Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

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 : 2026-01-12 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

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 : 2026-01-12 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 : 2026-01-12 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

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 : 2026-01-12 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

Novel event-triggered finite/fixed-time cluster synchronization of coupled reaction-diffusion neural networks under mixed cyber-attacks 混合网络攻击下新的事件触发有限/固定时间集群同步耦合反应-扩散神经网络

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-11 DOI: 10.1016/j.cnsns.2026.109684

Lanfeng Hua , Qishui Zhong , Sheng Han , Oh-Min Kwon , Kaibo Shi , Huaicheng Yan

This paper addresses the event-triggered fixed-time cluster synchronization of coupled reaction-diffusion neural networks under mixed cyber-attacks. First, some improved Lyapunov-based criteria for fixed-time stability are derived, offering a less conservative upper-bound estimate of the settling time. A novel event-triggering mechanism with a time-varying threshold is then introduced, and a security-based cluster synchronization scheme is developed based on this mechanism. By leveraging the piecewise Lyapunov function approach and hybrid systems analysis methods, we establish sufficient conditions to ensure fixed-time synchronization between follower nodes with interacting clusters and target nodes, even in the presence of mixed cyber-attacks. Moreover, this paper quantifies the relationship between mixed cyber-attacks and the convergence rate of the synchronization strategy. The effectiveness of the proposed approach is validated through comprehensive simulations and experiments, demonstrating its superiority over existing fixed-time stability strategy and event-triggered synchronization protocol.

研究了混合网络攻击下事件触发的耦合反应-扩散神经网络固定时间集群同步问题。首先，导出了一些改进的基于lyapunov的固定时间稳定性准则，提供了一个不太保守的沉降时间上界估计。在此基础上，提出了一种具有时变阈值的事件触发机制，并在此基础上提出了一种基于安全的集群同步方案。通过利用分段Lyapunov函数方法和混合系统分析方法，我们建立了足够的条件来确保具有交互集群的跟随节点和目标节点之间的固定时间同步，即使在存在混合网络攻击的情况下。此外，本文还量化了混合网络攻击与同步策略收敛速度的关系。通过综合仿真和实验验证了该方法的有效性，表明其优于现有的固定时间稳定性策略和事件触发同步协议。

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引用次数: 0

Switching event-triggered-based adaptive fuzzy cooperative control for multiagent systems: A connectivity-preserving method with dynamic boundary adjustment 基于切换事件触发的多智能体系统自适应模糊协同控制：一种具有动态边界调整的保持连通性方法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-11 DOI: 10.1016/j.cnsns.2026.109740

Congyan Lv , Guangliang Liu , Yingnan Pan , Liqi Wang

With the widespread application of multiagent systems (MASs) in complex industrial environments, their cooperative control capabilities are limited by the effective coverage range of communication devices. The information exchange between agents is only feasible within the preset communication radius. Exceeding this threshold will lead to network connectivity loss, thereby interrupting real-time cooperation between agents. Considering the above issues, this paper formulates a connectivity-preserving cooperative control strategy for MASs with constrained communication ranges. A new nonlinear transformation method for synchronization error is proposed, which not only avoids the singularity problem of tracking errors at the initial time, but also dynamically adjusts the boundary function based on the initial distances of the agents. A modified switching dynamic event-triggered mechanism is presented to reduce the transmission burden, its advantage is that it can adaptively select an ideal communication threshold based on the tracking performance indicators and improve the flexibility of control scheme. In addition, a privacy preservation mechanism with adjustable protection time is applied to improve the security of the system. By using Lyapunov stability theory, it is demonstrated that all signals remain bounded in the closed-loop systems and all followers converge to the neighborhood of the leader output. At last, we verify the effectiveness of the proposed scheme through a simulation example.

随着多智能体系统在复杂工业环境中的广泛应用，其协同控制能力受到通信设备有效覆盖范围的限制。agent之间的信息交换只能在设定的通信半径内进行。超过该阈值将导致网络连通性丧失，从而中断代理之间的实时协作。考虑到上述问题，本文提出了一种通信范围受限的质量保持连通性的协同控制策略。提出了一种新的同步误差非线性变换方法，既避免了初始时刻跟踪误差的奇异性问题，又能根据agent的初始距离动态调整边界函数。为了减少传输负担，提出了一种改进的交换动态事件触发机制，其优点是可以根据跟踪性能指标自适应选择理想的通信阈值，提高了控制方案的灵活性。此外，还采用了保护时间可调的隐私保护机制，提高了系统的安全性。利用李雅普诺夫稳定性理论，证明了在闭环系统中所有信号保持有界，所有跟随者收敛于领导输出的邻域。最后，通过仿真算例验证了所提方案的有效性。

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引用次数: 0

Predefined-time synchronization of cyclic memristive neural networks via adaptive sliding mode control: Comparative analysis and application in secure communication 基于自适应滑模控制的循环记忆记忆神经网络的预定义时间同步：比较分析及其在保密通信中的应用

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-11 DOI: 10.1016/j.cnsns.2026.109734

Qiang Lai, Jun Wang

This paper presents an innovative adaptive sliding mode predefined-time synchronization (PTS) control scheme tailored for cyclic memristive neural networks (CMNNs) with uncertain internal parameters. Distinguishing itself from finite-time synchronization (FTS), fixed-time synchronization (FxTS), and traditional PTS methods, the proposed scheme achieves rapid convergence within a predefined-time and exhibits exceptional robustness against internal uncertainties and external disturbances. The scheme incorporates a novel Lyapunov condition alongside adaptive control laws to improve synchronization performance and ensure system stability. Comparative experiments reveal that the proposed approach substantially outperforms conventional methods in terms of convergence speed, robustness, and adaptability. Furthermore, a multi-stage chaotic secure communication framework is developed leveraging the CMNN. The deployment of the designed PTS scheme within multi-stage secure communication underscores its practicality for reliable and efficient encryption and decryption of complex signals. Numerical simulations validate the proposed scheme’s extensive applicability to secure communication and advanced control systems.

针对具有不确定内参数的循环记忆神经网络，提出了一种创新的自适应滑模预定义时间同步（PTS）控制方案。与有限时间同步（FTS）、固定时间同步（FxTS）和传统的PTS方法不同，该方法在预定义时间内实现快速收敛，并对内部不确定性和外部干扰具有出色的鲁棒性。该方案结合了一种新的李雅普诺夫条件和自适应控制律，以提高同步性能并保证系统的稳定性。对比实验表明，该方法在收敛速度、鲁棒性和适应性方面都明显优于传统方法。在此基础上，设计了多级混沌安全通信框架。所设计的PTS方案在多级安全通信中的应用，突出了其对复杂信号进行可靠、高效加解密的实用性。数值仿真验证了该方案在安全通信和高级控制系统中的广泛适用性。

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引用次数: 0

Prescribed-time non-smooth optimization for multi-agent systems with mixed constraints 混合约束下多智能体系统的规定时间非光滑优化

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-11 DOI: 10.1016/j.cnsns.2026.109696

Xuening Xu , Zhiyong Yu , Haijun Jiang , Chunxia Zhu

This paper investigates the prescribed-time non-smooth distributed optimization problems (DOPs) with mixed constraints for multi-agent systems (MASs). First, a lemma is introduced to describe the relationship between any two vectors in a convex set and their elements in a normal cone, which plays a crucial role in the convergence analysis of the algorithm. Second, a non-singular prescribed-time distributed optimization algorithm (DOA) is proposed based on the time-varying transformation function, and the optimal solution of the DOP is obtained through the projection sub-gradient algorithm and the proximal operator algorithm. In particular, the proposed algorithm reduces the conservativeness that the objective function is strongly convex and smooth. Finally, the effectiveness and feasibility of the DOA are validated through numerical simulation, and the impact of the adjustable parameter on the convergence performance is discussed, along with a comparison to existing algorithms.

研究了具有混合约束的多智能体系统的规定时间非光滑分布优化问题。首先，引入了一个引理来描述凸集中任意两个向量与其法锥上元素之间的关系，这对算法的收敛性分析起着至关重要的作用。其次，提出了一种基于时变变换函数的非奇异规定时间分布优化算法（DOA），并通过投影子梯度算法和近端算子算法得到了DOP的最优解；特别地，该算法降低了目标函数是强凸光滑的保守性。最后，通过数值仿真验证了该方法的有效性和可行性，讨论了可调参数对收敛性能的影响，并与现有算法进行了比较。

引用次数: 0

Finite-time synchronization and anti-synchronization of fuzzy memristive competitive neural networks with reaction-diffusion terms 具有反应扩散项的模糊记忆竞争神经网络的有限时间同步与反同步

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-11 DOI: 10.1016/j.cnsns.2026.109657

Ting Yang, Jie Yan, Li Cao, Wanli Zhang

This brief concerns with the finite-time synchronization (FTS) and finite-time anti-synchronization (FTAS) for fuzzy memristive competitive neural networks (FMCNNs) with reaction-diffusion (RD) terms. The studied neural networks (NNs) are transformed into network systems with uncertain parameters. In particular, the uncertain parameters in the fuzzy feedback connection weights are addressed through two low-conservatism inequalities. By introducing a scale parameter, both types of synchronization are studied in a unified framework. Using a non-delay-dependent control strategy, we establish the conditions for FTS and FTAS by means of a weighted 2-norm Lyapunov-Krasovskii functional (LKF) and linear matrix inequalities (LMIs). Moreover, corresponding estimates for the settling time are provided. Numerical examples are also provided to demonstrate the feasibility of the theoretical results.

本文简要讨论了具有反应扩散（RD）项的模糊记忆竞争神经网络（FMCNNs）的有限时间同步（FTS）和有限时间反同步（FTAS）。将所研究的神经网络转化为具有不确定参数的网络系统。特别地，通过两个低保守性不等式解决了模糊反馈连接权值中的不确定参数。通过引入尺度参数，在统一的框架下对两种类型的同步进行了研究。采用非时滞相关控制策略，利用加权2范数Lyapunov-Krasovskii泛函（LKF）和线性矩阵不等式（lmi）建立了FTS和FTAS的条件。并给出了相应的沉降时间估计。数值算例验证了理论结果的可行性。

引用次数: 0

Impulsive adaptive control meets iterative learning: A hybrid algorithm for tracking analysis of drive-response neural networks 脉冲自适应控制与迭代学习：一种驱动-反应神经网络跟踪分析的混合算法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-11 DOI: 10.1016/j.cnsns.2026.109704

Yanting Shen, Yuqing Wu, Zhenkun Huang

Iterative learning control (ILC) is an effective control strategy that has been widely applied in dynamic systems requiring repetitive task execution. However, drive-response neural networks face challenges in achieving high-precision tracking in applications, particularly under dynamic conditions and uncertainties, where traditional control methods often fail to meet performance requirements. To address this issue, this paper investigates a class of tracking control problems for drive-response neural networks based on P-type and impulsive adaptive iterative learning control. The goal is to design a novel hybrid iterative learning control algorithm to enhance the system’s tracking capability. P-type control effectively reduces tracking errors by utilizing historical control information, while the impulsive adaptive mechanism improves the system’s adaptability in dynamic environments, allowing control parameters to be adjusted based on real-time feedback. Furthermore, by applying the Bellman-Gronwall inequality, new criteria are established to realize tracking control for drive-response neural networks. Finally, the simulation results show that the control strategy exhibits significant advantages in reducing the tracking error and improving the convergence speed.

迭代学习控制（ILC）是一种有效的控制策略，在需要重复任务执行的动态系统中得到了广泛应用。然而，驱动-响应神经网络在实现高精度跟踪应用方面面临挑战，特别是在动态条件和不确定性下，传统的控制方法往往无法满足性能要求。为了解决这一问题，本文研究了一类基于p型和脉冲自适应迭代学习控制的驱动-响应神经网络跟踪控制问题。目标是设计一种新的混合迭代学习控制算法，以提高系统的跟踪能力。p型控制利用历史控制信息有效降低了跟踪误差，脉冲自适应机制提高了系统对动态环境的适应性，可以根据实时反馈调整控制参数。利用Bellman-Gronwall不等式，建立了驱动-响应神经网络跟踪控制的新准则。仿真结果表明，该控制策略在减小跟踪误差和提高收敛速度方面具有显著优势。

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