real Hilbert spaces. Our method is designed such that the stepsize sequence is increasing after a finite number of iterations. This distinguishes our method from most other extragradient-type methods for equilibrium problems. The weak and strong convergence of new algorithms under standard assumptions are established. We examine the performance of our methods on the Nash-Cournot oligopolistic equilibrium models of electricity markets. The reported numerical results demonstrate the efficiency of the proposed method.

本文将惯性技术和亚梯度法结合起来，采用一种新的步长选择策略，提出了一种新的求解实数Hilbert空间中伪单调平衡问题的梯度法。我们的方法被设计成步长序列在有限次迭代后增加。这使我们的方法区别于大多数其他用于平衡问题的外梯度型方法。建立了新算法在标准假设下的弱收敛性和强收敛性。我们检验了我们的方法在电力市场的纳什-古诺寡头垄断均衡模型上的性能。数值结果表明了该方法的有效性。

引用次数: 0

Credit risk for large portfolios of green and brown loans: Extending the ASRF model 大型绿色和棕色贷款组合的信用风险：扩展ASRF模型

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-22 DOI: 10.1016/j.cnsns.2026.109750

Alessandro Ramponi, Sergio Scarlatti

Inspired by the classical Vasicek approach to credit risk, we propose an extended model for portfolios composed of green and brown loans, widening the Asymptotic Single Risk Factor framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, collateralized default obligations pricing, and empirical analysis of green loan portfolios.

受经典的Vasicek信贷风险分析方法的启发，我们提出了一个由绿色贷款和棕色贷款组成的投资组合的扩展模型，通过一个双因素关联结构扩大了渐近单风险因素框架。系统风险使用可能偏斜的分布建模，允许不对称的信誉效应，而特殊风险仍然是高斯的。在非均匀风险敞口设置下，我们建立了投资组合损失的二次均值收敛到反映两个贷款部分不同特征的极限。数值结果证实了理论发现，并说明了风险价值如何受到投资组合粒度、违约概率、因素负荷和偏度的影响。我们的模型适应了对系统性冲击的不同敏感性，并为信用风险建模的进一步发展提供了可处理的基础，包括粒度调整、抵押违约债券定价和绿色贷款组合的实证分析。

引用次数: 0

Lazy-learning-based Koopman model predictive control for synchronization of unknown nonlinear systems 基于延迟学习的未知非线性系统同步库普曼模型预测控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-22 DOI: 10.1016/j.cnsns.2026.109746

Xinlong Xu , Xia Huang , Qingyu Shi , Zhen Wang

This paper studies the synchronization problem of a class of unknown nonlinear systems. In response to the challenges in controller design resulting from unknown models, a lazy-learning-based Koopman model predictive control (LL-KMPC) strategy is proposed. The distinctiveness of the proposed control strategy is twofold: (i) exploitation of the global linearization property of the Koopman operator, enabling linear-control methods for synchronization control of unknown nonlinear systems; and (ii) integration of lazy learning (LL), which substantially reduces model mismatch in Koopman-based modeling. Moreover, theoretical results prove that the synchronization error is bounded under the proposed control strategy. Finally, two examples are provided to verify the effectiveness of the proposed control strategy. The experimental results demonstrate that the introduction of the LL technique can effectively improve the modeling performance, and compared to the model-free adaptive control (MFAC) and the model-free adaptive predictive control (MFAPC) approaches, the LL-KMPC strategy exhibits a faster convergence rate and a smaller synchronization error.

研究了一类未知非线性系统的同步问题。针对未知模型给控制器设计带来的挑战，提出了一种基于惰性学习的Koopman模型预测控制（LL-KMPC）策略。该控制策略的独特之处在于：(i)利用Koopman算子的全局线性化特性，使线性控制方法能够用于未知非线性系统的同步控制；（ii）懒学习（LL）的集成，这大大减少了基于koopman的建模中的模型不匹配。此外，理论结果证明了在该控制策略下，同步误差是有界的。最后，通过两个算例验证了所提控制策略的有效性。实验结果表明，引入LL- kmpc技术可以有效地提高建模性能，与无模型自适应控制（MFAC）和无模型自适应预测控制（MFAPC）方法相比，LL- kmpc策略具有更快的收敛速度和更小的同步误差。

{"title":"Lazy-learning-based Koopman model predictive control for synchronization of unknown nonlinear systems","authors":"Xinlong Xu , Xia Huang , Qingyu Shi , Zhen Wang","doi":"10.1016/j.cnsns.2026.109746","DOIUrl":"10.1016/j.cnsns.2026.109746","url":null,"abstract":"<div><div>This paper studies the synchronization problem of a class of unknown nonlinear systems. In response to the challenges in controller design resulting from unknown models, a lazy-learning-based Koopman model predictive control (LL-KMPC) strategy is proposed. The distinctiveness of the proposed control strategy is twofold: (i) exploitation of the global linearization property of the Koopman operator, enabling linear-control methods for synchronization control of unknown nonlinear systems; and (ii) integration of lazy learning (LL), which substantially reduces model mismatch in Koopman-based modeling. Moreover, theoretical results prove that the synchronization error is bounded under the proposed control strategy. Finally, two examples are provided to verify the effectiveness of the proposed control strategy. The experimental results demonstrate that the introduction of the LL technique can effectively improve the modeling performance, and compared to the model-free adaptive control (MFAC) and the model-free adaptive predictive control (MFAPC) approaches, the LL-KMPC strategy exhibits a faster convergence rate and a smaller synchronization error.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109746"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Lyapunov methods for dissipative Caputo fractional differential equations with two indices 双指标耗散卡普托分数阶微分方程的Lyapunov方法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-22 DOI: 10.1016/j.cnsns.2026.109737

Peter E. Kloeden , Doan Thai Son , Hoang The Tuan

The asymptotic behaviour of a class of dissipative Caputo fractional differential equations with two indices is investigated. Using Lyapunov methods and a comparison principle, results on ultimate boundedness and Mittag-Leffler stability are obtained for these systems. Two examples illustrate these results.

研究了一类双指标耗散Caputo分数阶微分方程的渐近性质。利用Lyapunov方法和比较原理，得到了这些系统的极限有界性和Mittag-Leffler稳定性。两个例子说明了这些结果。

引用次数: 0

首页上一页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Communications in Nonlinear Science and Numerical Simulation

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀