Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

Tertiary, quaternary and higher order states in the sequence of bifurcations approach (SBA) to turbulence for laterally heated shear flows within a rectangular tube 矩形管内横向加热剪切流湍流的分岔序列方法（SBA）中的三级、四级和高阶态

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-15 DOI: 10.1016/j.cnsns.2026.109756

T. Akinaga , P.M.J. Trevelyan , S.C. Generalis

We consider a vertical rectangular tube of large aspect ratio with side-wall heating in order to mimic realistic experimental conditions. We therefore impose the condition that across any lateral cross-section of the rectangular tube the fluid flow vanishes. We find through our numerical analysis that oscillatory modes yield critical conditions and offer therefore sequential bifurcations that lead to the turbulent regime. Although the linear stability analysis is the same as the case where the imposed constant flux condition is absent, the corresponding nonlinear regime displays fundamentally different characteristics to the open narrow channel case. Here we focus on the sequence of bifurcations approach of a fluid enclosed in a rectangular tube, aligning with engineering applications. We additionally assume the limit of small Prandtl number and thus the effects caused by temperature perturbations are negligible. Finally we identify the oscillatory states that lead to turbulence as the Grashof number increases up to the value 1000. Our fully nonlinear numerical analysis shows that all bifurcations are supercritical and here we concentrate on the critical axial wavenumber of the linear stability analysis of the laminar flow and its pairing with a specific azimuthal wavenumber.

为了模拟真实的实验条件，我们考虑了一个具有侧壁加热的大宽高比垂直矩形管。因此，我们施加一个条件，即在矩形管的任何横向截面上，流体流动都消失。通过数值分析，我们发现振荡模式产生临界条件，并因此提供导致湍流状态的顺序分岔。虽然线性稳定性分析与不施加恒定通量条件的情况相同，但相应的非线性状态与开放窄通道情况表现出根本不同的特征。本文针对工程应用，重点研究了矩形管内流体分岔序列的求解方法。我们还假定了小普朗特数的极限，因此温度扰动引起的影响可以忽略不计。最后，我们确定了当格拉什夫数增加到1000时导致湍流的振荡状态。我们的全非线性数值分析表明，所有的分岔都是超临界的，这里我们集中讨论层流线性稳定性分析的临界轴向波数及其与特定方位角波数的配对。

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引用次数: 0

Almost surely exponential stability of nonlinear stochastic systems with random impulses and its application in chaos synchronization 具有随机脉冲的非线性随机系统的指数稳定性及其在混沌同步中的应用

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-14 DOI: 10.1016/j.cnsns.2026.109664

Zenghui Hu , Jiamin Liu , Yiming Wang , Lijie You

The almost surely exponential stability (ES a.s.) is investigated for nonlinear systems subject to the effects of stochastic noises and random impulses. The randomness of impulsive effects is considered in two aspects: impulsive intensity and density. In detail, the impulsive instants and jumps are respectively impelled by a renewal process and a Markov chain. By analyzing the coupling effect among stochastic noise, randomly impulsive intensity and density, novel criteria of ES a.s. are obtained by employing Lyapunov-based approach. The proposed results not only capture the positive effect of stochastic noise, but also remove the non-zero property of solution required in existing works. As an application, the synchronization problem of master-slave stochastic chaotic systems is solved by applying the randomly impulsive control method. Two examples are provided to illustrate the effectiveness and application of the proposed results.

研究了受随机噪声和随机脉冲影响的非线性系统的指数稳定性。从脉冲强度和脉冲密度两个方面考虑脉冲效应的随机性。脉冲瞬间和跳跃分别由更新过程和马尔可夫链驱动。通过分析随机噪声、随机脉冲强度和密度之间的耦合效应，采用基于李雅普诺夫的方法得到了新的ES as准则。所提出的结果不仅捕获了随机噪声的积极影响，而且消除了现有工作中要求的解的非零性质。作为应用，采用随机脉冲控制方法解决主从随机混沌系统的同步问题。给出了两个实例来说明所提结果的有效性和应用。

引用次数: 0

Envelope bursting waves and exotic solitons in the network of N- elastically rotating pendulums with smooth and discontinuous nonlinearities coupled in the transverse direction 横向耦合光滑不连续非线性的N弹性旋转摆网络中的包络爆破波和奇异孤子

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-12 DOI: 10.1016/j.cnsns.2026.109728

Fabien Kenmogne , Martine Limi Wokwenmendam , Joël Bruno Gonpe Tafo , Michael Jordan Tsokou Noumeyi , Désiré Ndjanfang

The possible propagation of envelope waves in a network of N elastically rotating pendulums, featuring both smooth and discontinuous nonlinearities and coupled in the transverse direction, is investigated in this paper. Using the Lagrange formulation, the set of irrational equations describing the network is derived and subsequently reduced, via the continuum medium approximation, to the irrational extended sine-Gordon equation, which extends the basic sine-Gordon equation by incorporating additional nonlinear irrational terms as well as nonlinear derivative terms in space. These irrational terms are responsible for the emergence of a new envelope signal in the form of bursting waves. The solutions of the network equation are analyzed through phase portrait bifurcation and the stability of equilibrium points, revealing the existence of vertical homoclinic orbits that predict compact-like kink solutions. Some exact expressions of these solutions are obtained for specific parameter ranges, including envelope kink and periodic solitons, while for other cases, the compact-like kink solitons and additional solutions are approximated as trigonometric functions of a specific function expanded in a power series.

本文研究了包络波在具有光滑非线性和不连续非线性并在横向耦合的N个弹性旋转摆网络中的可能传播。使用拉格朗日公式，推导出描述网络的一组非理性方程，并随后通过连续介质近似将其简化为非理性扩展正弦-戈登方程，该方程通过在空间中加入额外的非线性非理性项以及非线性导数项来扩展基本正弦-戈登方程。这些不合理的术语导致了以爆发波形式出现的新包络信号。通过相画像分岔和平衡点的稳定性分析了网络方程的解，揭示了垂直同斜轨道的存在性，可以预测类紧扭结解。在包络结孤子和周期孤子的特定参数范围内，得到了这些解的精确表达式，而在其他情况下，将类紧结孤子及其附加解近似为一个特定函数展开成幂级数的三角函数。

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引用次数: 0

T -S fuzzy singular cascade networked systems with integrated privacy protection and dynamic event-triggered mechanisms 集成隐私保护和动态事件触发机制的T -S模糊奇异级联网络系统

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-09 DOI: 10.1016/j.cnsns.2026.109669

Xin-Yue Zhao, Xiao-Heng Chang, Li-Juan Cai

Currently, the role of the network in the control system is becoming increasingly crucial, making network security a topic of significant importance. This paper addresses the

H_{\infty}

control problem of T-S fuzzy singular networked cascade systems by designing a novel dynamic triggering strategy that integrates privacy-preserving output mask and event-triggered mechanisms. Departing from prior research, it introduces a segmented privacy mask algorithm from a defender’s perspective and addresses the convergence issue of the privacy output mask. To further reduce communication burdens, a novel dynamic event-triggered scheme is introduced for Takagi-Sugeno (T-S) fuzzy singular networked control systems, enhancing efficiency and reducing communication resource consumption. This scheme integrates two auxiliary internal dynamic variables into the event-triggered condition, one of which is linked to the design of the finite-time privacy output mask. By constructing an appropriate Lyapunov functional, sufficient conditions are derived to guarantee system stability and

H_{\infty}

performance. Finally, the effectiveness of the proposed design is verified by the main steam temperature control system.

当前，网络在控制系统中的作用越来越重要，使得网络安全成为一个非常重要的课题。本文通过设计一种集成了隐私保护输出掩码和事件触发机制的动态触发策略，解决了T-S模糊奇异网络级联系统的H∞控制问题。在前人研究的基础上，从防御者的角度引入了一种分段隐私掩码算法，并解决了隐私输出掩码的收敛问题。为了进一步减轻通信负担，在T-S模糊奇异网络控制系统中引入了一种新的动态事件触发方案，提高了控制效率，减少了通信资源消耗。该方案将两个辅助的内部动态变量集成到事件触发条件中，其中一个与有限时间隐私输出掩码的设计相关联。通过构造适当的Lyapunov泛函，得到了保证系统稳定性和H∞性能的充分条件。最后，通过主汽温控制系统验证了所提设计的有效性。

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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 : 2026-06-01 Epub 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。

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引用次数: 0

H∞ quantized control for interval type-2 fuzzy systems under dual-channel event triggering [公式略]区间2型模糊系统双通道事件触发下的量化控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-12 DOI: 10.1016/j.cnsns.2026.109747

Fan Xiao , Bo Wu , Xisheng Zhan , Lingli Cheng , Huaicheng Yan

This article investigates the problem of quantized

H_{\infty}

dynamic output feedback control for discrete-time nonlinear systems with dual-channel event triggering. Firstly, an interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model is adopted to describe the nonlinear dynamics of the plant. Then, uniform dynamic quantizers and improved event-triggered mechanisms are introduced into the communication network to reduce the number of network packets and efficiently allocate limited communication resources. This paper aims to design an IT2 fuzzy dynamic output feedback controller, such that the asymptotic stability and

H_{\infty}

performance of the closed-loop systems can be guaranteed under dual-channel event triggering and quantization. Moreover, all design parameters can be calculated through a set of linear matrix inequalities. Finally, a simulation example is presented to verify the effectiveness of the proposed method.

研究了具有双通道事件触发的离散非线性系统的量化H∞动态输出反馈控制问题。首先，采用区间type-2 (IT2) Takagi-Sugeno （T-S）模糊模型来描述植物的非线性动力学。然后，在通信网络中引入统一的动态量化和改进的事件触发机制，以减少网络数据包的数量，有效地分配有限的通信资源。本文旨在设计一种IT2模糊动态输出反馈控制器，以保证闭环系统在双通道事件触发和量化下的渐近稳定性和H∞性能。此外，所有的设计参数都可以通过一组线性矩阵不等式来计算。最后，通过仿真算例验证了所提方法的有效性。

引用次数: 0

Intermittent fixed-time stability analysis for nonlinear systems and application to synchronization in spatiotemporal networks 非线性系统的间歇定时稳定性分析及其在时空网络同步中的应用

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-12 DOI: 10.1016/j.cnsns.2026.109732

Shanshan Li , Lifei Wang , Huaiqin Wu , Jinde Cao

This paper focuses on the fixed-time synchronization (FXS) of spatiotemporal networks (STNs) with Robin boundary condition by designing an intermittent event-triggered control scheme. Firstly, a new criterion with respect to the intermittent fixed-time stability, is established for nonlinear systems. Secondly, an intermittent dynamic event-triggered boundary controller is designed to achieve the FXS for the considered STNs. Meanwhile, a continuous function with the lower bound is introduced to avoid the Zeno behavior for the designed event-triggered mechanism. By applying the Lyapunov functional method, inequality analysis technique and the proposed fixed-time stability criterion, the FXS condition is addressed in terms of linear matrix inequalities (LMIs). In addition, the settling-time (ST), which is irrelative to the initial value of network systems, is estimated exactly. Finally, a simulation example and an application in the image encryption are performed to verify the validity of the theoretical analysis.

本文通过设计一种间歇事件触发控制方案，研究具有Robin边界条件的时空网络（STNs）的定时同步问题。首先，对非线性系统建立了一个新的间歇定时稳定性判据。其次，设计了一个间歇动态事件触发边界控制器来实现所考虑的stn的FXS。同时，为避免所设计的事件触发机制的芝诺行为，引入了具有下界的连续函数。利用Lyapunov泛函方法、不等式分析技术和所提出的定时稳定性判据，从线性矩阵不等式（lmi）的角度解决了FXS条件。此外，还准确估计了与网络系统初始值无关的沉降时间（ST）。最后，通过仿真算例和在图像加密中的应用验证了理论分析的有效性。

引用次数: 0

Solving variational inequalities using an algorithm with extrapolations from the past and relaxation 用过去外推法和松弛法求解变分不等式

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-15 DOI: 10.1016/j.cnsns.2026.109681

Yonghong Yao , Sani Salisu , Yekini Shehu

This paper introduces a relaxed version of the forward-backward-forward algorithm with extrapolation from the past iterates to solve variational inequality problems in Hilbert spaces. The relaxation parameter is added to the proposed algorithm to reduce oscillations, providing robustness to a poor choice of initial guess during implementations. Some recently proposed forward-backward-forward algorithms with extrapolation from the past are recovered from our algorithm. We establish that the sequence of iterates generated by our algorithm weakly converges to a solution of the variational inequality problem guided by a pseudo-monotone and Lipschitz continuous operator. We also provide the error bounds of the algorithm in terms of the gap function for the ergodic iterates, which have a convergence rate of

O (1 / n)

. Numerical results are given from optimal control and image restoration problems.

本文介绍了一种松弛版本的前向后向前演算法，并从过去的迭代中进行外推，以解决Hilbert空间中的变分不等式问题。松弛参数被添加到算法中以减少振荡，在实现过程中对初始猜测的不良选择提供鲁棒性。从我们的算法中恢复了一些最近提出的具有过去外推的前向后向前向算法。证明了该算法生成的迭代序列弱收敛于伪单调和Lipschitz连续算子引导下的变分不等式问题的解。对于收敛速度为0 （1/n）的遍历迭代，给出了用间隙函数表示的算法的误差界。给出了最优控制和图像恢复问题的数值结果。

引用次数: 0

Fixed-time impulsive synchronization of heterogeneous complex networks 异构复杂网络的定时脉冲同步

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-15 DOI: 10.1016/j.cnsns.2026.109682

Yufei Ye , Wen Qin , Mouquan Shen , Zhihao Zhang , Hany M. Hasanien , Zheng H. Zhu

This paper is devoted to fixed-time synchronization for a class of heterogeneous complex networks. A composite controller is developed by two main parts, namely, a hyperbolic sine functions instead of summation of two power functions is adopted to supply a smaller fixed time and less design parameters and a compensation term is utilized to deal with the network node heterogeneity. Resorting impulsive interval partitioning and convex combination, a sufficient condition expressed by matrix inequalities is established to guarantee fixed-time synchronization of the resultant systems. A numerical simulation is employed to validate the efficiency of the proposed fixed-time synchronization control scheme.

研究了一类异构复杂网络的固定时间同步问题。复合控制器主要由两部分组成，即采用双曲正弦函数代替两个幂函数的和来提供更小的固定时间和更少的设计参数，并利用补偿项来处理网络节点的异构性。利用脉冲区间划分和凸组合，建立了用矩阵不等式表示的保证系统定时同步的充分条件。通过数值仿真验证了所提出的定时同步控制方案的有效性。

引用次数: 0

Edge-dynamics consensus of matrix-weighted multi-agent systems 矩阵加权多智能体系统的边缘动力学一致性

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-12 DOI: 10.1016/j.cnsns.2026.109668

Lei Tian , Zhijian Ji , Yungang Liu

This paper investigates the consensus problem of edge dynamics in matrix-weighted multi-agent systems and explores its relationship with corresponding node-dynamics. First, we study consensus in directed networks with matrix-weights, establishing algebraic necessary and sufficient conditions for achieving edge-dynamics consensus. Then, from a topological perspective, we derive several sufficient or necessary conditions for edge-dynamics consensus. To enhance system control, we improve consensus protocols by adding a control term and propose algorithms for achieving asymptotic consensus under matrix-weights. Finally, we explore and validate the relationship between node-dynamics and corresponding edge-dynamics through numerical simulations.

本文研究了矩阵加权多智能体系统中边缘动力学的一致性问题，并探讨了其与相应的节点动力学的关系。首先，我们研究了具有矩阵权值的有向网络的一致性，建立了边缘动力学一致性的代数充要条件。然后，从拓扑学的角度，我们得到了边缘动力学一致的几个充要条件。为了增强系统的控制，我们通过增加控制项来改进共识协议，并提出了在矩阵权重下实现渐近共识的算法。最后，通过数值模拟探讨并验证了节点动力学与相应边缘动力学之间的关系。

引用次数: 0

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