Applied Mathematics and Computation最新文献

英文中文

Impact of interaction diversity and interlayer coupling on the evolution of human-AI cooperation 交互多样性和层间耦合对人类-人工智能合作进化的影响

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-29 DOI: 10.1016/j.amc.2025.129894

Bo Gao , Pengfei Zuo , Chengyi Xia , Tianyi Zhang , Suyalatu Dong , Chunyang Liu

In the context of a digitized society characterized by profound human-artificial intelligence (AI) interaction, the evolutionary dynamics of cooperative behavior confront novel challenges. This study develops a two-layer network evolutionary game model that couples a human decision-making layer with an AI system layer, aiming to investigate how bidirectional interlayer coupling mechanisms influence the emergence and sustainability of cooperation. We find that interlayer coupling facilitates the emergence and stabilization of cooperative behavior across both the AI and human layers. However, the efficacy of this facilitative effect is highly contingent upon the relative dependency configurations between two networks. When interaction diversity (link-strategy) is introduced within the AI layer, the system’s resilience to the temptation of defection is markedly enhanced, resulting in elevated levels of cooperation. Conversely, excessive interaction diversity within the human layer may, under certain conditions, undermine cooperative coordination, particularly in scenarios characterized by high interlayer dependency. Moreover, the AI layer exhibits substantial adaptive capacity, maintaining relatively stable behavioral patterns across varying human decision-making regimes, thereby enabling the emergence of a robust mixed equilibrium of cooperation and defection. This study proposes a computational model to explore the evolutionary dynamics of cooperation in human-AI collaborative environments, offering new insights into AI governance, multi-agent system design, and related domains.

在以人类与人工智能（AI）深度互动为特征的数字化社会背景下，合作行为的进化动力学面临着新的挑战。本研究建立了人类决策层与人工智能系统层耦合的两层网络进化博弈模型，旨在探讨双向层间耦合机制如何影响合作的产生和可持续性。我们发现，层间耦合促进了人工智能和人类层之间合作行为的出现和稳定。然而，这种促进效应的有效性在很大程度上取决于两个网络之间的相对依赖配置。当人工智能层引入交互多样性（链接策略）时，系统对背叛诱惑的抵御能力显著增强，从而提高了合作水平。相反，在某些条件下，人类层面内部过度的互动多样性可能会破坏合作协调，特别是在以高度层间依赖为特征的场景中。此外，人工智能层表现出大量的适应能力，在不同的人类决策机制中保持相对稳定的行为模式，从而使合作与背叛的强大混合均衡得以出现。本研究提出了一个计算模型来探索人类-人工智能协作环境中合作的进化动力学，为人工智能治理、多智能体系统设计和相关领域提供了新的见解。

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引用次数: 0

New method of oscillatory integrals involving two Bessel functions 涉及两个贝塞尔函数的振荡积分的新方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-29 DOI: 10.1016/j.amc.2025.129906

Hong Du , Zhong Chen

New method based on numerical steepest descent method (NSDM) is proposed for highly oscillatory integrals (HOIs) with products of two Bessel functions on [a, b]. The calculation of the HOIs is provided for the two cases a > 0 and

a = 0

. Especially under Case

a = 0

, the recurrence relation of moment functions is obtained, the key calculation of four moment functions of degree 0 is solved using the NSDM and the stability of the recurrence relation is also analyzed. Two numerical tests verified the effectiveness of the proposed method.

提出了基于数值最陡下降法（NSDM）的高振荡积分[a， b]上两个贝塞尔函数积的新方法。给出了a >； 0和a=0两种情况下hoi的计算。特别是在a=0的情况下，得到了矩函数的递归关系，利用NSDM求解了4个0阶矩函数的关键计算，并分析了递归关系的稳定性。两个数值试验验证了该方法的有效性。

引用次数: 0

A second-order unconditionally energy stable scheme for the Lifshitz-Petrich model integrated with observational data 结合观测资料的Lifshitz-Petrich模型的二阶无条件能量稳定格式

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-27 DOI: 10.1016/j.amc.2025.129914

Xiaochuan Hu , Junseok Kim , Yibao Li

In this paper, we introduce a modified Lifshitz-Petrich model that incorporates a data assimilation term. This model is used to investigate the nucleation of quasicrystalline structures in polycrystalline materials by leveraging information from observational data. Guided by the principle of feedback control, the data assimilation term drives the solution toward the observational data sampled from the reference process. Using the second-order backward differentiation formula and the scalar auxiliary variable method, we introduce an efficient numerical scheme for the modified Lifshitz-Petrich model. We employ the Fourier spectral method to achieve second-order accuracy and high computational efficiency. And we prove the numerical discrete energy is unconditionally stable. A series of numerical experiments are conducted to evaluate the efficiency and robustness of the proposed method.

在本文中，我们引入了一个包含数据同化项的改进Lifshitz-Petrich模型。该模型利用观测数据的信息来研究多晶材料中准晶结构的成核。在反馈控制原理的指导下，数据同化项将解推向从参考过程中采样的观测数据。利用二阶后向微分公式和标量辅助变量法，给出了修正Lifshitz-Petrich模型的有效数值格式。我们采用傅里叶谱方法来达到二阶精度和较高的计算效率。并证明了数值离散能量是无条件稳定的。通过一系列数值实验验证了该方法的有效性和鲁棒性。

引用次数: 0

Finite-time trajectory tracking of multi-agent systems via higher-order dynamic networks with channel damage 基于高阶动态网络的多智能体系统有限时间轨迹跟踪

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-27 DOI: 10.1016/j.amc.2025.129918

Junfeng Mao , Lilan Tu , Xianjia Wang , Fujuan Gao , Qiuyue Zhao

For multi-agent trajectory tracking, strong communication channels between agents are crucial for group motion. In this paper, using undirected and directed higher-order complex networks described by second-order simplicial complexes, we investigated finite-time trajectory tracking of multi-agent systems when communication channels are damaged. By introducing the effective and damaged rates to the first-order and second-order channels of the multi-agent networks, and employing Lyapunov stability theory, and finite-time control techniques, we proposed several theoretical sufficient conditions that enable multiple agents in the response networks with damaged channels to track the trajectories of multiple agents in the drive networks within finite time. Extensive numerical simulations were conducted not only to verify the feasibility and effectiveness of the proposed theoretical results, but also to explore the effects of first-order channel, second-order channel, random damage, deliberate damage, one-time damage, and cascade damage on the finite-time tracking performance of multi-agent systems. We found that damage to first-order channels significantly impacts the tracking performance of multi-agent systems, while damage to second-order channels has a comparatively smaller impact. Deliberate damage is more detrimental to multi-agent systems than random damage. Random damage triggers significant phase fluctuations in tracking time. The directionality makes the network more vulnerable to channel damage.

在多智能体轨迹跟踪中，智能体之间的强通信通道对群体运动至关重要。本文利用二阶简单复数描述的无向和有向高阶复杂网络，研究了通信信道被破坏时多智能体系统的有限时间轨迹跟踪问题。通过引入多智能体网络的一阶和二阶通道的有效率和损坏率，利用Lyapunov稳定性理论和有限时间控制技术，提出了几个理论充分条件，使具有损坏通道的响应网络中的多个智能体能够在有限时间内跟踪驱动网络中多个智能体的轨迹。通过大量的数值模拟，不仅验证了所提理论结果的可行性和有效性，而且探讨了一阶通道、二阶通道、随机损伤、故意损伤、一次性损伤和级联损伤对多智能体系统有限时间跟踪性能的影响。我们发现，一阶通道的损坏显著影响多智能体系统的跟踪性能，而二阶通道的损坏影响相对较小。对多智能体系统来说，故意损害比随机损害更有害。随机损伤在跟踪时间中引起显著的相位波动。方向性使网络更容易受到信道损坏。

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引用次数: 0

An alternating direction implicit method for 2D nonlinear Schrödinger equation with accelerated evaluation of Caputo derivative 二维非线性Schrödinger方程的交替方向隐式加速卡普托导数求值方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-26 DOI: 10.1016/j.amc.2025.129905

Himanshu Kumar Dwivedi , Rajeev , Shengda Zeng

We propose an efficient time-space discretization for nonlinear fractional Schrödinger equations involving Caputo tempered derivatives. A new tempered Alikhanov scheme with parameter λ is introduced, together with a fast sum-of-exponentials (SOE) implementation, reducing complexity to

O (M K_{t} \log K_{t})

and memory to

O (M \log K_{t})

. Spatial derivatives are approximated using a compact scheme, and an alternating direction implicit formulation is derived with perturbation terms for stability. A graded time mesh resolves the initial singularity, while adaptive time-stepping ensures long-time efficiency. Stability and maximum-norm error bounds are established via a discrete Grönwall inequality. Numerical tests confirm the theoretical convergence and demonstrate substantial savings in CPU time and storage over classical methods. This work presents a novel nonuniform tempered Alikhanov time-stepping framework for nonlinear tempered fractional Schrödinger equation(NL-TFSEs), combining robustness, high accuracy, and computational scalability.

我们提出了一种有效的非线性分数阶Schrödinger方程的时间-空间离散化方法。引入了一种新的带λ参数的调质Alikhanov格式，以及快速的指数和（SOE）实现，将复杂度降低到O(MKtlogKt)，内存降低到O（MlogKt）。利用紧格式对空间导数进行了近似，并导出了带有扰动项的交替方向隐式公式。渐变时间网格解决了初始奇异性，自适应时间步进保证了长时间效率。稳定性和最大范数误差边界是通过一个离散Grönwall不等式建立的。数值测试证实了理论的收敛性，并证明了与经典方法相比，在CPU时间和存储方面有很大的节省。本文提出了一种新的非均匀回火Alikhanov时间步进框架，用于非线性回火分数阶Schrödinger方程（NL-TFSEs），该框架结合了鲁棒性、高精度和计算可扩展性。

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引用次数: 0

Local and global optima: Sheaves and polynomial approximations 局部和全局最优：轴和多项式近似

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-26 DOI: 10.1016/j.amc.2025.129904

Fernando Tohmé

This paper develops a sheaf-theoretic framework to reconstruct an economic agent’s global preference optima from solutions to local decision problems. We formalize how local utility maximizations, represented as a category of problems, can be consistently glued to approximate the global utility function using a contravariant functor and sheaf properties. When only a limited number of local solutions are available, we propose polynomial approximations to construct a global utility function, ensuring minimal complexity via a Gröbner basis approach. This contribution presents a categorical characterization of global-local relationships, conditions for unique global solutions under concave utilities, and a polynomial-based method to approximate optima in general cases.

本文建立了一个从局部决策问题的解重构经济主体全局偏好最优的框架。我们形式化了如何将局部效用最大化表示为一类问题，可以使用逆变函子和束性质一致地粘合到近似全局效用函数。当只有有限数量的局部解可用时，我们提出多项式近似来构建全局效用函数，通过Gröbner基方法确保最小的复杂性。这篇文章提出了全局-局部关系的分类特征，凹效用下唯一全局解的条件，以及在一般情况下近似最优的基于多项式的方法。

引用次数: 0

Efficient diffusion for high order non-oscillatory entropy stable schemes 高阶非振荡熵稳定格式的有效扩散

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-26 DOI: 10.1016/j.amc.2025.129901

Anuradha Sahu , Prashant Kumar Pandey , Ritesh Kumar Dubey

This paper proposes an efficient approach to construct non-oscillatory entropy stable fluxes (

\hat{F}

) by adding an efficient diffusion term to the entropy conservative fluxes. Computation of proposed diffusion term does not require restrictive and logically expensive sign stability condition on high order reconstruction process or flux sign stability on high order fluxes. The diffusion term is defined as the absolute difference of non-oscillatory (

\overset{˘}{F}

) and entropy conservative fluxes (

\tilde{F}

) multiplied with sign of jump in entropy variable. The amount of diffusion is adjusted using a limiter function without compromising the entropy stability of the resulting scheme which exhibits both high resolution and the non-oscillatory property. The proposed approach is tested on various standard benchmark test problems. Numerical results demonstrate the effectiveness of the method in achieving high resolution entropy stable schemes, Moreover the scheme maintains formal order of accuracy of the lower order flux used in defining the diffusion term.

本文提出了一种构造非振荡熵稳定通量（F^）的有效方法，即在熵保守通量中加入有效扩散项。所提出的扩散项的计算不需要高阶重建过程的限制性和逻辑上昂贵的符号稳定性条件，也不需要高阶通量上的通量符号稳定性条件。扩散项定义为非振荡（F ×）和熵保守通量（F ×）的绝对差乘以熵变量的跳跃符号。扩散量使用限制函数进行调整，而不影响所得到的方案的熵稳定性，该方案具有高分辨率和非振荡性质。该方法在各种标准基准测试问题上进行了测试。数值结果证明了该方法在获得高分辨率熵稳定格式方面的有效性，并且该格式保持了用于定义扩散项的低阶通量的形式精度。

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引用次数: 0

A posteriori-driven adaptive strategy for solving inverse Cauchy problems in diffusion-reaction models 扩散反应模型中求解逆柯西问题的后验驱动自适应策略

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-24 DOI: 10.1016/j.amc.2025.129902

Hafida Hamdi , Mourad Nachaoui , Amal Bergam , Abdeljalil Nachaoui

This work addresses the inverse Cauchy problem for the modified Helmholtz equation using an alternating iterative approach. The central contribution lies in the design of novel local error indicators based on a posteriori analysis, which simultaneously assess the accuracy of the spatial discretization and the convergence behavior of the iterative algorithm. Unlike standard methods, our strategy leverages a comparative assessment of these indicators to drive an adaptive mesh refinement process. This adaptive framework ensures a more balanced distribution of computational resources, significantly reducing the numerical cost while maintaining high solution accuracy. The proposed methodology is validated through a series of synthetic and application-driven numerical experiments, demonstrating both its effectiveness and robustness in reconstructing inaccessible boundary data.

本文采用交替迭代的方法解决了修正亥姆霍兹方程的反柯西问题。其核心贡献在于基于后验分析设计了新的局部误差指标，同时评估了空间离散化的准确性和迭代算法的收敛性。与标准方法不同，我们的策略利用这些指标的比较评估来驱动自适应网格细化过程。这种自适应框架确保了计算资源的更均衡分布，在保持高解精度的同时显著降低了数值成本。通过一系列综合和应用驱动的数值实验，验证了该方法在重建不可达边界数据方面的有效性和鲁棒性。

引用次数: 0

A sampling sub-interval error-based stochastic feedback sampled-data control for nonlinear stochastic Markovian jump systems 非线性随机马尔可夫跳变系统基于抽样子区间误差的随机反馈采样数据控制

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-22 DOI: 10.1016/j.amc.2025.129895

Yingchun Wang, Siyong Song, Yunfei Mu, Huaguang Zhang

This paper addresses the exponential stabilization of nonlinear stochastic Markovian jump systems (NSMJSs) based on stochastic feedback sampled-data controllers. Firstly, a stochastic sampled-data-based switching control framework is established for NSMJSs, in which the switching controller modes do not match the system mode. The advantages are that it does not require real-time detection of system modes and relaxes the strict condition that the system mode remains unchanged between the sampling intervals. Secondly, a novel sampling sub-interval error analysis method is developed for the design of the stochastic feedback sampling controller, such that the NSMJSs are

p

-th exponentially stable, and the conditions for the maximum allowable upper bound of sampling intervals (UBOSIs) are achieved, which can not only increase the sampling intervals significantly but also decrease the computation resource. Moreover, some enhanced

p

-th exponential stabilization results for general stochastic systems are given. Compared with some existing important results, the conservatism of the UBOSIs is reduced greatly by simulation examples.

研究了基于随机反馈采样数据控制器的非线性随机马尔可夫跳变系统的指数镇定问题。首先，针对切换控制器模式与系统模式不匹配的NSMJSs，建立了基于随机采样数据的切换控制框架；它的优点是不需要实时检测系统模式，并且放宽了在采样间隔之间系统模式保持不变的严格条件。其次，针对随机反馈采样控制器的设计，提出了一种新的采样子区间误差分析方法，使随机反馈采样控制器具有p次指数稳定性，并得到了采样区间最大允许上界的条件，既能显著提高采样区间，又能减少计算资源；此外，还给出了一般随机系统的一些增强的p指数镇定结果。通过仿真算例，与已有的一些重要结果相比，UBOSIs的保守性大大降低。

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引用次数: 0

Weak degeneracy of the square of planar graphs with given girth 给定周长的平面图的平方的弱简并性

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-12-20 DOI: 10.1016/j.amc.2025.129896

Jing Ye , Miaomiao Han , Murong Xu

Bernshteyn and Lee introduced weak degeneracy, showing that its value plus one bounds various graph coloring parameters. In this paper, we prove that if G is a planar graph with maximum degree Δ and girth g, then weak degeneracy

w d (G^{2}) = Δ

holds independently under each of the following conditions: (i) Δ ≥ 16 and

g = 7

; (ii) Δ ≥ 10 and 8 ≤ g ≤ 9; (iii) Δ ≥ 6 and 10 ≤ g ≤ 11; (iv)

Δ = 5

and g ≥ 12. This work generalizes the results obtained by Ivanova in [Journal of Applied and Industrial Mathematics, 5(2)(2011), 221–230].

Bernshteyn和Lee引入了弱简并性，证明了它的值加上一个边界的各种图着色参数。在本文中，我们证明了如果G是一个最大度数Δ，周长G的平面图，那么弱简并度wd(G2)=Δ在以下条件下独立成立：(i) Δ ≥ 16且G =7；（ii） Δ ≥ 10和8 ≤ g ≤ 9；（iii） Δ ≥ 6和10 ≤ g ≤ 11；（iv） Δ=5, g ≥ 本文推广了Ivanova在[应用与工业数学学报，5(2)(2011)，221-230]中得到的结果。

引用次数: 0

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