Applied Mathematics and Computation最新文献

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Stochastic ecoevolutionary dynamics under coupled behavioral and environmental feedback 行为与环境耦合反馈下的随机生态进化动力学

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-20 DOI: 10.1016/j.amc.2026.129959

Xiaoqian Zhao , Kaipeng Hu , Yewei Tao , Lei Shi

The behavioral patterns and dynamics of biological populations are shaped by the combined influences of interaction outcomes and environmental resources. Numerous coevolutionary mechanisms proposed in previous studies have extended the exploration of biological behavior into system level modeling, deepening our understanding of long-term population dynamics. Yet from a modeling perspective, deterministic dynamical frameworks often fail to capture many subtle real world factors, thereby limiting their predictive reliability, particularly for critical system outcomes. To address this limitation, this study extends existing approaches by introducing independent stochastic processes to construct a stochastic dynamical model with bidirectional feedback mechanisms. The model characterizes the coevolutionary dynamics between collective behavior and environmental states, and analytical conditions for internal equilibrium points and stochastic asymptotic stability are derived. Numerical simulations not only verify the theoretical results but also reveal multiple dynamic regimes that emerge under different levels of stochasticity, including small oscillations near equilibrium, amplified oscillations, and unstable fluctuations. This research deepens our comprehension of the coevolution of behavior and environment from a stochastic dynamics perspective and provides a fundamental theoretical framework.

生物种群的行为模式和动态受相互作用结果和环境资源的综合影响。在以往的研究中提出的许多共同进化机制已经将对生物行为的探索扩展到系统级建模，加深了我们对长期种群动态的理解。然而，从建模的角度来看，确定性动态框架往往不能捕捉到许多微妙的现实世界因素，从而限制了它们的预测可靠性，特别是对于关键的系统结果。为了解决这一局限性，本研究通过引入独立的随机过程来扩展现有方法，构建具有双向反馈机制的随机动力学模型。该模型描述了集体行为与环境状态之间的协同进化动力学，并推导了内部平衡点和随机渐近稳定性的解析条件。数值模拟不仅验证了理论结果，而且揭示了在不同随机性水平下出现的多种动态机制，包括接近平衡的小振荡、放大振荡和不稳定波动。本研究深化了我们从随机动力学角度对行为与环境共同进化的理解，提供了一个基本的理论框架。

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引用次数: 0

Depolarization in the coevolutionary dynamics of opinion and cooperation 意见和合作的共同进化动力学中的去极化

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-20 DOI: 10.1016/j.amc.2026.129955

Jiayuan Li , Haojie Xu , Fuying Huang , Wenchen Han , Changwei Huang

Cooperation and consensus have long been essential drivers of social development and stability. In human societies, personal opinions continually shape individual behaviors, which in turn alter the trajectory of those very opinions. To explore the complex interplay between individual decisions and collective consensus in times of opinion polarization, we propose a coevolutionary model in this study, coupling opinion dynamics with agents’ game decisions to investigate their synergistic effects. Our simulation results show that a moderate opinion coupling strength promotes heterogeneity in individual opinions, thereby fostering the emergence of both cooperation and consensus. However, when this coupling becomes excessive, it reduces opinion heterogeneity. This leads to a rise in defection under high temptation, ultimately triggering the collapse of cooperation and consensus. These results challenge the conventional wisdom that “stronger coupling always promotes cooperation and consensus,” revealing a deeper, nonlinear interdependence between human behavior and opinions. Our study thus offers a novel framework for research in collective governance and societal opinion depolarization.

长期以来，合作与共识一直是社会发展稳定的重要动力。在人类社会中，个人观点不断塑造个人行为，而个人行为又反过来改变了这些观点的发展轨迹。为了探索意见极化时代个人决策与集体共识之间复杂的相互作用，本研究提出了一个共同进化模型，将意见动态与代理人的博弈决策耦合起来，以研究它们的协同效应。我们的模拟结果表明，适度的意见耦合强度促进了个体意见的异质性，从而促进了合作和共识的出现。然而，当这种耦合变得过度时，它会减少意见的异质性。这就导致高诱惑下的叛逃行为增加，最终引发合作与共识的崩溃。这些结果挑战了“强耦合总是促进合作和共识”的传统智慧，揭示了人类行为和意见之间更深层次的非线性相互依存关系。因此，我们的研究为集体治理和社会舆论去极化的研究提供了一个新的框架。

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引用次数: 0

Sensor attack detection and identification for cyber-physical systems: A data-driven approach 网络物理系统的传感器攻击检测和识别：数据驱动的方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-15 DOI: 10.1016/j.amc.2026.129954

Kaiyu Wang , Dan Ye

This paper investigates the problem of sensor attack detection and identification in cyber-physical systems, leveraging the advantage of zonotopes in dealing with stochastic properties. Unlike previous research that relies on system dynamics knowledge to infer safety boundaries and monitoring schemes, the proposed approach is geared toward addressing the challenges posed by unknown system dynamics, attack strategies, and attack locations. Firstly, we analyze the feasibility of using zonotopes for attack detection and deduce the necessary information quantity and observation window length requirement for effective detection. Subsequently, a zonotopes-based algorithm is proposed for computing the over-approximated reachable set and measurement set from noisy data. Then, an attack detection and identification strategy based on the predicted measurement set is developed. To reduce the computational complexity of the presented detection method, a column truncation algorithm is proposed. The effectiveness of the proposed method is validated through numerical simulations.

本文研究了网络物理系统中传感器攻击的检测和识别问题，利用带拓扑在处理随机特性方面的优势。与以往依靠系统动力学知识推断安全边界和监测方案的研究不同，本文提出的方法旨在解决未知系统动力学、攻击策略和攻击位置带来的挑战。首先，我们分析了利用分区进行攻击检测的可行性，并推导出有效检测所需的信息量和观测窗口长度要求。随后，提出了一种基于分区拓扑的算法，用于计算噪声数据的过逼近可达集和测量集。然后，提出了一种基于预测测量集的攻击检测与识别策略。为了降低检测方法的计算复杂度，提出了一种列截断算法。通过数值仿真验证了该方法的有效性。

引用次数: 0

A nonstandard finite difference scheme for an SEIQR epidemiological PDE model SEIQR流行病学PDE模型的非标准有限差分格式

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-14 DOI: 10.1016/j.amc.2026.129953

Achraf Zinihi , Matthias Ehrhardt , Moulay Rchid Sidi Ammi

This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear parabolic partial differential equations (PDEs), the model extends classical compartmental models by incorporating spatial diffusion to account for population movement and spatial heterogeneity. The proposed NSFD discretization is designed to preserve the continuous model’s essential qualitative features, such as positivity, boundedness, and stability, which are often compromised by standard finite difference methods. We rigorously analyze the model’s well-posedness, construct a structure-preserving NSFD scheme for the PDE system, and study its convergence and local truncation error. Numerical simulations validate the theoretical findings and demonstrate the scheme’s effectiveness in preserving biologically consistent dynamics.

本文将非标准有限差分（NSFD）方法引入到反应-扩散SEIQR流行病学模型中，该模型捕捉了传染病传播的时空动态。该模型以半线性抛物型偏微分方程（PDEs）系统的形式表述，通过纳入空间扩散来解释人口移动和空间异质性，扩展了经典的区室模型。所提出的NSFD离散化旨在保留连续模型的基本定性特征，如正性、有界性和稳定性，这些特征通常被标准有限差分方法所损害。严格分析了模型的适定性，构造了PDE系统的保结构NSFD格式，并研究了其收敛性和局部截断误差。数值模拟验证了理论结果，并证明了该方案在保持生物一致性动力学方面的有效性。

引用次数: 0

A simplified discontinuous reproducing kernel method for impulsive differential equations 脉冲微分方程的简化不连续再现核方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-14 DOI: 10.1016/j.amc.2026.129950

Liangcai Mei , Yingchao Zhang , Boying Wu , Yingzhen Lin

In this article, a spatial concept of direct sum space based on the discontinuous reproducing kernel method (RKM for short) is proposed for impulsive differential equations, and a reproducing kernel numerical solution method is constructed. Based on the piecewise smoothness of the solution, a discontinuous reproducing kernel is constructed, and a direct sum space is constructed in vector form to represent the structure of the equation system. Furthermore, the simplified RKM is used to solve the operator equation, and an approximate solution in series form is obtained. Finally, the regularity analysis and uniform convergence analysis are carried out, and numerical experiments verify the second-order convergence and stability of the algorithm.

针对脉冲微分方程，提出了基于不连续再现核法（简称RKM）的直接和空间概念，并构造了再现核数值求解方法。基于解的分段平滑性，构造了一个不连续的再现核，并以向量形式构造了一个直接和空间来表示方程组的结构。在此基础上，利用简化的RKM对算子方程进行求解，得到了近似的级数解。最后进行了正则性分析和一致收敛性分析，并通过数值实验验证了算法的二阶收敛性和稳定性。

引用次数: 0

Evolutionary dynamics of cooperation in two-layer lattice networks with a leader-follower hierarchy: integrating dominant strategy and time cost 具有领导-追随者层级的两层晶格网络中合作的演化动力学：优势策略和时间成本的整合

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-11 DOI: 10.1016/j.amc.2026.129951

Bolin Yang , Guanghui Yang

This study explores the evolution of cooperative behavior in two-layer lattice networks by introducing time cost and a dominant-strategy mechanism within a leader-follower hierarchy network framework. The findings reveal that time cost acts as a stabilizer for system-wide cooperation, effectively mitigating the inhibitory effect of high cooperation costs. Meanwhile, the dominant-strategy mechanism provides clear behavioral references for the follower layer, significantly enhancing cooperation both within individual layers and across the entire network. Numerical simulations demonstrate that the follower layer exhibits higher cooperative synergy under the cooperation-dominant mechanism, whereas the cooperation level in the leader layer is instead enhanced under the defection-dominant mechanism. The study further shows that parameters such as selection intensity, consistency incentives, and inter-layer coupling strength all promote the emergence of cooperation under specific conditions. This work provides a mechanistic explanation and analytical tools for the evolution of cooperation in hierarchical social structures.

本文通过引入时间成本和优势策略机制，探讨了两层格子网络中合作行为的演化。研究结果表明，时间成本对全系统合作具有稳定器作用，有效缓解了高合作成本的抑制效应。同时，优势策略机制为追随者层提供了明确的行为参考，显著增强了个体层内部和整个网络的合作。数值模拟结果表明，在合作优势机制下，跟随者层表现出更高的合作协同效应，而在缺陷优势机制下，领导层的合作水平反而有所提高。研究进一步表明，在特定条件下，选择强度、一致性激励和层间耦合强度等参数都促进了合作的出现。本研究为等级制社会结构中合作的演化提供了一种机制解释和分析工具。

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引用次数: 0

Effects of directed migration toward a high-reputation exemplar in evolutionary games 在进化博弈中，向高声誉范例定向迁移的影响

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-11 DOI: 10.1016/j.amc.2026.129952

Yue Cheng, Qianxi Yang, Yanlong Yang

Migration plays an essential role in the evolution of cooperation. Previous research typically assumes that migration directions are either random or influenced by factors linked to payoff. However, to pursue profitable circumstances, individuals may be inclined to migrate toward exemplars with positive reputations, observing and learning their behavioral strategies. This paper proposes a directed migration model toward a high-reputation exemplar. In this model, the migration probability of individuals is negatively correlated with the average reputation of their neighbors within the current environment. Individuals probabilistically select an exemplar based on reputation weights and then migrate toward the chosen exemplar. Simulation results show that, compared to random migration, migrating toward a high-reputation exemplar significantly improves the population’s cooperation level and effectively resists temptations to defect.

移民在合作的演变过程中起着至关重要的作用。以前的研究通常假设迁移方向是随机的，或者受到与回报相关的因素的影响。然而，为了追求有利可图的环境，个人可能倾向于迁移到具有积极声誉的榜样，观察和学习他们的行为策略。本文提出了一个针对高声誉范例的定向迁移模型。在该模型中，个体的迁移概率与其邻居在当前环境中的平均声誉呈负相关。个体基于声誉权重概率地选择一个样本，然后向所选样本迁移。仿真结果表明，与随机迁移相比，向高声誉样本迁移显著提高了群体的合作水平，有效地抵抗了背叛的诱惑。

引用次数: 0

Graph-instructed neural networks for sparse grid-based discontinuity detectors 基于稀疏网格的不连续检测器的图指示神经网络

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-10 DOI: 10.1016/j.amc.2025.129946

Francesco Della Santa , Sandra Pieraccini

In this paper, we present a novel approach for detecting the discontinuity interfaces of a discontinuous function. This approach leverages Graph-Instructed Neural Networks (GINNs) and sparse grids to address discontinuity detection even in domains of dimension larger than 3. GINNs, trained to identify troubled points on sparse grids, exploit graph structures built on the grids to achieve efficient and accurate discontinuity detection performance. We also introduce a recursive algorithm for general sparse grid-based detectors, characterized by convergence properties and ease of applicability. Numerical experiments on functions with dimensions

n = 2

and

n = 4

demonstrate the efficiency and robust generalization properties of GINNs in detecting discontinuity interfaces; test cases with

n = 6

and

n = 8

show the applicability of the method when the discontinuity interface presents specific structures. Notably, the trained GINNs offer portability and versatility, allowing integration into various algorithms and sharing among users.

本文提出了一种检测不连续函数的不连续界面的新方法。这种方法利用图指示神经网络（ginn）和稀疏网格来解决即使在维度大于3的域中也能进行不连续检测。ginn通过训练来识别稀疏网格上的问题点，利用建立在网格上的图结构来实现高效准确的不连续检测性能。我们还介绍了一种用于一般稀疏网格检测器的递归算法，该算法具有收敛性和易于应用的特点。在n=2和n=4维函数上的数值实验证明了ginn在检测不连续界面方面的有效性和鲁棒性；n=6和n=8的测试用例显示了该方法在不连续界面呈现特定结构时的适用性。值得注意的是，经过训练的ginn提供了可移植性和多功能性，允许集成到各种算法中并在用户之间共享。

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引用次数: 0

Reinforcement learning-based optimal false data injection attack against control signals in probabilistic Boolean control networks 基于强化学习的概率布尔控制网络控制信号最优假数据注入攻击

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-10 DOI: 10.1016/j.amc.2025.129939

Xianlun Peng , Fangfei Li , Yang Liu

In this paper, we focus on the challenges of optimal false-data injection attacks in Probabilistic Boolean Control Networks (PBCNs) where attackers lack system model knowledge. Attack optimization is formulated as a Markov Decision Process (MDP) policy search problem. Theoretical guidance for reward design in the MDP is provided, proving the existence of optimal policies under Theorem 1. An enhanced Q-learning (QL) algorithm is developed to overcome scalability limitations of the standard QL in large-scale PBCNs. Experimental validation on both 10-node and 28-node networks demonstrates the efficacy of the method.

本文重点研究了概率布尔控制网络（PBCNs）中攻击者缺乏系统模型知识的最优假数据注入攻击所面临的挑战。攻击优化是一个马尔可夫决策过程（MDP）策略搜索问题。为MDP下的奖励设计提供了理论指导，证明了定理1下最优策略的存在性。为了克服标准QL在大规模PBCNs中的可扩展性限制，提出了一种增强型Q-learning （QL）算法。在10节点和28节点网络上的实验验证表明了该方法的有效性。

引用次数: 0

Prosocial behavior on testing and quarantine in an epidemic disease 传染病检测检疫中的亲社会行为

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-10 DOI: 10.1016/j.amc.2026.129949

Khadija Khatun , Md Mamun-Ur-Rashid Khan , Jun Tanimoto

Effective management of disease outbreaks requires a comprehensive understanding of the complex interplay between individual decision-making, disease dynamics, and societal objectives. We incorporate a mathematical disease model coupling with behavior-driven testing and quarantining to mitigate disease and capture the social dilemma behind the dynamics using social efficiency deficit. The results obtained from the numerical finite difference method indicate that a behavior-driven approach is more effective in controlling outbreaks and limiting disease spread compared to a constant strategy. The social dilemma reaches its peak at a critical transmission rate threshold, wherein either the proportion of symptomatic infectious individuals attains its maximum value or the rate of waning immunity surpasses a specific threshold. Furthermore, the social dilemma culminates when both the economic cost associated with the disease and the cost of quarantining symptomatic individuals reach their respective maxima, giving rise to a convergence of conflicting objectives between individual and societal interests. These findings underscore the complexity of disease management strategies and the importance of carefully balancing economic considerations with public health imperatives.

疾病暴发的有效管理需要对个人决策、疾病动态和社会目标之间复杂的相互作用有全面的了解。我们将数学疾病模型与行为驱动的检测和隔离相结合，以减轻疾病，并利用社会效率赤字捕捉动态背后的社会困境。数值有限差分法的结果表明，与恒定策略相比，行为驱动方法在控制疫情和限制疾病传播方面更有效。当出现传染率临界值时，即有症状感染者比例达到最大值或免疫力下降率超过特定阈值时，社会困境达到顶峰。此外，当与疾病相关的经济成本和隔离有症状个体的成本达到各自的最大值时，社会困境达到顶峰，导致个人利益与社会利益之间相互冲突的目标趋同。这些发现强调了疾病管理战略的复杂性，以及仔细平衡经济考虑与公共卫生需要的重要性。

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