Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

Detection of Pinning Attack in Dynamical Networks with Optimal Control Cost 具有最优控制代价的动态网络中钉住攻击检测

IF 3.9 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-11 DOI: 10.1016/j.cnsns.2026.109821

Saber Jafarizadeh, Hamideh Bour

引用次数: 0

Accelerated linearized alternating direction method of multipliers with Nesterov extrapolation Nesterov外推法乘法器的加速线性化交替方向法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-07 DOI: 10.1016/j.cnsns.2026.109818

Xin He , Nan-Jing Huang , Ya-Ping Fang

The alternating direction method of multipliers (ADMM) has been widely used for solving separable convex optimization problems. In this paper, by incorporating Nesterov-type extrapolation techniques, we propose two accelerated linearized ADMM schemes for two-block linearly constrained separable convex optimization problems, where each block of the objective function admits a composite structure consisting of a nonsmooth term and a smooth term. The proposed accelerated linearized ADMMs extend two classical Nesterov acceleration methods originally developed for unconstrained composite optimization to the linearly constrained setting. Under the assumption that one block of the objective function is strongly convex and that the gradients of the smooth components are Lipschitz continuous, we establish non-ergodic convergence rates of

O (1 / k^{2})

. Moreover, we show that the proposed methods reduce to accelerated linearized augmented Lagrangian methods (ALMs) when applied to one-block linearly constrained convex optimization problems. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed algorithms.

乘法器的交替方向法在求解可分离凸优化问题中得到了广泛的应用。本文结合nesterov型外推技术，提出了两种加速线性化ADMM方案，用于两块线性约束的可分离凸优化问题，其中目标函数的每个块允许由非光滑项和光滑项组成的复合结构。提出的加速线性化admm将最初用于无约束复合优化的两种经典Nesterov加速方法扩展到线性约束环境。假设目标函数的一个块是强凸的，光滑分量的梯度是Lipschitz连续的，我们建立了O（1/k2）的非遍历收敛速率。此外，我们还表明，当应用于单块线性约束凸优化问题时，所提出的方法可简化为加速线性化增广拉格朗日方法（ALMs）。数值实验验证了所提算法的有效性和鲁棒性。

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引用次数: 0

Analysis and numerical simulations of fractional order model of ring formation due to plant-soil negative feedback 植物-土壤负反馈形成环的分数阶模型分析与数值模拟

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-07 DOI: 10.1016/j.cnsns.2026.109820

Zubair Ahmad , Angelamaria Cardone , Francesco Giannino , Gerardo Toraldo

Vegetation ring formation is a spatial pattern observed in ecosystems influenced by plant-soil negative feedback. Classical integer-order models capture only instantaneous interactions and cannot represent the history-dependent processes shaping these dynamics. To overcome this limitation, we propose a new time-fractional reaction-diffusion problem, that extends the model of Cartenì et al. of 2012 [1], by incorporating memory effects through Caputo derivatives. The system, consisting of coupled fractional partial differential equations (FPDEs) for biomass and toxicity, is analyzed for existence and uniqueness of solutions, equilibrium states, and stability in both homogeneous and heterogeneous cases. Since the analytical solution is not available, a numerical approach has been proposed. The numerical experiments illustrate variations in ring formation throughout time and space. The study covers multiple aspects, such as the influence of the fractional derivation index κ on pattern formation, showing that when κ decreases, the biomass spreads over a larger area with fewer oscillations and amplitudes. Moreover, reducing κ has the effect of slowing down the dynamics, requiring more time to reach the equilibrium points, and causes the ring’s width to expand, which shrinks the internal ring diameter until only disks are visible as κ tends to 0.6.

植被环的形成是在植物-土壤负反馈作用下，在生态系统中观测到的一种空间格局。经典的整阶模型只捕获瞬时的相互作用，不能表示形成这些动态的依赖历史的过程。为了克服这一限制，我们提出了一个新的时间分数反应扩散问题，该问题扩展了Cartenì等人2012[1]的模型，通过Caputo导数纳入记忆效应。该系统由生物量和毒性的耦合分数阶偏微分方程（FPDEs）组成，分析了在齐次和非均相情况下解的存在唯一性、平衡状态和稳定性。由于无法得到解析解，因此提出了一种数值方法。数值实验说明了环的形成随时间和空间的变化。该研究涉及多个方面，如分数衍生指数κ对模式形成的影响，表明当κ降低时，生物量分布的面积更大，振荡和振幅更小。此外，减小κ具有减缓动力学的作用，需要更多的时间来达到平衡点，并导致环的宽度扩大，这缩小了内环直径，直到只有磁盘可见，因为κ趋于0.6。

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引用次数: 0

Secure containment control for switched nonlinear stochastic multi-agent systems under denial of service attacks 拒绝服务攻击下切换非线性随机多智能体系统的安全包容控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-06 DOI: 10.1016/j.cnsns.2026.109800

Jie Kong , Bo Zhao

This article investigates the secure containment control problem for switched nonlinear stochastic multi-agent systems (MASs) by using the mode-dependent average dwell time (MDADT) method. As a class of cyber-physical systems, MASs are vulnerable to denial of service (DoS) attacks, which can greatly degrade the control performance or even influence the stability of controlled systems. By combining the backstepping method, a secure containment control method is developed with the event-triggering mechanism. Based on the connectivity information between communication links, this method eliminates the effects of DoS attacks. In the backstepping recursive design process, the problem of “explosion of complexity” caused by the derivation of virtual control is addressed by introducing a command filter. Additionally, the event-triggering mechanism is designed in the backstepping process to effectively save the communication resources. Then, the event-triggered secure containment control policy is derived to ensure the stability of single follower and MASs under synchronous and asynchronous switchings. The followers led by multiple leaders eventually enter and keep moving in the convex hull composed of leaders. A simulation example demonstrates the effectiveness of the present secure containment control scheme.

本文利用模态相关平均停留时间（MDADT）方法研究了切换非线性随机多智能体系统的安全控制问题。MASs作为一类网络物理系统，容易受到拒绝服务攻击（DoS）的攻击，这将大大降低控制性能，甚至影响被控系统的稳定性。结合回溯法，提出了一种带有事件触发机制的安全控制方法。该方法基于通信链路间的连通性信息，消除了DoS攻击的影响。在回溯递归设计过程中，通过引入命令滤波器解决了由虚拟控制推导引起的“复杂度爆炸”问题。在回溯过程中设计了事件触发机制，有效地节省了通信资源。然后，导出了事件触发的安全包容控制策略，以保证同步和异步切换下单个follower和MASs的稳定性。在多个领导者的带领下，追随者最终进入并在由领导者组成的凸壳中不断移动。仿真实例验证了该控制方案的有效性。

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引用次数: 0

On the hydrostatic approximation of the micropolar fluid system in a thin strip domain 薄带域微极流体系统的流体静力学近似

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-05 DOI: 10.1016/j.cnsns.2026.109791

Dongxiang Chen, Qian He, Xiaoli Chen

This paper focuses on the hydrostatic approximation for the two-dimensional micropolar fluid system in a thin strip domain. We first establish the global well-posedness of a scaled anisotropic micropolar fluid system and the hydrostatic micropolar fluid system in a two-dimensional strip domain, under the assumption that the initial data are analytic and sufficiently small in the tangential variable. We then rigorously justify the convergence from the anisotropic system to the hydrostatic system within the analytic framework.

本文研究了二维微极流体系统在薄带域的流体静力学近似。首先在假设初始数据是解析的且切向变量足够小的条件下，在二维条形域建立了尺度各向异性微极流体系统和静压微极流体系统的全局适定性。然后，我们在分析框架内严格证明了从各向异性系统到流体静力系统的收敛性。

引用次数: 0

Disturbance estimator-based tracking control for fractional-order Takagi-Sugeno fuzzy switched control systems 基于扰动估计的分数阶Takagi-Sugeno模糊切换控制系统跟踪控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-05 DOI: 10.1016/j.cnsns.2026.109817

R. Vanitha , T. Satheesh , V.T. Elayabharath , Y. Ren , R. Sakthivel

This article examines the output tracking and disturbance rejection issue of fractional-order Takagi-Sugeno fuzzy switched control systems with state delay, uncertainties, and external disturbance with the assistance of a parallel-equivalent-input-disturbance estimator and a two-dimensional multi-periodic modified repetitive controller. First and foremost, the parallel-equivalent-input-disturbance concept has been laid out with the intention of minimizing the occurrence of disturbance estimation errors, wherein these errors are deemed as artificial disturbances, and an array of equivalent-input-disturbance compensator have been implemented in order to make up for them. Meanwhile, in the framework of proportional integral observer, a variable for relaxation is encompassed, thereby enhancing the precision of the disturbance estimation. Subsequently, by unifying the two-dimensional multi-periodic modified repetitive controller approach with the data gleaned from the proportional integral observer and parallel-equivalent-input-disturbance, cohesive disturbance rejection-based tracking control is built, which ensures effective tracking performance while suppressing the detrimental effects of disturbances on the system. Moreover, in light of Lyapunov stability theory, an adequate set of constraints is derived in terms of linear-matrix inequalities to assure desirable outcomes. Ultimately, numerical simulation results are shown to verify the potency of the offered control scheme.

本文研究了具有状态延迟、不确定性和外部干扰的分数阶Takagi-Sugeno模糊切换控制系统的输出跟踪和干扰抑制问题，该控制系统采用并行等效输入干扰估计器和二维多周期修正重复控制器。首先，提出了并联-等效输入-干扰的概念，目的是尽量减少干扰估计误差的发生，其中这些误差被视为人为干扰，并实施了一系列等效输入-干扰补偿器来弥补它们。同时，在比例积分观测器的框架中加入了松弛变量，从而提高了扰动估计的精度。随后，通过将二维多周期修正重复控制器方法与比例积分观测器采集的数据和并联等效输入扰动相结合，建立了基于内聚扰动抑制的跟踪控制，在保证有效跟踪性能的同时抑制了扰动对系统的不利影响。此外，根据李雅普诺夫稳定性理论，根据线性矩阵不等式导出了一组足够的约束，以保证期望的结果。最后，通过数值仿真验证了所提控制方案的有效性。

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引用次数: 0

Sigma compact pullback attractors and statistical solutions for discrete semi-dissipative nonlinear Schrödinger equations 离散半耗散非线性Schr odinger方程的Sigma紧拉吸引子和统计解

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-04 DOI: 10.1016/j.cnsns.2026.109816

Caidi Zhao , Jing Dou , Lele He , Tomás Caraballo

In this article, we study the pullback asymptotic behavior and the existence of statistical solutions for the coupled lattice system of nonlinear semi-dissipative Schrödinger equations describing a Bose-Einstein condensate with an impurity. Firstly, we prove that the generated evolution process of the solution mappings possesses a pullback attractor which pullback attracts any bounded subset of the phase space with respect to a certain mixed distance. Secondly, we establish that the process possesses a family of invariant Borel probability measures which is a statistical solution of the addressed equations. Our results reveal that the semi-dissipative lattice nonlinear Schrödinger equations satisfy the Liouville theorem, and that the Boson wave function plays the dominant role while the impurity wave function plays the subordinate role in the evolution dynamics. The approaches presented here can be extended to investigate the invariant measures and statistical solutions for other nonlinear semi-dissipative partial differential equations.

本文研究了描述含杂质玻色-爱因斯坦凝聚的非线性半耗散Schrödinger方程的耦合晶格系统的回拉渐近行为和统计解的存在性。首先，我们证明了所生成的解映射演化过程具有一个回拉吸引子，该吸引子在一定的混合距离上回拉吸引相空间的任何有界子集。其次，我们建立了该过程具有一组不变的Borel概率测度，这是所述方程的统计解。结果表明，半耗散晶格非线性Schrödinger方程满足Liouville定理，玻色子波函数在演化动力学中起主导作用，杂质波函数起次要作用。本文提出的方法可以推广到研究其他非线性半耗散偏微分方程的不变测度和统计解。

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引用次数: 0

Periodic wave propagation of a discrete diffusive vector-borne epidemic model in spatially periodic patchy environment 空间周期性斑块环境中离散扩散矢量传播流行病模型的周期波传播

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-03 DOI: 10.1016/j.cnsns.2026.109815

Xibei Jiang, Weixin Wu

In this paper, a discrete diffusive vector-borne epidemic model in a spatially periodic patchy environment is proposed. That is, in this discrete model, all parameters exhibit periodic changes with period N. We establish the basic reproduction number

R_{0}

and the critical wave speed c*. By the upper and lower-solution method and Schauder’s fixed theorem, the existence of periodic traveling wave solutions satisfying specific boundary conditions is established when

R_{0} > 1

and c ≥ c*. Additionally, the asymptotic behaviors of traveling wave solutions are given by the asymptotic spreading speed theory. By employing eigenvalue analysis of the linearized system with comparison principles, the non-existence of traveling wave solutions is established when

R_{0} \leq 1

R_{0} > 1, c < c^{*}

. The numerical simulation eventually verified the correctness of the theoretical results.

本文提出了一种空间周期性斑块环境下的离散扩散病媒传染病模型。即在该离散模型中，所有参数都以周期n为周期变化。我们建立基本再现数R0和临界波速c*。利用上下解法和Schauder固定定理，建立了当R0>；1和c ≥ c*时满足特定边界条件的周期行波解的存在性。此外，利用渐近传播速度理论给出了行波解的渐近性质。利用比较原理对线性化系统进行特征值分析，建立了当R0≤1或R0>；1,c<；c*时行波解的不存在性。数值模拟最终验证了理论结果的正确性。

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引用次数: 0

A class of feedback control problems in Bingham flow 一类Bingham流的反馈控制问题

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-03 DOI: 10.1016/j.cnsns.2026.109813

Jiangfeng Han , Yanhe Mo , Zhenhai Liu , Stanislaw Migórski

This paper investigates a system governed by the Bingham fluid model with a nonmonotone frictional slip boundary condition and a control constraint set. We first analyze the existence of feasible pairs for the system. Under suitable assumptions, the problem is reformulated as a feedback control system for a subdifferential inclusion. Using the Rothe method, we establish the existence of a solution for the associated operator inclusion involving Clarke’s subgradient and, further, prove its uniqueness. Leveraging Filippov’s and Mazur’s theorems, and convergence analysis, we derive an existence theorem for feasible pairs of the system. Finally, under appropriate hypotheses, we study the Lagrange optimal feedback control problem via a “limiting” argument and prove existence of optimal solutions.

本文研究了具有非单调摩擦滑移边界条件和控制约束集的Bingham流体模型控制系统。首先分析了系统可行对的存在性。在适当的假设下，问题被重新表述为一个次微分包含的反馈控制系统。利用Rothe方法，我们建立了涉及Clarke子梯度的关联算子包含解的存在性，并进一步证明了其唯一性。利用Filippov定理和Mazur定理，结合收敛性分析，导出了系统可行对的存在性定理。最后，在适当的假设下，通过“极限”论证研究了拉格朗日最优反馈控制问题，并证明了最优解的存在性。

引用次数: 0

Vanishing, balancing and spreading for an impulsive faecal-oral model 消失，平衡和扩散的冲动粪-口模型

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-02-02 DOI: 10.1016/j.cnsns.2026.109814

Qi Zhou , Zhigui Lin , Carlos Alberto Santos

In the transmission of faecal-oral diseases, the infected area does not always expand outward continuously. To model this phenomenon under pulse interventions, this paper proposes a free boundary problem. Our free boundary condition is governed by a nonlocal integro-differential equation, which encompasses the classical Stefan condition as a special case. First, we establish the well-posedness of the proposed problem using parabolic regularity and the contraction mapping principle. We then provide sufficient conditions for vanishing, balancing, or spreading. Finally, three numerical examples validate the theoretical results and demonstrate that this model generates more complex and realistic spatiotemporal dynamics compared to models employing the classical Stefan condition.

在粪口疾病的传播中，感染区域并不总是不断向外扩展。为了模拟脉冲干涉下的这种现象，本文提出了一个自由边界问题。我们的自由边界条件由一个非局部积分微分方程控制，该方程包含了经典的Stefan条件作为特例。首先，我们利用抛物线正则性和收缩映射原理建立了所提问题的适定性。然后，我们为消失、平衡或扩散提供充分的条件。最后，通过三个数值算例验证了理论结果，表明该模型比经典Stefan条件下的模型产生更复杂、更真实的时空动力学。

引用次数: 0

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