Applied Mathematics and Computation最新文献

英文中文

Performances and correlations of centrality measures in complex networks 复杂网络中中心性测度的性能和相关性

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-02 DOI: 10.1016/j.amc.2026.129972

Yilin Bi, Xinshan Jiao, Tao Zhou

Numerous centrality measures have been proposed to evaluate the importance of nodes in networks, yet comparative analyses of these measures remain limited. Based on 80 real-world networks, we conducted an empirical analysis of 16 representative centrality measures. In general, node rankings produced by different measures show moderate to high correlations. We identified two distinct communities: one comprising 4 measures and the other comprising 7. Measures within the same community exhibit exceptionally strong pairwise correlations (all exceeding 0.7 as measured by Kendall’s τ). In contrast, the remaining five measures display markedly different behavior, showing weak correlations not only among themselves but also with the other measures. This suggests that each of these five measures likely captures unique properties of node importance. Using the Susceptible-Infected-Recovered (SIR) epidemic spreading model, we evaluated the performance of those considered measures. We found that LocalRank, Subgraph Centrality, and Katz Centrality perform best at identifying the most influential single node. In contrast, Leverage Centrality, Collective Influence, and Cycle Ratio excel at identifying influential node sets. Interestingly, despite using the same dynamical process, the rankings of the 16 centrality measures in identifying a single influential node versus an influential node set are negatively correlated. This reinforces our conviction that there is no one-size-fits-all centrality measure. We further showed that measures generating spatially clustered influential nodes tend to perform better in identifying a single influential node, while measures producing influential nodes with larger distances between them are likely to excel in an identifying influential node set.

已经提出了许多中心性度量来评估网络中节点的重要性，但对这些度量的比较分析仍然有限。基于80个真实网络，我们对16个具有代表性的中心性测度进行了实证分析。通常，由不同度量产生的节点排名显示出中度到高度的相关性。我们确定了两个不同的社区：一个包括4个措施，另一个包括7个措施。同一群落内的测量显示出异常强的两两相关性（均超过0.7，由肯德尔τ测量）。相比之下，其余五个措施表现出明显不同的行为，表现出弱相关性，不仅在他们之间，而且与其他措施。这表明这五个度量中的每一个都可能捕获节点重要性的独特属性。使用易感-感染-恢复（SIR）流行病传播模型，我们评估了这些考虑措施的性能。我们发现LocalRank、子图中心性和Katz中心性在识别最具影响力的单个节点方面表现最好。相比之下，杠杆中心性、集体影响力和周期比率擅长识别有影响力的节点集。有趣的是，尽管使用相同的动态过程，在确定单个影响节点和影响节点集时，16个中心性指标的排名是负相关的。这加强了我们的信念，即没有放之四海而皆准的中心性衡量标准。我们进一步表明，产生空间聚类影响节点的度量往往在识别单个影响节点方面表现更好，而产生具有较大距离的影响节点的度量可能在识别影响节点集方面表现更好。

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引用次数: 0

Distributed tracking of high-order nonlinear multi-agent systems perturbed by second-order moment processes 二阶矩扰动下高阶非线性多智能体系统的分布式跟踪

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-09 DOI: 10.1016/j.amc.2026.129986

Wuquan Li, Yanzhu Jiang, Meiqiao Wang, Hui Wang

This paper studies the distributed tracking for the nonlinear multi-agent systems perturbed by second-order moment processes. What makes the case here unique from the prior results is that on the one hand, the system is more practical than those with white noise since it is more in line with practical engineering applications, and on the other hand, the system has inherently nonlinear distinguishing from those with second-order moment processes. In this paper, a distributed tracking controller is designed by employing the algebraic graph theorem and the distributed backstepping method, in which, extensive computational skills are taken to offset the difficulties from the system’s high-order. Furthermore, by using stochastic control theory, the tracking errors can be adjusted to an arbitrarily small value while all the states of the closed-loop system composed by the multi-agent systems are bounded in probability. At last, a simulation example with three agents demonstrates the effectiveness of the distributed tracking controller.

研究了二阶矩过程扰动下非线性多智能体系统的分布式跟踪问题。与先前结果不同的是，一方面，该系统比具有白噪声的系统更实用，因为它更符合实际工程应用，另一方面，该系统与具有二阶矩过程的系统具有固有的非线性区别。本文采用代数图定理和分布式反演方法设计了分布式跟踪控制器，利用大量的计算技巧来抵消系统高阶性带来的困难。利用随机控制理论，在多智能体系统组成的闭环系统的所有状态都有概率界的情况下，跟踪误差可以调整到任意小的值。最后，通过三个智能体的仿真实例验证了分布式跟踪控制器的有效性。

引用次数: 0

Coevolution modeling for network public opinion with bidirectional feedback mechanism 基于双向反馈机制的网络舆情协同进化模型

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-06 DOI: 10.1016/j.amc.2026.130008

Yinxin Chang , Xiaojuan Cheng , Yalun Wu , Peng Wu , Gang Li

The evolution of network public opinion arises from strategic interactions among key actors. While existing literature predominantly emphasizes the unidirectional influence of the information environment on actors’ strategies, it often overlooks the bidirectional feedback mechanism through which strategies and the environment co-evolve.

To address this gap, we propose a novel COEVOLUTION framework (COEVOLUtionary game wiTh InfOrmatioN ecology theory), which integrates information ecology theory with coevolutionary game modeling. Specifically, we identify three fundamental elements, information, actors (including influencers and managers), and the information environmentbased on information ecology theory. We then explicitly model the coevolutionary dynamics between actors’ strategies and the evolving information environment driven by a bidirectional feedback mechanism. Finally, we employ Lyapunov’s first method to analyze system stability, mapping the resulting equilibria to real-world public opinion scenarios. Simulation results demonstrate that the bidirectional feedback mechanism slows the pace of opinion evolution while amplifying the influence of strategic behavior on reshaping the information environment. These findings demonstrate the importance of incorporating bidirectional feedback mechanism into intervention design and offer practical guidance for the governance of network public opinion.

网络舆论的演变源于关键行动者之间的战略互动。现有文献主要强调信息环境对行为者策略的单向影响，但往往忽视了策略与环境共同演化的双向反馈机制。为了解决这一差距，我们提出了一个新的协同进化框架（信息生态学的协同进化博弈理论），它将信息生态学理论与协同进化博弈模型相结合。具体而言，基于信息生态学理论，我们确定了三个基本要素：信息、行动者（包括影响者和管理者）和信息环境。然后，我们明确地建立了参与者的策略与双向反馈机制驱动的不断变化的信息环境之间的共同进化动力学模型。最后，我们采用Lyapunov的第一种方法来分析系统稳定性，将结果均衡映射到现实世界的公众舆论场景。仿真结果表明，双向反馈机制减缓了意见演变的速度，同时放大了战略行为对信息环境重塑的影响。这些发现证明了将双向反馈机制纳入干预设计的重要性，并为网络舆情治理提供了实践指导。

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引用次数: 0

Global dynamics of generalized Duffing oscillators with global centers 具有全局中心的广义Duffing振子的全局动力学

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-06 DOI: 10.1016/j.amc.2026.130007

Gabriel Rondón , Nasrin Sadri

This study provides a comprehensive investigation of the generalized Duffing oscillator

\dot{x} = y, \dot{y} = - α y - ϵ x^{m} - σ x,

where

α, σ \in R

, ϵ ≠ 0 and m ≥ 1. We establish a complete topological classification of the phase portraits for all m ≥ 1 and all real parameter values. A key finding is the existence of global centers when the linear damping vanishes (

α = 0

), with explicit conditions given for both linear (

m = 1

) and nonlinear (m > 1) cases. To achieve this classification, we employ quasi-homogeneous blow-up techniques adapted to arbitrary degree m, overcoming the limitations of classical directional blow-up methods that typically require case-by-case analysis. In the conservative limit

α = 0

, we fully resolve the center–focus problem and characterize the rich structure of homoclinic and heteroclinic cycles that organize the phase space. These results provide a unified framework for understanding the global dynamics of Duffing-type oscillators and identify the precise parameter regimes where purely periodic, conservative behavior emerges.

本文全面研究了广义Duffing振子x˙=y,y˙= - α˙y−ϵxm−σx，其中α，σ∈R, λ ≠ 0,m ≥ 1。我们建立了所有m ≥ 1和所有实参数值的相位肖像的完整拓扑分类。一个关键的发现是当线性阻尼消失（α=0）时全局中心的存在，对于线性（m=1）和非线性（m >； 1）情况给出了明确的条件。为了实现这种分类，我们采用了适用于任意m度的准齐次爆破技术，克服了经典定向爆破方法通常需要逐个分析的局限性。在保守极限α=0下，充分解决了中心焦点问题，刻画了组织相空间的同斜环和异斜环的丰富结构。这些结果为理解duffing型振子的全局动力学提供了一个统一的框架，并确定了纯周期、保守行为出现的精确参数体系。

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引用次数: 0

Ramsey numbers of generalized fans versus multiple cliques 拉姆齐球迷数量vs多个小团体

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-05 DOI: 10.1016/j.amc.2026.129985

Ze Wang, Yanbo Zhang

Let r(G, H) denote the Ramsey number for two graphs G and H. The notation nH represents the union of n disjoint copies of H, and

K_{1} + n H

denotes the graph obtained by joining a new vertex to every vertex in nH. Let

h = | V (H) |

and

ℓ = r (K_{p}, H)

. Hamm, Hazelton, and Thompson (Discrete Appl. Math., 2021) proved that for sufficiently large nh,

r (t K_{p}, K_{1} + n H) = n h (p - 1) + t

. Subsequently, Chung and Lin (Adv. Appl. Math., 2025) observed that the proof requires further justification. In this paper, we prove that if

n \geq \max {6 (p - 1) (ℓ + t) / h, (p - 1) (t - 1)}

, then

r (t K_{p}, K_{1} + n H) = n h (p - 1) + t .

Our proof combines the theorem by Andrásfai, Erdős, and Sós (Discrete Math., 1974) with a result by Haxell (Combin. Probab. Comput., 2001) on independent transversals.

设r（G， H）表示两个图G和H的拉姆齐数，符号nH表示n个不相交的H副本的并，K1+nH表示将一个新顶点连接到nH中的每个顶点所得到的图。设h=|V(h)|和r（Kp, h）哈姆，黑兹尔顿和汤普森（离散苹果）。数学。， 2021)证明了对于足够大的nh， r(tKp,K1+ nh)=nh(p−1)+t。随后，钟某和林某（adh . aapl .）数学。（2025）观察到证据需要进一步的证明。在本文中,我们证明如果n≥马克斯{6 (p−1)(ℓ+ t) / h, (p−1)(t−1)},thenr (tKp, K1 + nH) = nH (p−1)+ t。我们的证明结合了Andrásfai， Erdős和Sós（离散数学）定理。（1974），结果由哈克塞尔(Combin。Probab。第一版。（2001）的独立截线。

引用次数: 0

Revisiting deterministic evolution: Robustness of cooperation under stochastic mutations and delayed feedback 再论确定性进化：随机突变与延迟反馈下合作的鲁棒性

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-03 DOI: 10.1016/j.amc.2026.129994

Kaipeng Hu , Xiaoqian Zhao , Zhouhong Li , Mahmut Özer , Lei Shi , Matjaž Perc

Stochastic mutations are intrinsic to evolutionary processes, reflecting both random genetic variation and broader uncertainties in strategic behavior. Here we extend our previous work on delayed evolutionary dynamics in a two species system by introducing Gaussian stochastic mutations into replicator equations with time delays. This framework captures both intra and interspecific interactions, with delays representing inevitable lags in feedback and response in biological and social systems. Using Lyapunov based stability analysis and numerical simulations, we show that while stochasticity mutations transient trajectories, cooperative equilibria remain robust even under very strong noise, with only extreme perturbations leading to divergence. These findings demonstrate that deterministic models retain strong predictive power for long term evolutionary outcomes across realistic conditions, offering new insights into how memory and randomness jointly shape the evolution of cooperation.

随机突变是进化过程的内在特征，既反映了随机遗传变异，也反映了策略行为中更广泛的不确定性。在这里，我们通过将高斯随机突变引入到具有时滞的复制子方程中，扩展了我们之前在两物种系统中的延迟进化动力学研究。该框架涵盖了种内和种间的相互作用，延迟代表了生物和社会系统中反馈和反应的不可避免的滞后。利用基于李雅普诺夫的稳定性分析和数值模拟，我们表明，当随机突变瞬态轨迹时，即使在很强的噪声下，合作平衡仍然保持鲁棒性，只有极端扰动导致发散。这些发现表明，确定性模型对现实条件下的长期进化结果具有很强的预测能力，为记忆和随机性如何共同塑造合作进化提供了新的见解。

引用次数: 0

On well-posedness and Euler scheme for regime-switching stochastic differential equations with discontinuous drift coefficient 具有不连续漂移系数的状态切换随机微分方程的适定性和欧拉格式

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-04 DOI: 10.1016/j.amc.2026.129992

Divyanshu Vashistha , Chaman Kumar , Raj Karan Gupta , Tejinder Kumar

In this article, we study well-posedness and Euler scheme for regime-switching stochastic differential equations where the drift coefficient is piecewise Lipschitz continuous and the diffusion coefficient is Lipschitz continuous and non-degenerate at the discontinuity points of the drift coefficient. The entangling of the discontinuous dynamics of the underlying Markov chain and the continuous dynamics of the solution process, along with the discontinuities in the drift coefficient, gives rise to various challenges which are resolved through a Markov chain-dependent transformation and a numerical scheme with a non-uniform discretization induced by the jump–times of the chain. To achieve mean-square convergence of order 1/2, we investigate conditional local and occupation times of the scheme near the points of discontinuity. Our approach also incorporates the case where the behaviour of discontinuity points of the drift coefficient can vary from regime to regime. Finally, we illustrate our results through numerical examples.

本文研究了漂移系数为分段Lipschitz连续，扩散系数为分段Lipschitz连续且在漂移系数的不连续点处不退化的状态切换随机微分方程的适定性和欧拉格式。底层马尔可夫链的不连续动力学与求解过程的连续动力学的纠缠，以及漂移系数的不连续，引起了各种各样的挑战，这些挑战通过马尔可夫链相关的变换和由链的跳跃时间引起的非均匀离散化的数值格式来解决。为了达到1/2阶的均方收敛，我们研究了该方案在不连续点附近的条件局部时间和占用时间。我们的方法还包含了漂移系数的不连续点的行为可以从制度变化到制度的情况。最后，通过数值算例对结果进行了说明。

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引用次数: 0

Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation 基于熵方程的非等温Cahn-Hilliard系统的保结构近似

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-01 DOI: 10.1016/j.amc.2026.129987

Aaron Brunk , Dennis Höhn , Mária Lukáčová-Medvi d'ová

We present and investigate a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation, employing conforming finite elements for spatial discretisation and a tailored mixed explicit-implicit scheme for time integration. To guarantee the preservation of key structural properties, namely mass and internal energy conservation, along with entropy production, we formulate the continuous problem within an appropriate variational framework based on the entropy equation. Our analytical results are validated through numerical experiments, including a convergence study

我们提出并研究了非等温Cahn-Hilliard方程的结构保持近似，采用符合的有限元进行空间离散和定制的混合显式-隐式格式进行时间积分。为了保证关键的结构性质，即质量和内能守恒，以及熵的产生，我们基于熵方程在适当的变分框架内制定了连续问题。我们的分析结果通过数值实验验证，包括收敛性研究

引用次数: 0

From C2 to CM weighted piecewise rational interpolation 从C2到C的加权分段有理插值

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-08-01 Epub Date: 2026-02-10 DOI: 10.1016/j.amc.2026.129990

Peng Xia , Zixia Liu , Na Lei

Beong In Yun’s weighted piecewise interpolation is a new piecewise interpolation method where the obtained interpolation function is twice continuously differentiable. Its interpolation function on each subinterval is constructed from two piecewise interpolation polynomials and a special rational weight function. However, how to further increase the smoothness of the weighted piecewise interpolation function, without changing the degree of the piecewise interpolation polynomial, is still a challenging and unsolved topic.

In this work, we accomplish this goal by elaborately constructing new rational weight functions, where the construction problem is subtly converted to an osculatory rational interpolation problem. These new rational weight functions can let the resulting weighted piecewise interpolation function be M times continuously differentiable, where M does not depend on the degree of the piecewise interpolation polynomial. The proposed interpolation method with new weight functions also retains the advantage that when some interpolation data are changed, the expression only changes on some subintervals. Furthermore, we extend the proposed weighted piecewise interpolation method to rational cases. That is, on each subinterval, the interpolation function is instead constructed from two piecewise rational functions and the weight function. In this case, the resulting interpolation function on the overall interpolation interval is also M times continuously differentiable. Numerical experiments demonstrate that, for given weight functions, the approximation effects of the piecewise interpolation functions in rational cases are better than those in polynomial cases.

Beong In Yun的加权分段插值是一种新的分段插值方法，所得到的插值函数是两次连续可微的。它在每个子区间上的插值函数由两个分段插值多项式和一个特殊的有理权函数构成。然而，如何在不改变分段插值多项式度的情况下进一步提高加权分段插值函数的平滑度，仍然是一个具有挑战性和未解决的课题。在这项工作中，我们通过精心构造新的有理权函数来实现这一目标，其中构造问题被巧妙地转换为一个接触有理插值问题。这些新的有理权函数可以使得到的加权分段插值函数是M次连续可微的，其中M不依赖于分段插值多项式的阶数。该方法还保留了当插值数据发生变化时，表达式仅在部分子区间上发生变化的优点。进一步，我们将提出的加权分段插值方法推广到有理情况。也就是说，在每个子区间上，插值函数由两个分段有理函数和权函数构造而成。在这种情况下，得到的插值函数在整个插值区间上也是M次连续可微的。数值实验表明，对于给定的权函数，分段插值函数在有理情况下的逼近效果优于多项式情况下的逼近效果。

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引用次数: 0

Adaptive parameter-space refinement and Markov state models for eco-epidemiological dynamics 生态流行病学动态的自适应参数空间细化和马尔可夫状态模型

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-07-15 Epub Date: 2026-01-29 DOI: 10.1016/j.amc.2026.129974

Eymard Hernández-López , Mohammad Sharif Ullah , Giovanni Wences , Jin Wang

We propose a computational framework that combines Adaptive Mesh Refinement in Parameter Space (AMR-PS), ensemble stochastic simulation, and Markov state model (MSM) coarse-graining to characterize metastable dynamics in an infection-predator-prey eco-epidemiological system. By adaptively refining regions near bifurcations, the strategy dramatically reduces the cost of exploring high-dimensional parameter spaces while preserving fidelity. Ensemble simulations capture the stochastic pathways connecting metastable states, highlighting regimes in which noise qualitatively reshapes basins of attraction. MSM coarse-graining supplies interpretable macrostates and transition matrices that permit efficient computation of quantities of interest, and that faithfully summarize long-time behavior. Applied to representative eco-epidemiological regimes, the workflow identifies parameter regions where stochasticity most realistically reflects the deterministic bifurcation structure, quantifies escape times between endemic and disease-extinction basins, and could provide practical diagnostics for ecological management. The method is scalable, modular, and applicable to multiscale problems where rare events and parametric sensitivity influence complex system dynamics.

我们提出了一个结合参数空间自适应网格细化（AMR-PS）、集合随机模拟和马尔可夫状态模型（MSM）粗粒度的计算框架，以表征感染-捕食者-猎物生态流行病学系统的亚稳态动力学。通过自适应细化分岔附近的区域，该策略大大降低了探索高维参数空间的成本，同时保持了保真度。集合模拟捕获了连接亚稳态的随机路径，突出了噪声定性地重塑吸引力盆地的制度。MSM粗粒度提供可解释的宏观状态和转换矩阵，允许对感兴趣的数量进行有效计算，并忠实地总结长期行为。应用于代表性生态流行病学制度，该工作流程确定了随机性最能真实反映确定性分岔结构的参数区域，量化了流行和疾病灭绝盆地之间的逃逸时间，并可为生态管理提供实用的诊断。该方法具有可扩展性和模块化，适用于罕见事件和参数敏感性影响复杂系统动力学的多尺度问题。

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引用次数: 0

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