Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

A very simple, efficient and accurate dynamic interpolation BFGS algorithm for three-dimensional moment of fluid method 一个非常简单、高效、准确的动态插值BFGS算法用于三维流体矩法

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.cnsns.2026.109755

Deng Wang , Zupeng Jia

The Moment of Fluid (MOF) method is a widely used and accurate interface reconstruction method. It performs iterations to solve an implicit nonlinear optimization problem to obtain the optimal approximate interface. As far as we know, the current optimization algorithms employed in MOF methods all directly minimize the implicit objective function, and the interface reconstruction procedure has to be executed for each calculation of the objective function, which is very expensive. There have been numerous measures to improve the computational efficiency, accuracy and robustness of the MOF method, but we will achieve the improvements from a new perspective. In this paper, a very simple, efficient and accurate dynamic interpolation BFGS (DIBFGS) algorithm is proposed, based on the classical Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The new algorithm introduces a dynamic interpolation function to approximate the implicit objective function during the optimization process. The dynamic interpolation function is explicit and the interpolation nodes utilized for constructing it are dynamically selected from a gradually expanding set of candidate interpolation nodes. The new algorithm minimizes the dynamic interpolation function instead of the original objective function, thus the number of original objective function calculations will be significantly reduced and the computational efficiency can be improved. Moreover, in previous MOF methods, the gradient of the objective function involved in the iterations are either estimated by finite difference approximation or derived analytically with complex analyses, both of which require interface reconstruction. On the contrary, our algorithm uses the analytical gradient of the interpolation function, which is also explicit and quite easy to calculate. Then the accuracy, convergence rate as well as robustness of the iteration process can be improved. Last but not least, our algorithm is very simple and easy to code. A variety of numerical tests collectively show that compared to the MOF method using BFGS algorithm, our new method can not only effectively reduce the number of original objective function calculations and computational time, but also improve the accuracy and robustness particularly in complex cases with large interface deformations.

流体矩法（MOF）是一种应用广泛、精度较高的界面重建方法。通过迭代求解隐式非线性优化问题，得到最优近似接口。据我们所知，目前MOF方法中采用的优化算法都是直接最小化隐式目标函数，每次计算目标函数都要执行界面重构过程，成本非常高。为了提高MOF方法的计算效率、准确性和鲁棒性，已经有了许多措施，但我们将从一个新的角度来实现这些改进。本文在经典的BFGS （Broyden-Fletcher-Goldfarb-Shanno）算法的基础上，提出了一种简单、高效、精确的动态插值BFGS （DIBFGS）算法。该算法在优化过程中引入动态插值函数来逼近隐式目标函数。动态插值函数是显式的，用于构造动态插值函数的插值节点是从逐渐扩大的候选插值节点集中动态选择的。新算法以动态插值函数代替原目标函数最小化，从而大大减少了原目标函数的计算次数，提高了计算效率。此外，在以往的MOF方法中，迭代所涉及的目标函数的梯度要么通过有限差分逼近估计，要么通过复分析解析推导，这两种方法都需要重建界面。相反，我们的算法使用插值函数的解析梯度，这也是显式的，很容易计算。从而提高迭代过程的精度、收敛速度和鲁棒性。最后但并非最不重要的是，我们的算法非常简单，易于编码。各种数值试验共同表明，与采用BFGS算法的MOF方法相比，新方法不仅可以有效减少原始目标函数的计算次数和计算时间，而且可以提高精度和鲁棒性，特别是在具有大界面变形的复杂情况下。

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引用次数: 0

Optimal consensus control for multiagent networks of distributed parameter systems 分布参数系统多智能体网络的最优一致性控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.cnsns.2026.109745

Jin You , Yan Li , Xiangyang Cao , YangQuan Chen

In this paper, diffusive representation (DR) is shown to be effective in addressing optimal consensus control problems in DPS-based multiagent systems (MASs) for both leader-following and leaderless cases, leading to significant advancements in meeting engineering requirements, facilitating cost savings and enhancing efficiency for optimal performance. First, the concept of DR approach is introduced to transform the original causal convolution pseudo-differential operator (PDO) into DPS, exhibiting infinite dimensional properties. Second, the proposed spatial product operation helps establish a theoretical system of the converted DPSs, including the linear representation for state space model, the Lyapunov functions and the reformulation of LQR optimal control problem with generalized performance indexes. Furthermore, the inverse optimality technique is conducted to develop distributed strategies for the cooperative control of the distributed parameter multiagent systems using DR approach, and derive the solution of globally optimal LQR problem. Finally, fractional-order multiagent systems (FOMASs) to both leaderless and leader-follower UAV formation control scenarios are presented to validate the effectiveness of the proposed results.

在本文中，扩散表示（DR）在解决基于dps的多智能体系统（MASs）中领导者跟随和无领导者情况下的最优共识控制问题上是有效的，从而在满足工程要求，促进成本节约和提高效率以实现最佳性能方面取得了重大进展。首先，引入DR方法的概念，将原因果卷积伪微分算子（PDO）转化为具有无限维特性的DPS。其次，提出的空间积运算有助于建立转换后的dps的理论体系，包括状态空间模型的线性表示、Lyapunov函数和广义性能指标的LQR最优控制问题的重新表述。在此基础上，利用逆最优性技术开发了分布式多智能体系统协同控制的分布式策略，并推导了全局最优LQR问题的解。最后，将分数阶多智能体系统（FOMASs）应用于无领导和领导-跟随无人机编队控制场景，验证了所提结果的有效性。

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引用次数: 0

Strict mittag-leffler stability of fractional unperturbed systems 分数阶无摄动系统的严格mittag-leffler稳定性

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.cnsns.2026.109757

Dilara Karslıoğlu , Coşkun Yakar

This study concentrates on investigating strict Mittag-Leffler stability for fractional differential systems operating without external perturbations. The focus is on unperturbed systems, where the dynamics are solely intrinsic and free from outside influences. Utilizing Caputo fractional derivatives alongside a suitably constructed Lyapunov-like functional, we establish new sufficient conditions guaranteeing that solutions converge strictly to the equilibrium point. The findings offer a sharper and more detailed description of stability than classical asymptotic notions, emphasizing the significance of memory properties inherent in fractional-order models. Several illustrative examples are provided to demonstrate the practical applicability and robustness of the derived criteria in such autonomous systems.

本文主要研究无外部扰动的分数阶微分系统的严格Mittag-Leffler稳定性。重点是无扰动系统，其中动态完全是内在的，不受外界影响。利用Caputo分数阶导数和适当构造的lyapunov泛函，我们建立了保证解严格收敛于平衡点的新的充分条件。这些发现提供了比经典渐近概念更清晰、更详细的稳定性描述，强调了分数阶模型中固有的记忆特性的重要性。给出了几个说明性的例子来证明所导出的准则在这种自治系统中的实际适用性和鲁棒性。

引用次数: 0

Dynamic analysis of a stochastic three species predator-prey model with intraguild predation and predator-switching 具有内捕食和捕食切换的随机三物种捕食-食饵模型的动态分析

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.cnsns.2026.109748

Yonghui Lv , Hui Wang , Jian Ding , Quanxin Zhu

In this paper, we consider the effects of intraguild predation, predator-switching, and stochastic factors on the dynamics of a stochastic three species predator-prey model. It is assumed that the interactions between the two predators and the prey follow the Holling type II functional response. Meanwhile, the predation between the top predator and the intermediate predator is governed by a preference mechanism modulated by prey density. The existence of positive solutions and the boundedness are established. The analysis of the Lyapunov exponents reveals that intraguild predation and predator-switching can maintain species coexistence under certain conditions. Furthermore, we provide a comprehensive classification of persistence and extinction for all populations. Finally, we conduct numerical simulations to verify the theoretical results by employing the Monte Carlo method to calculate the Lyapunov exponents of the two-dimensional boundary measures.

本文考虑了一个三种随机捕食-食饵模型中捕食、切换和随机因素对动力学的影响。假设两种捕食者与猎物之间的相互作用遵循Holling II型功能反应。同时，顶端捕食者和中间捕食者之间的捕食受猎物密度调节的偏好机制支配。建立了正解的存在性和有界性。Lyapunov指数分析表明，在一定条件下，种群内捕食和捕食者转换可以维持物种共存。此外，我们还提供了所有种群的持续和灭绝的综合分类。最后，利用蒙特卡罗方法计算二维边界测度的Lyapunov指数，进行数值模拟验证理论结果。

引用次数: 0

Adaptive optimal-time consensus control for stochastic multi-agent systems with layered control approach 基于分层控制方法的随机多智能体系统自适应最优时一致性控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.cnsns.2026.109701

Guanli Xiao , Lulu Ren , Yi Guan

This paper investigates the adaptive optimal-time consensus control for stochastic multi-agent systems by employing predefined-time control techniques and the layered control approach. The objective is to develop an efficient methodology for achieving optimal-time consensus, along with systematic approaches for control protocol design and parameter matching. Firstly, a novel layered control structure is proposed, where the upper layer consists of the multi-agent system, and the lower layer serves as a settling-time indicator monitoring system. Secondly, two adaptive fault-tolerant predefined-time consensus control protocols are developed for stochastic multi-agent systems subject to actuator faults. By determining the optimal settling-time of the monitoring system, the time parameters of the control protocol are dynamically adjusted to ensure that the actual settling-time aligns with the optimal value. Within this control framework, the optimal-time consensus problem is transformed into minimizing an independent index function and adjusting the settling-time, thereby significantly simplifying the design process of control protocols and the computational complexity associated with optimal time determination. Finally, a multi-motor system is presented to validate the theoretical analysis.

本文采用预定义时间控制技术和分层控制方法，研究随机多智能体系统的自适应最优时间一致性控制。目标是开发一种有效的方法来实现最佳时间共识，以及控制协议设计和参数匹配的系统方法。首先，提出了一种新的分层控制结构，其中上层为多智能体系统，下层为沉降时间指标监控系统。其次，针对执行器故障的随机多智能体系统，提出了两种自适应容错的预定义时间共识控制协议。通过确定监测系统的最优沉降时间，动态调整控制协议的时间参数，保证实际沉降时间与最优值一致。在该控制框架中，将最优时间一致性问题转化为最小化独立指标函数和调整沉降时间，从而大大简化了控制协议的设计过程和与最优时间确定相关的计算量。最后，给出了一个多电机系统来验证理论分析。

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引用次数: 0

Forward and backward problems for abstract time-fractional Schrödinger equations 抽象时间分数Schrödinger方程的正向和后向问题

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-16 DOI: 10.1016/j.cnsns.2026.109758

Salah-Eddine Chorfi , Fouad Et-Tahri , Lahcen Maniar , Masahiro Yamamoto

We investigate forward and backward problems associated with abstract time-fractional Schrödinger equations

i^{ν} \partial_{t}^{α} u (t) + A u (t) = 0

, α ∈ (0, 1) ∪ (1, 2) and ν ∈ {1, α}, where A is a self-adjoint operator with compact resolvent on a Hilbert space H. This kind of equation, which incorporates the Caputo time-fractional derivative of order α, models quantum systems with memory effects and anomalous wave propagation. We first establish the well-posedness of the forward problems in two scenarios: (

ν = 1

, α ∈ (0, 1)) and (

ν = α

, α ∈ (0, 1) ∪ (1, 2)). Then, we prove well-posedness and stability results for the backward problems depending on the two cases

ν = 1

and

ν = α

. Our approach employs the solution’s eigenvector expansion along with the properties of the Mittag-Leffler functions, including the distribution of zeros and asymptotic expansions. Finally, we conclude with a discussion of some open problems.

我们研究了与抽象时间分数Schrödinger方程相关的前向和后向问题，其中ν∂tαu(t)+Au(t)=0, α ∈ (0,1)∪(1,2)和ν ∈ {1，α}，其中A是Hilbert空间h上具有紧解的自伴随算子。这类方程包含了阶α的Caputo时间分数导数，模拟了具有记忆效应和异常波传播的量子系统。我们首先建立了（ν=1, α ∈ （0,1））和(ν=α, α ∈ （0,1)∪(1,2)）两种情形下正问题的适定性。然后，我们证明了依赖于ν=1和ν=α两种情况的后向问题的适定性和稳定性结果。我们的方法采用了解的特征向量展开以及Mittag-Leffler函数的性质，包括零的分布和渐近展开。最后，我们对一些有待解决的问题进行了讨论。

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引用次数: 0

Implicit-explicit time discretization with complex time for parabolic equations 抛物型方程的复时间隐显时间离散化

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109743

Henghui Tang, Daopeng Yin, Xiaohao Zhang, Liquan Mei

This paper presents a novel high-order time discretization scheme on the time complex plane for parabolic equations. The innovation of this method lies in its ability to straightforwardly construct temporal discretization schemes of arbitrary order while achieving stability comparable to explicit Runge-Kutta methods, and simultaneously enhancing computational efficiency without compromising stability. By employing a matrix construction method, we unify the characterization of the stability region for both ordinary differential equations and partial differential equations. We prove the L² stability and arbitrary-order convergence of the method. Numerical experiments demonstrate that, compared to explicit Runge-Kutta methods, the proposed scheme improves computational efficiency. This method offers an efficient and accurate solution for applications with stringent precision.

提出了抛物型方程在时间复平面上的一种新的高阶时间离散格式。该方法的创新之处在于能够直接构建任意阶的时间离散化格式，同时获得与显式龙格-库塔方法相当的稳定性，同时在不影响稳定性的情况下提高计算效率。利用矩阵构造的方法，统一了常微分方程和偏微分方程稳定域的表征。证明了该方法的L2稳定性和任意阶收敛性。数值实验表明，与显式龙格-库塔方法相比，该方法提高了计算效率。该方法为精度要求高的应用提供了高效、准确的解决方案。

引用次数: 0

Finite-time sliding mode secure control with dynamic-memory event-triggered for semi-Markov jump systems subject to hybrid network attacks and general transition probabilities 受混合网络攻击和一般转移概率影响的半马尔可夫跳跃系统的动态记忆事件触发有限时间滑模安全控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109658

Yajing Li, Dan Peng, Yuechao Ma

This study focuses on the issue of memory-based dynamic event-triggered secure sliding mode control (SMC) for semi-Markov jump systems (S-MJSs) under false data injection (FDI) attacks and aperiodic denial-of-service (DoS) attacks. Firstly, a mode-dependent state observer is designed to obtain system state estimates. By incorporating historical transmission data and auxiliary dynamic variables into a dynamic-memory event-triggered mechanism (DMETM), the transmission efficiency can be optimized and bandwidth resources can be saved. Secondly, an observer-based SMC law is formulated based on event-triggered state information to guarantee that the system state trajectory can achieve finite-time reachability. Moreover, by constructing a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), the sufficient conditions are derived for the stochastic finite-time bounded (SFTB) realization of S-MJSs with H_∞ performance under various network attacks and in the presence of uncertain or unknown transition probabilities (TPs). Through the designed collaborative scheme, the triggering parameters, controller and observer gain matrices can be derived. At last, two simulation examples are employed to verify the validity and practicality of the introduced approach.

本文研究了半马尔可夫跳变系统（S-MJSs）在虚假数据注入（FDI）攻击和非周期性拒绝服务（DoS）攻击下基于记忆的动态事件触发安全滑模控制（SMC）问题。首先，设计了依赖于模式的状态观测器来获得系统状态估计。通过将历史传输数据和辅助动态变量整合到动态记忆事件触发机制（DMETM）中，可以优化传输效率，节省带宽资源。其次，基于事件触发状态信息，构造了基于观测器的SMC律，保证系统状态轨迹达到有限时间可达性；此外，通过构造一个模式相关的分段Lyapunov-Krasovskii泛函（LKF），推导了在各种网络攻击和存在不确定或未知转移概率（TPs）的情况下，具有H∞性能的s - mjs的随机有限时间有界（SFTB）实现的充分条件。通过设计的协同方案，推导出触发参数、控制器和观测器增益矩阵。最后，通过两个仿真实例验证了所提方法的有效性和实用性。

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引用次数: 0

Reinforcement learning-based prescribed-time event-triggered optimal consensus control for multi-agent systems with privacy preservation 具有隐私保护的多智能体系统基于强化学习的规定时间事件触发最优共识控制

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109680

Peng Sun , Xiaona Song , Shuai Song , Inés Tejado , Qingtao Wu

In this paper, the reinforcement learning (RL)-based prescribed-time optimal consensus control issue is studied for multi-agent systems (MASs) with privacy-preserving. Given agents that incur confidential state messages that demand guarding in the user-defined time, a preassigned-time mask function is delicately implemented to enhance encryption capabilities and alleviate the effect on system performance. In addition, with the aid of a time-varying constraint issue, an adaptive prescribed-time optimal consensus control scheme is developed to realize the specified steady-state precision and settling time. Technically, an emerging intermediate variable is constructed to address the issue of unknown control coefficients, allowing for the smooth execution of the optimized controller within the RL-based backstepping procedure. Subsequently, the drawback of semi-global boundedness of the error surface caused by dynamic surface control can be removed by the use of the novel Lyapunov-like energy function. Notably, needless resource consumption and monitoring criteria were considerably avoided by utilizing a distinctive hybrid threshold event-triggered mechanism. Upon the final results, it can be guaranteed that the whole variables in the closed-loop MASs remain bounded, and the prescribed time constraints of the protected consensus errors are quantified. Herein, the efficacy of the established tactic is demonstrated through a practical example.

针对具有隐私保护的多智能体系统，研究了基于强化学习（RL）的约定时间最优共识控制问题。对于产生需要在用户定义时间内进行保护的机密状态消息的代理，可以精确地实现预分配时间掩码函数，以增强加密功能并减轻对系统性能的影响。此外，借助时变约束问题，提出了一种自适应规定时间最优一致控制方案，以实现指定的稳态精度和稳定时间。从技术上讲，一个新兴的中间变量被构造来解决未知控制系数的问题，允许优化控制器在基于rl的反演过程中顺利执行。随后，利用新颖的类李雅普诺夫能量函数消除了动态曲面控制导致误差曲面半全局有界的缺点。值得注意的是，通过使用独特的混合阈值事件触发机制，可以在很大程度上避免不必要的资源消耗和监控标准。在最终结果的基础上，保证了闭环质量中所有变量保持有界，并对保护共识误差的规定时间约束进行了量化。在此，通过实例验证了所建立策略的有效性。

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引用次数: 0

Efficient Halpern inertial extragradient-based algorithms for solving constrained pseudomonotone VIP systems and their application in blurred image recovery 基于高效Halpern惯性外聚的约束伪单调VIP系统求解算法及其在模糊图像恢复中的应用

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109749

Lu-Chuan Ceng , Prasit Cholamjiak , André A. Keller , Papinwich Paimsang , Jen-Chih Yao , Xiaopeng Zhao

This paper is mainly centered on studying iterative algorithms for tackling a pair of pseudomonotone VIPs with MVIP and CFPP constraints in a uniformly smooth Banach space E possessing 2-uniform convexity. Here the MVIP, VIP and CFPP denote a monotone variational inclusion problem, a variational inequality problem and a common fixed-point problem of a relatively asymptotically-nonexpansive mapping and a finite family of relatively-nonexpansive mappings, respectively. We design and discuss Halpern inertial extragradient-like approach for this pair of pseudomonotone VIPs with MVIP and CFPP constraints in E through Tseng’s extragradient technique with proximal-contraction term. The strongly convergent results for the proposed algorithms are derived through certain suitable postulations. Applied to image restoration, the method effectively reconstructs blurred and noisy images with high SNR and SSIM.

本文主要研究了在具有2-一致凸性的一致光滑Banach空间E中处理一对具有MVIP和CFPP约束的伪单调vip的迭代算法。其中，MVIP、VIP和CFPP分别表示相对渐近非扩张映射和有限族相对非扩张映射的单调变分包含问题、变分不等式问题和公共不动点问题。我们通过Tseng的近端收缩项的超梯度技术，设计并讨论了E中具有MVIP和CFPP约束的伪单调vip对的Halpern惯性类超梯度方法。通过适当的假设，得到了该算法的强收敛结果。将该方法应用于图像恢复，可以有效地重建具有高信噪比和SSIM的模糊和噪声图像。

引用次数: 0

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