Applied Mathematics and Computation最新文献_第9页

Corrigendum to “An Evolutionary Game Analysis of a Dynamically Switching Zero-Determinant Strategy” [Applied Mathematics and Computation 515 (2026) 129862] “动态切换零行列式策略的进化博弈分析”的更正[应用数学与计算515 (2026)129862]

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-15 DOI: 10.1016/j.amc.2025.129898

Huaihe Huang , Ye Ye , Wei Bao , Yue Zhang , Nenggang Xie

引用次数: 0

Consensus control and optimization analysis of multi-agent system with time-varying delay based on the Lyapunov-Krasovskii functional: Novel order-reduction methods 基于Lyapunov-Krasovskii泛函的时变时滞多智能体系统的共识控制与优化分析：新型降阶方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-04 DOI: 10.1016/j.amc.2025.129870

Hang Xu , Xing-Chen Shangguan , Yun-Hao An , Hong-Zhang Wang

This paper investigates consensus control and controller-gain optimisation for multi-agent systems with time-varying delays. To mitigate the high-dimensional linear matrix inequalities (LMIs) induced by Kronecker products, two novel order-reduction methods are developed. These methods integrate the controller design and optimisation within a unified framework. These techniques simplify two zero-equation structures structures with free-weighting matrices (including a new type related to Laplacian matrix) and significantly alleviating computational dimension. A Lyapunov-Krasovskii functional is constructed to simultaneously assess and facilitate the controller design, and the proposed reductions markedly decrease conservatism in the consensus conditions. Specifically, one proposed reduction method directly yields a suitable controller without iterative optimization, whereas the other embeds a particle-swarm optimisation (PSO) strategy into the synthesis process. Furthermore, the paper considers both types of zero equations and presents a hybrid approach that combines the advantages of the two order-reduction methods. Even if the number of decision variables increases, the resulting methodology substantially reduces LMI dimensionality. Simulation studies confirm the theoretical effectiveness and applicability of the integrated control and optimization framework.

研究了时变时滞多智能体系统的共识控制和控制器增益优化问题。针对Kronecker积引起的高维线性矩阵不等式，提出了两种新的降阶方法。这些方法将控制器的设计和优化集成在一个统一的框架内。这些技术简化了两种具有自由权重矩阵的零方程结构（包括一种与拉普拉斯矩阵相关的新型结构），并显著降低了计算维数。构造了Lyapunov-Krasovskii泛函来同时评估和简化控制器设计，所提出的约简显著降低了共识条件下的保守性。具体来说，一种提出的约简方法直接产生合适的控制器，而不需要迭代优化，而另一种提出的约简方法将粒子群优化（PSO）策略嵌入到合成过程中。此外，本文考虑了这两种类型的零方程，并提出了一种结合两种降阶方法优点的混合方法。即使决策变量的数量增加了，所得到的方法也大大降低了LMI的维数。仿真研究证实了该综合控制与优化框架的理论有效性和适用性。

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引用次数: 0

Lower bounds on irregularity measure of irregular uniform hypergraphs 不规则均匀超图的不规则测度下界

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-06 DOI: 10.1016/j.amc.2025.129879

Xiaodan Chen, Yiming Zhu

For an irregular connected k-uniform hypergraph H, let Δ(H) and ρ_α(H) denote its maximum degree and α-spectral radius respectively. We bound from below

Δ (H) - ρ_{α} (H)

, an irregularity measure of H, by using the number of vertices and the diameter of H, which partially improve the work in [H. Lin, H. Guo, B. Zhou, On the α-spectral radius of irregular uniform hypergraphs, Linear Multilinear and Algebra 68 (2020) 265–277].

对于不规则连通k-均匀超图H，设Δ(H)和ρα(H)分别表示其最大度和α-谱半径。利用H的顶点数和H的直径，从下下界取H的不规则度测度Δ(H)−ρα(H)，部分改进了[H]中的功。林宏，郭宏，周斌，不规则均匀超图的α-谱半径，线性多线性，数学学报（2020），265-277。

引用次数: 0

Dynamic response of a floating elastic plate supported on a viscoelastic foundation under moving periodic load: Analytical and neural modelling 周期移动荷载作用下粘弹性基础上浮动弹性板的动力响应：分析与神经网络模型

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-05 DOI: 10.1016/j.amc.2025.129872

Susam Boral

This work examines analytically and computationally the dynamic behavior of an infinitely long floating elastic plate resting on an elastic foundation when subjected to a spatially distributed moving load that oscillates in time. The mathematical model incorporates flexural rigidity, compressive force, viscous and shear damping, and foundation stiffness. A complex dispersion relation is derived, and the presence of viscous and shear damping ensures that the dispersion relation possesses no real roots, eliminating the chance of the occurrence of wave blocking observed in non-dissipative systems. The dynamic plate response is derived via residue-based evaluation of the inverse Fourier transform at the complex poles, yielding a physically consistent plate response. Parametric studies reveal that viscous damping governs global attenuation, shear damping primarily suppresses high-frequency wave components and load speed introduces pronounced asymmetry in the plate response. The presence of an elastic foundation constant modifies both the amplitude and wavelength of the plate responses. Under specific parameter combinations, the dispersion relation develops closely spaced complex roots with very small imaginary components, leading to strongly localised wave patterns with slow spatial decay. These quasi-resonant responses persist even in the presence of damping and are highly sensitive to variations in foundation stiffness, damping coefficients, and load speed. As a complementary contribution, a Physics-Informed Neural Network (PINN) model is introduced in evaluating the response of a plate–foundation system to reproduce the dispersion relation and plate deflection efficiently, demonstrating high accuracy and a substantial reduction in computational cost. The trained model offers reliable prediction across a broad parameter space, with the full implementation provided in the Appendix. The results are relevant to hydroelastic problems involving ice sheets, floating platforms, and wave–structure interaction.

本研究分析和计算了弹性基础上的无限长浮动弹性板在受到随时间振荡的空间分布移动载荷时的动态行为。数学模型考虑了抗弯刚度、压缩力、粘性和剪切阻尼以及基础刚度。导出了一个复杂的色散关系，粘性和剪切阻尼的存在保证了色散关系没有真正的根，消除了在非耗散系统中观察到的波阻塞发生的机会。动态板响应是通过基于残差的傅立叶反变换在复杂极点的评估，产生一个物理一致的板响应。参数研究表明，粘性阻尼控制整体衰减，剪切阻尼主要抑制高频波分量，载荷速度在板响应中引入明显的不对称性。弹性基础常数的存在改变了板响应的振幅和波长。在特定的参数组合下，色散关系发展出间隔紧密的复根，虚分量非常小，导致空间衰减缓慢的强局域波形。这些准共振响应即使在存在阻尼的情况下也会持续存在，并且对基础刚度、阻尼系数和加载速度的变化高度敏感。作为补充，引入了物理信息神经网络（PINN）模型来评估板-基础系统的响应，以有效地再现色散关系和板挠度，显示出高精度和大幅降低的计算成本。经过训练的模型提供了跨广泛参数空间的可靠预测，并在附录中提供了完整的实现。这些结果与涉及冰盖、浮动平台和波浪-结构相互作用的水弹性问题有关。

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引用次数: 0

A Review on estimation of stability region for nonlinear systems 非线性系统稳定域估计的研究进展

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-11-29 DOI: 10.1016/j.amc.2025.129845

K. Mathiyalagan, A. Vignesh

The estimation of stability region for nonlinear systems are evolved into a significant research topic of literature with a variety of perspectives during the few decades. The purpose of this article is to provide a comprehensive review of the research carried out on the stability region of nonlinear systems including deterministic and stochastic systems. The methodologies for computation of stability region of nonlinear systems are briefly described and also some features, advantages and drawbacks of the proposed methods are detailed. Since stability region of nonlinear systems are important in practice, a survey of the results on stability region of nonlinear systems are useful for the researchers. Furthermore, a thorough review of around 252 articles published from 1960 to 2025 are discussed with bibliometric analysis. Finally, concluding remarks and some future directions on stability region analysis of nonlinear systems are given.

非线性系统稳定域的估计是近几十年来发展起来的一个重要的研究课题，具有多种研究视角。本文的目的是提供一个全面的研究进行了非线性系统的稳定区域，包括确定性和随机系统。简要介绍了非线性系统稳定域的计算方法，并详细介绍了各种方法的特点和优缺点。由于非线性系统的稳定区域在实际应用中具有重要意义，因此对非线性系统稳定区域的研究成果进行综述对研究人员有一定的参考价值。此外，对1960年至2025年发表的约252篇论文进行了文献计量分析。最后，对非线性系统的稳定域分析作了总结，并对今后的研究方向作了展望。

引用次数: 0

On the permanent indices of graphs 关于图的永久指标

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-09 DOI: 10.1016/j.amc.2025.129883

Tingzeng Wu , Jianxuan Luo , Yuping Gao

Let M be a matrix, the permanent index of M, defined as pind(M), is the smallest integer k for which there be a matrix M′ having nonzero permanent, every column of M′ is identical to a column of M, and every distinct column of M appears in M′ no more than k times. A graph G is defined as (k, k′)-choosable if, for every total list assignment L assigning a k-set to each vertex and a k′-set to each edge, there exists a proper vertex-edge weighting

l : V \cup E \to R

such that the value l(y) belongs to the set L(y) for all y ∈ V ∪ E, and for every pair of adjacent vertices x, x′ ∈ V,

\sum_{x \sim e} l (e) + l (x) \neq \sum_{x^{'} \sim e} l (e) + l (x^{'})

. In this paper, we show that if G is T × P₂, U × P₂, hexagonal system or a certain class of quasi-tree graphs, then permanent index of matrix A_G is 1, permanent index of matrix B_G is less than or equal to 2. Consequently, these also show the (2,2)-choosability and (1,3)-choosability of the above graphs. Furthermore, we also prove that the (1,3)-choosability of some almost complete graphs and almost complete bipartite graphs. Eventually, based on the Alon-Jaeger-Tarsi Conjecture, we conjecture the relationship between the (1,3)-choosability and the non-singularity of matrix B_G.

设M是一个矩阵，M的永久索引，定义为pind(M)，是最小的整数k，其中存在一个矩阵M ‘具有非零的永久，M ’的每一列都与M的一列相同，并且M的每一列在M '中出现不超过k次。图G被定义为（k, k ‘）可选，如果对于每一个总列表赋值L，给每个顶点赋一个k集，给每条边赋一个k ’集，存在一个适当的点边加权L:V∪E→R，使得对于所有y ∈ V∪E，对于每一对相邻顶点x， x ‘ ∈ V， L(y)属于集合L(y),∑x ~ el(E)+ L(x)≠∑x ’ ~ el(E)+ L（x '）。本文证明了如果G是T × P2， U × P2，六边形系统或一类拟树图，则矩阵AG的永久指标为1，矩阵BG的永久指标小于等于2。因此，这些也显示了上述图的(2,2)-可选择性和(1,3)-可选择性。此外，我们还证明了一些几乎完全图和几乎完全二部图的(1,3)-可选性。最后，基于Alon-Jaeger-Tarsi猜想，我们推测了矩阵BG的（1,3）可选择性与非奇异性之间的关系。

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引用次数: 0

Monthly rural-urban scaling of road accidents in England, Wales and Scotland (2019-2023) 英格兰、威尔士和苏格兰每月城乡道路交通事故比例（2019-2023年）

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-09 DOI: 10.1016/j.amc.2025.129874

Isabel Copsey , Quentin Hanley , Jack Sutton

Road traffic accidents remain a major public health challenge worldwide, with urbanisation and population density identified as key factors influencing risk. This study analyses monthly accident data from 2009 to 2023 across 632 parliamentary constituencies in England, Wales, and Scotland, using an area-normalised approach based on population density. Segmented power law models consistently identified breakpoints separating sublinear rural from superlinear urban scaling behaviours. Seasonal variation in scaling exponents was pronounced in rural regions but less evident in urban ones. Fourier-based cross-spectral analysis of yearly cycles revealed systematic phase shifts: rural exponents lagged pre-exponential factors by 4.5 months, while urban exponents were 2.7 months out of phase, producing a 5.3 month shift between rural and urban exponents. These findings highlight the importance of pre-exponentials—defined as the expected density of accidents at unit population density—as comparable descaled metrics, revealing both long-term national declines and recurring seasonal peaks. Notably, the phase offsets suggest structurally distinct causes of rural and urban accident risk, with urban regions exhibiting increasing acceleration in accident scaling, potentially linked to growth in vehicle numbers, size, and weight. Residuals, modelled with the Type I Generalised Logistic Distribution (GLD), captured skewness and heterogeneity more effectively than normal assumptions. Geospatial mapping highlighted persistent urban hotspots alongside rural and coastal constituencies with systematically lower accident densities than predicted. Together, these findings advance understanding of how density and urbanisation shape accident risk and provide evidence to support more targeted road safety interventions and policy planning.

道路交通事故仍然是世界范围内的一个重大公共卫生挑战，城市化和人口密度被确定为影响风险的关键因素。本研究采用基于人口密度的区域标准化方法，分析了2009年至2023年英格兰、威尔士和苏格兰632个议会选区的每月事故数据。分段幂律模型一致地确定了分离亚线性农村和超线性城市扩展行为的断点。尺度指数的季节变化在农村地区明显，而在城市地区不太明显。基于傅里叶的年周期交叉光谱分析揭示了系统性的相移：农村指数滞后于指数前因子4.5个月，而城市指数滞后于指数前因子2.7个月，造成城乡指数之间5.3个月的相移。这些发现强调了指数前指数的重要性——定义为单位人口密度下的预期事故密度——作为可比较的非标度指标，揭示了长期的国家下降和周期性的季节性高峰。值得注意的是，相位抵消表明农村和城市事故风险在结构上是不同的，城市地区的事故规模呈现出日益加速的趋势，这可能与车辆数量、尺寸和重量的增长有关。残差用I型广义Logistic分布（GLD）建模，比正常假设更有效地捕获偏度和异质性。地理空间地图突出了持续存在的城市热点以及农村和沿海选区，这些地区的事故密度比预测的要低。总之，这些发现促进了对密度和城市化如何影响事故风险的理解，并为支持更有针对性的道路安全干预措施和政策规划提供了证据。

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引用次数: 0

Dynamic pricing mechanisms for generative artificial intelligence models across heterogeneous scenarios: An evolutionary game and complex network approach 跨异构场景的生成式人工智能模型的动态定价机制：进化博弈和复杂网络方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-05 DOI: 10.1016/j.amc.2025.129878

Minglong Han, Yupeng Liu

Generative artificial intelligence (GAI) models have shown significant versatility and reusability in applications such as natural language generation, image synthesis, and code completion. However, when applied across industries, these models face challenges due to differences in model performance, risk tolerance, and price sensitivity. The "one-size-fits-all" pricing model not only increases the administrative burden on model providers but also diminishes the willingness of users to adopt these technologies. This paper views GAI models as a new type of data asset, combining traditional data characteristics with unique attributes. To address this, we develop a dynamic pricing framework that combines evolutionary game theory and complex network theory. By incorporating a Q-learning algorithm, a model for edge disconnection and reconnection, and a trust-based dynamic mechanism, we model the strategy evolution of both providers and demanders in the face of information asymmetry, bounded rationality, and heterogeneous network connections. The simulation results indicate that cooperation rates tend to follow an "inverted U-shaped" evolution. Among the factors influencing long-term cooperation, the continuous usage fee is found to be the most sensitive parameter. Additionally, the study examines how factors like customization costs, company size, and scenario-specific needs shape pricing strategies and market cooperation. The results highlight the importance of differentiated and flexible pricing strategies for fostering sustainable cooperation. These findings provide both a theoretical framework and empirical evidence to guide the development of adaptive and sustainable pricing strategies for GAI models.

生成式人工智能（GAI）模型在自然语言生成、图像合成和代码完成等应用中显示出显著的多功能性和可重用性。然而，在跨行业应用时，由于模型性能、风险承受能力和价格敏感性的差异，这些模型面临挑战。“一刀切”的定价模式不仅增加了模式提供者的管理负担，而且降低了用户采用这些技术的意愿。本文将GAI模型视为一种新型的数据资产，将传统的数据特征与独特的属性相结合。为了解决这个问题，我们开发了一个结合进化博弈论和复杂网络理论的动态定价框架。通过结合q -学习算法、边缘断开和重新连接模型以及基于信任的动态机制，我们模拟了在信息不对称、有限理性和异构网络连接条件下供需双方的策略演化。仿真结果表明，合作率呈“倒u型”演化。在影响长期合作的因素中，连续使用费用是最敏感的参数。此外，该研究还考察了定制成本、公司规模和特定场景需求等因素如何影响定价策略和市场合作。研究结果强调了差异化和灵活的定价策略对促进可持续合作的重要性。这些发现为指导GAI模型的适应性和可持续定价策略的发展提供了理论框架和实证证据。

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引用次数: 0

The impact of inequality preferences on the evolution of cooperation in spatial public goods games 空间公共物品博弈中不平等偏好对合作演化的影响

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-08 DOI: 10.1016/j.amc.2025.129886

Xingyu An , Xiaogang Li , Wei Wang , Shulan Li , Jiuming Feng , Lei Shi

Evolutionary game theory has revealed powerful mechanisms for the emergence of cooperation, but it often falls short in explaining human behavior because it neglects psychological traits that are well documented empirically. One such trait is concern for inequality, yet its evolutionary consequences remain unclear. We extend classic payoff-based selection by incorporating inequality preferences, characterised by two parameters: attitudes (inequality-averse vs inequality-seeking) and sensitivity (the weight placed on disparities). Relative to indifference, we find that inequality-averse populations achieve the highest cooperation at intermediate sensitivity, while inequality-seeking populations promote cooperation when sensitivity is either very low or very high. The mechanism lies in spatial dynamics: inequality preferences raise the effective fitness of cooperators at the boundary with defectors, driving cluster expansion. Thus, social preferences not only shape individual decisions but also transform evolutionary outcomes, linking behavioral evidence to theory and revealing inequality as a potent force sustaining cooperation.

进化博弈论揭示了合作产生的强大机制，但它在解释人类行为时往往不足，因为它忽略了有充分经验证明的心理特征。其中一个特征是对不平等的关注，但其进化后果尚不清楚。我们通过纳入不平等偏好来扩展经典的基于收益的选择，不平等偏好以两个参数为特征：态度（反对不平等vs寻求不平等）和敏感性（对差异的权重）。相对于冷漠，我们发现不平等厌恶人群在中等敏感性下的合作程度最高，而不平等寻求人群在非常低或非常高的敏感性下都促进了合作。其机制在于空间动力学：不平等偏好提高了合作者与叛逃者边界的有效适合度，从而推动集群扩张。因此，社会偏好不仅塑造了个人的决定，也改变了进化的结果，将行为证据与理论联系起来，揭示了不平等是维持合作的强大力量。

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引用次数: 0

Efficient linear implicit invariant-preserving fourth-order numerical scheme for damped nonlinear fourth-order wave equation 阻尼非线性四阶波动方程的有效线性隐式保持不变的四阶数值格式

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-05-01 Epub Date: 2025-12-05 DOI: 10.1016/j.amc.2025.129880

Jianqiang Xie , Zhiyue Zhang

In this study, an invariant-preserving linear implicit finite difference method (LIFDM) for damped nonlinear fourth-order wave equation (DNFOWE) is constructed. Firstly, by introducing the auxiliary variables (AVs), the DNFOWE is transformed into an equivalent system of equations with a first-order temporal derivative. Then a decoupled linear implicit invariant-preserving fourth-order difference scheme is designed for the resulting equations. The strategy decreases the amount of storage demanded for the unknowns to be calculated thereby enhancing the efficiency. Subsequently, the discrete invariant property and theoretical analyses of the present algorithm are explored. To our knowledge, the present work marks the first instance of deriving unconditional error estimates for the unknown variables in discrete L^∞-norm via energy analysis and mathematical induction. The main novelty of the scheme is invariant-preserving, linear implicit decoupled and suitable for long-duration computations. Eventually, some representative examples are showcased to substantiate the theoretical findings and dynamic behaviors of the presented algorithm.

本文构造了一种求解阻尼非线性四阶波动方程的保持不变的线性隐式有限差分法。首先，通过引入辅助变量（AVs），将DNFOWE转化为具有一阶时间导数的等价方程组；然后对得到的方程设计了一个解耦的线性隐式保持不变的四阶差分格式。该策略减少了待计算未知数所需的存储量，从而提高了效率。随后，对该算法的离散不变量性质和理论分析进行了探讨。据我们所知，目前的工作标志着通过能量分析和数学归纳法对离散L∞范数中的未知变量导出无条件误差估计的第一个实例。该方案的主要新颖之处在于保持不变性、线性隐式解耦和适合长时间计算。最后，给出了一些有代表性的算例来验证所提算法的理论发现和动态行为。

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引用次数: 0