Mathematics and Computers in Simulation最新文献_第2页

Spatiotemporal dynamics in a diffusive eco-epidemiological system with spatial memory and fear effect 具有空间记忆和恐惧效应的弥漫性生态流行病学系统的时空动态

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-17 DOI: 10.1016/j.matcom.2026.01.020

Jia Liu , Hongyong Zhao

This paper proposes and analyzes a novel delayed diffusive model to investigate the complex spatiotemporal dynamics of an eco-epidemiological system. The model is distinguished by its simultaneous integration of four critical ecological mechanisms: a fear effect that suppresses prey reproduction, disease transmission within the prey population, standard diffusion, and a memory-based anti-predator taxis, wherein prey actively avoid predators based on past information. Rigorous mathematical analysis establishes the system’s well-posedness and reveals intricate stability dynamics. We demonstrate that the prey’s anti-predator taxis can trigger a Turing instability, leading to the formation of stationary spatial patterns. Crucially, this destabilizing effect is counteracted by the fear mechanism, which acts as a spatial stabilizer by expanding the parameter domain for homogeneous coexistence. Furthermore, our analysis identifies the time delay in the prey’s response as a potent driver of temporal instability, inducing sustained population oscillations via a Hopf bifurcation. Beyond local bifurcations, we also derive sufficient conditions for the global asymptotic stability of both the infection-free and coexistence equilibria using Lyapunov functional methods. Numerical simulations not only corroborate our analytical predictions but also unveil the emergence of a rich variety of complex spatial structures in two dimensions, including spots, stripes, and mixed-mode patterns. In summary, our findings highlight that the sophisticated interplay between fear, memory, and movement can profoundly alter system stability and generate diverse spatiotemporal heterogeneity, offering significant insights into the mechanisms governing community structure and disease dynamics in natural ecosystems.

本文提出并分析了一种新的延迟扩散模型来研究生态流行病学系统的复杂时空动态。该模型的特点是同时整合了四种关键的生态机制：抑制猎物繁殖的恐惧效应、猎物种群内的疾病传播、标准扩散和基于记忆的反捕食者定向，其中猎物根据过去的信息主动避开捕食者。严格的数学分析建立了系统的适定性，揭示了复杂的稳定动力学。我们证明了猎物的反捕食者出租车可以触发图灵不稳定性，导致静止空间模式的形成。至关重要的是，这种不稳定效应被恐惧机制所抵消，恐惧机制通过扩大同质共存的参数域而起到空间稳定器的作用。此外，我们的分析确定了猎物反应的时间延迟是时间不稳定的有力驱动因素，通过Hopf分岔诱导持续的种群振荡。除了局部分岔外，我们还利用Lyapunov泛函方法推导了无感染平衡点和共存平衡点全局渐近稳定的充分条件。数值模拟不仅证实了我们的分析预测，而且揭示了在二维空间中出现的丰富多样的复杂空间结构，包括斑点、条纹和混合模式。总之，我们的研究结果强调了恐惧、记忆和运动之间复杂的相互作用可以深刻地改变系统的稳定性，并产生不同的时空异质性，为自然生态系统中控制群落结构和疾病动态的机制提供了重要的见解。

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引用次数: 0

S-ERKN methods solving Maxwell’s equations in source field under wide range of boundary conditions S-ERKN方法在宽边界条件下求解源场麦克斯韦方程组

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.matcom.2026.01.017

Hongli Yang , Xianyang Zeng , Hao Yu

For Maxwell’s equations for isotropic homogeneous media in a cubic domain, there have been few methods that can solve almost all problems under various boundary conditions in source field since the boundary conditions and the sources are diverse, by now. Fortunately, in this paper, we succeeded in giving a unified class of methods (called S-ERKN methods) that solve problems under a wide range of boundary conditions in source field. At first, we gave a detailed study on the spatial discretization to have a so-called semi-discrete system. Here we concluded that the boundary conditions had an unsurprising impact on the differentiation matrix (denoted as

L_{U}

in this paper) but had an unexpected effect on the perturbation term (denoted as

{\tilde{F}}_{U}

in this paper) of the semi-discrete system. Secondly, we chose the ERKN (Extended Runge–Kutta Nystrom) methods as the temporal solver to improve the temporal order which is normally limited to 2 in many traditional numerical solutions. To make the S-ERKN method (obtained by the spatial and temporal discretization shown above) easy to code at low cost, we studied the fast calculation of the matrix vector product

L_{U} V

, which is the basic computational unit of the method. In this paper, we also performed the divergence analysis of the methods. The numerical experiments illuminate that the method can be explicit, highly accurate, divergence-free in numerical terms, and of good long-term behavior.

对于三次域各向同性均匀介质麦克斯韦方程组，由于源场边界条件和源的多样性，目前几乎没有能够解决源场各种边界条件下所有问题的方法。幸运的是，在本文中，我们成功地给出了一类统一的方法（称为S-ERKN方法）来解决源场中各种边界条件下的问题。首先，我们对空间离散化进行了详细的研究，以得到所谓的半离散系统。在这里，我们得出结论，边界条件对微分矩阵（在本文中表示为LU）有意料之外的影响，但对半离散系统的扰动项（在本文中表示为F * U）有意想不到的影响。其次，我们选择了ERKN （Extended Runge-Kutta Nystrom）方法作为时间求解器，改善了许多传统数值解中通常限于2阶的时间阶数。为了使S-ERKN方法（由上文所示的时空离散化得到）易于低成本编码，我们研究了作为该方法基本计算单元的矩阵向量积LUV的快速计算。本文还对这些方法进行了发散性分析。数值实验表明，该方法清晰、精度高、无发散、长期性能好。

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引用次数: 0

Robust non-singular fixed-time sliding mode control for robot manipulators: Franka robot arm 机器人机械臂的鲁棒非奇异定时滑模控制：Franka机械臂

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.matcom.2026.01.010

Amine Mebarki, Moussa Labbadi, Mohamed Zerrougui

Modern robotic applications demand precise trajectory tracking, which is particularly challenging due to the nonlinear dynamics, model uncertainties, and external disturbances inherent in robotic manipulators. Robust control strategies, such as Sliding Mode Control (SMC), have proven effective in addressing these challenges. Advanced variants, including finite-time and fixed-time SMC, offer the added advantage of ensuring stabilization within a predefined time frame. This paper proposes various strategies for the Franka robot, ensuring global fixed-time convergence of the closed-loop system with a singularity-free design and the settling time estimation is independent of initial conditions. A non-singular terminal sliding surface is utilized to achieve precise trajectory tracking, enhanced robustness to external disturbances, and simplified implementation. The effectiveness of the proposed methods is validated through realistic simulations of the Franka robot.

现代机器人应用需要精确的轨迹跟踪，由于非线性动力学、模型不确定性和机器人操纵器固有的外部干扰，这尤其具有挑战性。事实证明，滑模控制（SMC）等鲁棒控制策略在解决这些挑战方面是有效的。高级版本，包括有限时间和固定时间SMC，提供了额外的优势，确保在预定义的时间范围内稳定。本文针对Franka机器人提出了各种策略，保证了闭环系统的全局定时收敛，具有无奇点设计，且沉降时间估计与初始条件无关。利用非奇异终端滑动面实现精确的轨迹跟踪，增强了对外界干扰的鲁棒性，简化了实现。通过对Franka机器人的仿真，验证了所提方法的有效性。

引用次数: 0

Global dynamics of a SARS-CoV-2 infection model with interferons, spatial heterogeneity and nonlocal diffusion 具有干扰素、空间异质性和非局部扩散的SARS-CoV-2感染模型的全球动力学

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-14 DOI: 10.1016/j.matcom.2026.01.012

Jiangxue Xu , Toshikazu Kuniya , Guihong Fan , Zhen Jin , Haitao Song

The global pandemic of the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) highlights the critical need to understand its complex within-host dynamics. To investigate the roles of interferons (IFNs), spatial heterogeneity, and nonlocal diffusion in SARS-CoV-2 infection, we propose a novel within-host dynamics model incorporating these factors. The well-posedness of the system is first proved, and the basic reproduction number

(ℛ_{0})

of the system is defined. We then analyze global dynamics of the system based on

ℛ_{0}

: when

ℛ_{0} < 1

, infection-free steady state is globally asymptotically stable; the system is uniformly persistent when

ℛ_{0} > 1

. In addition, for a special case, an appropriate Lyapunov function is constructed to prove global asymptotic stability of the unique infection steady state for

ℛ_{0} > 1

. Numerical simulations validate our theoretical findings and reveal that enhancing the antiviral potency of IFNs and maintaining the antiviral state are effective strategies to limit SARS-CoV-2 infection in its early stages. Moreover, our findings suggest that increasing the diffusion rates of cells and viruses can reduce

ℛ_{0}

and control viral transmission, with the diffusion of productively infected cells and viruses being particularly crucial. Our study provides theoretical insights for designing antiviral therapies and understanding SARS-CoV-2 persistence.

严重急性呼吸综合征冠状病毒-2 （SARS-CoV-2）的全球大流行突出表明，迫切需要了解其在宿主内的复杂动态。为了研究干扰素（ifn）、空间异质性和非局部扩散在SARS-CoV-2感染中的作用，我们提出了一个包含这些因素的新的宿主内动力学模型。首先证明了该系统的适定性，并定义了该系统的基本再现数。然后，我们分析了系统的全局动力学特性：当条件为1时，无感染稳态是全局渐近稳定的；当条件为1时，系统是一致持久的。此外，对于一个特殊情况，构造了一个适当的Lyapunov函数，证明了唯一感染稳态的全局渐近稳定性。数值模拟验证了我们的理论发现，并揭示了增强ifn的抗病毒效力和维持抗病毒状态是在SARS-CoV-2感染早期限制其感染的有效策略。此外，我们的研究结果表明，增加细胞和病毒的扩散速率可以降低贡献率并控制病毒传播，其中有效感染的细胞和病毒的扩散尤为重要。我们的研究为设计抗病毒疗法和理解SARS-CoV-2的持久性提供了理论见解。

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引用次数: 0

Percolation thresholds and epidemic spreading on small-world networks: Exact results and critical dynamics 小世界网络上的渗透阈值和流行病传播：精确结果和临界动力学

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-13 DOI: 10.1016/j.matcom.2026.01.011

Xiao-Long Peng , Shu-Yan Chang , Shanshan Chen , Gui-Quan Sun

Percolation theory provides a powerful framework for understanding the emergence of large-scale epidemic outbreaks on complex networks. Building on the seminal work of Moore and Newman (2000), we revisit and extend percolation-based models of disease spread on small-world networks that incorporate both local connections and long-range shortcuts. Specifically, we resolve two previously unresolved cases by deriving exact analytical expressions for the bond percolation threshold at local connectivity

K = 3

, and for the hybrid site-bond percolation threshold at

K = 2

. These results advance the theoretical foundations of epidemic modelling on structured networks. Complementing these theoretical results, we conduct extensive numerical simulations to characterize critical behaviour of both pure bond and hybrid site-bond percolation processes. We find that percolation thresholds are highly sensitive to shortcut density and local connectivity. Notably, the average size of finite percolating clusters exhibits a pronounced peak at criticality, offering a reliable early-warning signal for epidemic onset. Furthermore, we observe a clear transition in cluster size distributions — from exponential decay to heavy-tailed forms — as the system approaches the percolation threshold, culminating in the emergence of a giant component indicative of a large-scale epidemic. Temporal simulations further reveal abrupt epidemic transitions as control parameters cross critical thresholds, in agreement with our percolation-based predictions. Collectively, our results establish the percolation framework as a powerful tool for capturing both structural and dynamical features of epidemic spreading on small-world networks.

渗透理论为理解复杂网络中大规模流行病爆发的出现提供了一个强有力的框架。在Moore和Newman（2000）开创性工作的基础上，我们重新审视并扩展了疾病在小世界网络中传播的基于渗透的模型，该模型包含了本地连接和远程捷径。具体来说，我们通过推导局部连通性K=3时键渗透阈值和K=2时混合位点-键渗透阈值的精确解析表达式，解决了两个先前未解决的情况。这些结果为基于结构化网络的流行病建模提供了理论基础。为了补充这些理论结果，我们进行了广泛的数值模拟，以表征纯键和混合位点-键渗透过程的临界行为。我们发现渗透阈值对捷径密度和局部连通性高度敏感。值得注意的是，有限渗流簇的平均大小在临界时表现出明显的峰值，为流行病的发生提供了可靠的预警信号。此外，我们观察到集群大小分布的明显转变——从指数衰减到重尾形式——当系统接近渗透阈值时，最终出现一个表明大规模流行病的巨大组成部分。时间模拟进一步显示，当控制参数越过临界阈值时，流行病会突然转变，这与我们基于渗流的预测一致。总的来说，我们的结果建立了渗透框架作为捕获小世界网络中流行病传播的结构和动态特征的强大工具。

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引用次数: 0

Cooperative and robust object manipulation by multiple robots via linear estimated state feedback 基于线性估计状态反馈的多机器人协同鲁棒目标操作

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-12 DOI: 10.1016/j.matcom.2026.01.009

Saleh Mobayen , Alireza Izadbakhsh

In modern industrial automation, the deployment of multiple robotic manipulators for cooperative operations has become increasingly common, offering enhanced system flexibility and responsiveness. However, as the number of manipulators increases, the system dynamics become substantially more nonlinear and complex, giving rise to unmodeled dynamics and various sources of uncertainty. Moreover, external disturbances can further degrade control performance, while the lack of a comprehensive sensing infrastructure may result in incomplete state information. To address these challenges, this study proposes a robust, model-independent control framework based on function approximation techniques. The methodology leverages linear differential equations with unknown coefficients to capture the aggregated system uncertainties under the assumption that such uncertainties can be effectively described using this structure. The approximation capability of the proposed model is then justified via the Stone-Weierstrass theorem, establishing the role of linear differential equations as universal approximators. Notably, the control strategy does not require velocity measurements, thereby simplifying its practical implementation. Stability analysis based on Lyapunov’s direct method ensures that tracking errors remain uniformly ultimately bounded. The controller is validated within a dual-arm cooperative manipulation scenario involving a rigid object, and its performance is benchmarked against three contemporary approximation-based control methods. Simulation results confirm the efficacy and robustness of the proposed approach.

在现代工业自动化中，部署多个机器人机械手进行协作操作已经变得越来越普遍，从而提高了系统的灵活性和响应能力。然而，随着机械臂数量的增加，系统动力学变得更加非线性和复杂，产生了未建模的动力学和各种不确定性来源。此外，外部干扰会进一步降低控制性能，而缺乏全面的传感基础设施可能导致状态信息不完整。为了解决这些挑战，本研究提出了一种基于函数逼近技术的鲁棒、模型无关的控制框架。该方法利用具有未知系数的线性微分方程来捕获聚合系统的不确定性，假设这种不确定性可以使用该结构有效地描述。然后通过Stone-Weierstrass定理证明了所提出模型的近似能力，建立了线性微分方程作为通用近似器的作用。值得注意的是，该控制策略不需要速度测量，从而简化了其实际实现。基于Lyapunov直接法的稳定性分析保证了跟踪误差最终保持一致有界。该控制器在涉及刚性物体的双臂协作操作场景中进行了验证，并与三种现代基于近似的控制方法进行了性能基准测试。仿真结果验证了该方法的有效性和鲁棒性。

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引用次数: 0

A generalized Caputo fractional jerk equation with Caputo antiperiodic boundary conditions: Existence of solutions, stability and numerical simulations 一类具有Caputo反周期边界条件的广义Caputo分数阶jerk方程：解的存在性、稳定性及数值模拟

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-12 DOI: 10.1016/j.matcom.2026.01.005

Zeeshan Ali , Sandra Pinelas

This paper investigates the existence of solutions, stability, and numerical simulations for a generalized fractional jerk equation with fractional antiperiodic boundary conditions, both involving Caputo derivatives. The model features non-integer order derivatives in the equation and boundary conditions, resulting in a more general formulation. Fixed-point theory is employed to establish sufficient conditions for the existence and uniqueness, leading to novel results. Furthermore, Ulam-Hyers stability and its generalized form are analyzed to ensure robustness of the solutions. Examples are presented to demonstrate the applicability of the theoretical findings, with the system’s behavior and stability analyzed for various fractional orders

α

and

β

using MATLAB. A special case of the proposed system is also discussed in the conclusion.

研究一类具有分数阶反周期边界条件的广义分数阶jerk方程的解的存在性、稳定性和数值模拟。该模型在方程和边界条件中具有非整数阶导数，从而产生更一般的公式。利用不动点理论建立了存在唯一性的充分条件，得到了新的结果。进一步分析了Ulam-Hyers稳定性及其广义形式，以保证解的鲁棒性。通过实例验证了理论结果的适用性，并用MATLAB分析了系统在不同分数阶α和β下的行为和稳定性。结论部分还讨论了该系统的一个特例。

引用次数: 0

Modeling a delay-driven eco-epidemiological system with fear and migration under ratio-dependent predation 比例依赖捕食条件下具有恐惧和迁移的延迟驱动生态流行病学系统建模

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-12 DOI: 10.1016/j.matcom.2026.01.002

Kahuwa Kuwali Barman , Ankur Jyoti Kashyap , Hemanta Kumar Sarmah

This study investigates an eco-epidemiological predator–prey model that incorporates fear-driven behavioral changes in susceptible prey along with migration in both prey and predator populations. Predation on infected prey is modeled through a ratio-dependent functional response, and a transmission delay is introduced to represent the non-instantaneous nature of infection, adding novelty to the framework. We examine the local and global stability of the non-delayed system, and analyze the occurrence of transcritical and Hopf bifurcations. The results show that fear effects and susceptible prey migration may destabilize the system, whereas a higher conversion rate of infected prey biomass promotes stable coexistence. Delay-induced bifurcation analysis further reveals that increasing the transmission delay destabilizes the interior equilibrium, and numerical simulations support these analytical findings.

本研究调查了一个生态流行病学捕食者-猎物模型，该模型结合了易感猎物的恐惧驱动行为变化以及猎物和捕食者种群的迁移。对受感染猎物的捕食通过比率依赖的功能反应建模，并引入传输延迟来表示感染的非瞬时性质，为框架增加了新颖性。我们研究了非延迟系统的局部稳定性和全局稳定性，并分析了跨临界分岔和Hopf分岔的发生。结果表明，恐惧效应和易感猎物迁移可能会破坏生态系统的稳定，而较高的被感染猎物生物量转化率则有利于生态系统的稳定共存。延迟引起的分岔分析进一步揭示了增加传输延迟会破坏内部平衡，数值模拟支持了这些分析结果。

引用次数: 0

A statistics-based simplification method to the Distribution Network Reconfiguration problem for large-scale networks 基于统计的大规模配电网重构问题简化方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-12 DOI: 10.1016/j.matcom.2026.01.008

A. Graine , N. Karnib , J.-P. Gaubert , D. Larraillet

The Distribution Network Reconfiguration (DNR) consists of modifying the topology of a Distribution Network (DN) through the modification of the state of its switches, thus modifying the paths of power. It can be used to minimize losses or other physical quantities, while satisfying, among others, radial, electrical, and thermal constraints. It is an optimization problem of a type referred to as Mixed-Integer Programming (MIP). When the DNR is applied to large-scale DNs, which is the case for this paper since the aim is to optimize real networks for a French Distribution System Operator (DSO): this problem can be challenging to solve because the number of switches (and thus the number of binary variables) becomes very large, which can lead to a combinatorial explosion.

In this paper, a statistics-based simplification method is proposed to determine the most impactful switches for the DNR. The method can be fragmented into two phases: a training phase, then a deployment phase. Different strategies are tested and compared for the two phases. A simplified method is used for the training phase, during which the most impactful switches are identified. Then, these most impactful switches are used as decision variables in the deployment phase, while the non-impactful switches are considered as input parameters, hence greatly reducing the number of binary optimization variables. As a consequence, the computational time is decreased. The method’s performance is evaluated through simulations on a realistic 2 588-bus, 403-switch DN. Results show that the proposed method is able to speed up the computation.

DNR （Distribution Network Reconfiguration）是指通过改变配电网络交换机的状态来改变配电网络的拓扑结构，从而改变配电网络的供电路径。它可以用于最小化损耗或其他物理量，同时满足径向、电学和热约束。这是一种被称为混合整数规划（MIP）的优化问题。当DNR应用于大规模DNs时，这是本文的情况，因为目的是为法国配电系统运营商（DSO）优化真实网络：这个问题可能很难解决，因为开关的数量（以及二进制变量的数量）变得非常大，这可能导致组合爆炸。本文提出了一种基于统计的简化方法来确定最有效的DNR开关。该方法可以分成两个阶段：训练阶段，然后是部署阶段。对这两个阶段的不同策略进行了测试和比较。在训练阶段使用了一种简化的方法，在此期间识别最具影响力的开关。然后，将这些最具影响力的开关作为部署阶段的决策变量，而将不具影响力的开关作为输入参数，从而大大减少了二进制优化变量的数量。因此，计算时间减少了。通过在实际的2588总线、403交换机DN上的仿真，对该方法的性能进行了评价。结果表明，该方法能够提高计算速度。

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引用次数: 0

Secure synchronization of T–S fuzzy complex dynamical networks under critical-data-targeted DoS attacks 关键数据DoS攻击下T-S模糊复杂动态网络的安全同步

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-01-10 DOI: 10.1016/j.matcom.2026.01.007

Jinyuan Zhang , Yuechao Ma

This article focuses on the pinning synchronization issue for Takagi–Sugeno (T–S) fuzzy complex dynamical networks (CDNs) under critical-data-targeted denial-of-service (DoS) attacks. Firstly, a novel critical-data-targeted DoS attack method is considered for the attacker to enhance the destructiveness of the attack against various nodes. Contrasting with most existing DoS attack models, this attack scheme can selectively attack critical data, allowing the attacker to cause relatively large damage to system performance. Secondly, we establish a new pinning synchronization control model for T–S fuzzy CDNs with random coupling delays. It can describe the actual world more accurately compared with the general model of CDNs. And the issue of asynchronous premise variables is solved. Furthermore, a new secure synchronization criterion is presented by leveraging the appropriate Lyapunov–Krasovskii function to realize the

H_{\infty}

performance of the system against critical-data-targeted DoS attacks. Finally, three examples are offered to confirm the efficacy of the suggested results.

本文主要研究了针对关键数据的拒绝服务（DoS）攻击下的Takagi-Sugeno （T-S）模糊复杂动态网络（cdn）的钉住同步问题。首先，提出了一种新的针对关键数据的DoS攻击方法，增强了攻击对各节点的破坏性。与大多数现有的DoS攻击模型相比，该攻击方案可以选择性地攻击关键数据，使攻击者能够对系统性能造成较大的损害。其次，针对具有随机耦合延迟的T-S模糊cdn，建立了新的钉住同步控制模型。与cdn的一般模型相比，它能更准确地描述现实世界。解决了异步前提变量的问题。此外，利用适当的Lyapunov-Krasovskii函数提出了一种新的安全同步准则，以实现系统对针对关键数据的DoS攻击的H∞性能。最后，通过三个算例验证了建议结果的有效性。

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引用次数: 0