Pub Date : 2026-07-15Epub Date: 2026-02-05DOI: 10.1016/j.amc.2026.129995
Jiansong Zhang , Jiang Zhu , Rongpei Zhang
In the recent artcle published in [1] [Appl. Math. Comput. 278 (2016) 33-44], a mass-conservative characteristic mixed finite element method was developed for Keller-Segel chemotaxis models with a splitting technique. This paper presents corrections to several errors identified in the original work. It has been confirmed that the modification does not affect the primary results or conclusions presented in [1].
{"title":"Corrigendum to “Characteristic splitting mixed finite element analysis of Keller-Segel chemotaxis models” [Appl. Math. Compt. 278 (2016) 33-44]","authors":"Jiansong Zhang , Jiang Zhu , Rongpei Zhang","doi":"10.1016/j.amc.2026.129995","DOIUrl":"10.1016/j.amc.2026.129995","url":null,"abstract":"<div><div>In the recent artcle published in [1] [Appl. Math. Comput. 278 (2016) 33-44], a mass-conservative characteristic mixed finite element method was developed for Keller-Segel chemotaxis models with a splitting technique. This paper presents corrections to several errors identified in the original work. It has been confirmed that the modification does not affect the primary results or conclusions presented in <span><span>[1]</span></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129995"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-15Epub Date: 2026-01-24DOI: 10.1016/j.amc.2026.129962
Xiaoyu Jin , Guiying Yan , Weihua Yang , Shuang Zhao
A graph is equitably k-colorable [1] if its vertex set V can be partitioned into k independent sets such that for all s, t. The minimum such k is referred to as the equitable chromatic number of G, denoted .
Meyer conjectured that for any graph G that is neither a complete graph Km nor an odd cycle , the inequality holds. The decoding scheduling of multi-edge type QC-LDPC codes in channel coding can be regarded as an equitable coloring problem of a circulant graph. Motivated by the NP-hardness of determining optimal equitable colorings in general, we focus on circulant graphs with Δ(G) ≤ 4. We show that if then the circulant graph G(n; {d1, d2}) satisfies
{"title":"The equitable chromatic number of circulant graphs with maximum degree at most 4","authors":"Xiaoyu Jin , Guiying Yan , Weihua Yang , Shuang Zhao","doi":"10.1016/j.amc.2026.129962","DOIUrl":"10.1016/j.amc.2026.129962","url":null,"abstract":"<div><div>A graph <span><math><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></math></span> is <em>equitably k-colorable</em> [1] if its vertex set <em>V</em> can be partitioned into <em>k</em> independent sets <span><math><mrow><msub><mi>V</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>V</mi><mi>k</mi></msub></mrow></math></span> such that <span><math><mrow><mrow><mo>|</mo><mrow><mo>|</mo></mrow><msub><mi>V</mi><mi>s</mi></msub><mrow><mo>|</mo><mo>−</mo><mo>|</mo></mrow><msub><mi>V</mi><mi>t</mi></msub><mrow><mo>|</mo></mrow><mo>|</mo></mrow><mo>≤</mo><mn>1</mn></mrow></math></span> for all <em>s, t</em>. The minimum such <em>k</em> is referred to as the <em>equitable chromatic number</em> of <em>G</em>, denoted <span><math><mrow><msub><mi>χ</mi><mo>=</mo></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>.</div><div>Meyer conjectured that for any graph <em>G</em> that is neither a complete graph <em>K<sub>m</sub></em> nor an odd cycle <span><math><msub><mi>C</mi><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span>, the inequality <span><math><mrow><msub><mi>χ</mi><mo>=</mo></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mstyle><mi>Δ</mi></mstyle><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> holds. The decoding scheduling of multi-edge type QC-LDPC codes in channel coding can be regarded as an equitable coloring problem of a circulant graph. Motivated by the NP-hardness of determining optimal equitable colorings in general, we focus on circulant graphs with Δ(<em>G</em>) ≤ 4. We show that if <span><math><mrow><mi>gcd</mi><mrow><mo>(</mo><msub><mi>d</mi><mn>2</mn></msub><mo>,</mo><mi>n</mi><mo>)</mo></mrow><mo>∤</mo><msub><mi>d</mi><mn>1</mn></msub><mo>.</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi><mrow><mi>a</mi><mi>n</mi><mi>d</mi></mrow><mo>.</mo><mi>g</mi><mi>c</mi><mi>d</mi><mrow><mo>(</mo><msub><mi>d</mi><mn>1</mn></msub><mo>,</mo><mi>n</mi><mo>)</mo></mrow><mo>∤</mo><msub><mi>d</mi><mn>2</mn></msub><mo>,</mo></mrow></math></span> then the circulant graph <em>G</em>(<em>n</em>; {<em>d</em><sub>1</sub>, <em>d</em><sub>2</sub>}) satisfies <span><math><mrow><msub><mi>χ</mi><mo>=</mo></msub><mrow><mo>(</mo><mi>G</mi><mrow><mo>(</mo><mi>n</mi><mo>;</mo><mrow><mo>{</mo><msub><mi>d</mi><mn>1</mn></msub><mo>,</mo><msub><mi>d</mi><mn>2</mn></msub><mo>}</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>2</mn><mspace></mspace><mtext>or</mtext><mspace></mspace><mn>3</mn><mo>≤</mo><mstyle><mi>Δ</mi></mstyle><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span></div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129962"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-15Epub Date: 2026-01-29DOI: 10.1016/j.amc.2026.129973
Mengchen Wang, Haibo Bao
In this article, we tackle the problem of realizing boundedness for delayed Markov jump systems (MJSs) with deception attacks and imperfect transition probabilities. To alleviate the burden of communication and conserve bandwidth in the communication network channel, a novel model-dependent dynamic-memory event-triggered mechanism (DMETM) is designed. Different from the general dynamic event-triggered mechanism (ETM), the designed DMETM includes historical trigger data in its triggering conditions, so it is able to dynamically adjust data transmission according to the long-term changes in the system state, thereby improving resource utilization. A hidden Markov model (HMM) with unmeasured probabilities is employed to comprehensively characterize plant-controller asynchrony. Moreover, deception attacks, considering the vulnerability of communication links, are taken into account. While existing studies typically assume bounded false data injection in MJSs, establishing accurate bounds in practical scenarios remains challenging. Considering this problem, a neural network-based asynchronous memory compensation feedback controller is developed, which effectively identifies and mitigates the impact of deception attacks. By leveraging a Lyapunov-Krasovskii functional (LKF), sufficient conditions for bounded in probability of the closed-loop system are derived. The effectiveness of the theoretical analysis is illustrated through an illustrative example.
{"title":"Neural-network-based asynchronous security control for delayed Markov jump systems with imperfect transition probabilities via dynamic-memory event-triggered mechanism","authors":"Mengchen Wang, Haibo Bao","doi":"10.1016/j.amc.2026.129973","DOIUrl":"10.1016/j.amc.2026.129973","url":null,"abstract":"<div><div>In this article, we tackle the problem of realizing boundedness for delayed Markov jump systems (MJSs) with deception attacks and imperfect transition probabilities. To alleviate the burden of communication and conserve bandwidth in the communication network channel, a novel model-dependent dynamic-memory event-triggered mechanism (DMETM) is designed. Different from the general dynamic event-triggered mechanism (ETM), the designed DMETM includes historical trigger data in its triggering conditions, so it is able to dynamically adjust data transmission according to the long-term changes in the system state, thereby improving resource utilization. A hidden Markov model (HMM) with unmeasured probabilities is employed to comprehensively characterize plant-controller asynchrony. Moreover, deception attacks, considering the vulnerability of communication links, are taken into account. While existing studies typically assume bounded false data injection in MJSs, establishing accurate bounds in practical scenarios remains challenging. Considering this problem, a neural network-based asynchronous memory compensation feedback controller is developed, which effectively identifies and mitigates the impact of deception attacks. By leveraging a Lyapunov-Krasovskii functional (LKF), sufficient conditions for bounded in probability of the closed-loop system are derived. The effectiveness of the theoretical analysis is illustrated through an illustrative example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129973"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-15Epub Date: 2026-01-31DOI: 10.1016/j.amc.2026.129971
Animotu Mohammed , Golnaz Shahtahmassebi , Haroldo V. Ribeiro , Peter Scriven , Jack Sutton , Quentin S. Hanley
A variety of transparency initiatives have been introduced by governments to reduce corruption and allow citizens to independently evaluate the effectiveness and efficiency of spending. In 2010, the UK government mandated transparency for many expenditures exceeding £25,000. The resulting data is dispersed across a range of governmental organizations and presents an opportunity to understand expenditure at scale, interrogate organizational structures and develop transparency measures. Here, we focus on data from the top two layers of the National Health Service (NHS) within England, including NHS England (NHSE) and Integrated Care Boards (ICBs). As one of the largest government run healthcare organizations in the world and potentially the sixth largest employer globally, the NHS provides a distinctive case for studying healthcare delivery, contractor dynamics, and organizational self-organization. We find that limiting transparency to larger transactions conceals a substantial share of spending from scrutiny, including most transactions. The rank-frequency distributions of suppliers, expense types, and spending categories exhibit multiple scaling regimes similar to patterns observed in word frequency and urban scaling studies indicating these methodologies can be deployed to analyze financial transparency data at scale.
{"title":"Nonlinear rank scaling and hidden structure in NHS expenditure transparency data","authors":"Animotu Mohammed , Golnaz Shahtahmassebi , Haroldo V. Ribeiro , Peter Scriven , Jack Sutton , Quentin S. Hanley","doi":"10.1016/j.amc.2026.129971","DOIUrl":"10.1016/j.amc.2026.129971","url":null,"abstract":"<div><div>A variety of transparency initiatives have been introduced by governments to reduce corruption and allow citizens to independently evaluate the effectiveness and efficiency of spending. In 2010, the UK government mandated transparency for many expenditures exceeding £25,000. The resulting data is dispersed across a range of governmental organizations and presents an opportunity to understand expenditure at scale, interrogate organizational structures and develop transparency measures. Here, we focus on data from the top two layers of the National Health Service (NHS) within England, including NHS England (NHSE) and Integrated Care Boards (ICBs). As one of the largest government run healthcare organizations in the world and potentially the sixth largest employer globally, the NHS provides a distinctive case for studying healthcare delivery, contractor dynamics, and organizational self-organization. We find that limiting transparency to larger transactions conceals a substantial share of spending from scrutiny, including most transactions. The rank-frequency distributions of suppliers, expense types, and spending categories exhibit multiple scaling regimes similar to patterns observed in word frequency and urban scaling studies indicating these methodologies can be deployed to analyze financial transparency data at scale.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129971"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146095740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-15Epub Date: 2026-01-23DOI: 10.1016/j.amc.2026.129961
Sanjay L. Gosiya, Vikas H. Pradhan
The Richards’ equation (RE), a non-linear elliptic-parabolic partial differential equation, is extensively used to simulate the flow processes in the unsaturated porous medium. This equation’s coefficients include two highly non-linear functions associated with unsaturated hydraulic conductivity, soil water potential, and soil water content. Various standard models are available in the literature to express these non-linear functions, potentially leading to significantly different outcomes in unsaturated flow problems. van Genuchten model is most widely used to express these non-linear functions for measuring accurate moisture content profiles. This paper presents the numerical results of a mixed form of RE based on this model using the Crank-Nicolson finite difference scheme. We compare the obtained numerical results with the available analytical and experimental results to verify the model. Accurate numerical results are also presented by comparing them with those obtained from Hydrus-1D, a widely used numerical tool for solving the RE. Notwithstanding, the numerical results are extended in 2D and 3D.
{"title":"An efficient and accurate numerical modeling for measuring moisture content profiles in an unsaturated porous medium","authors":"Sanjay L. Gosiya, Vikas H. Pradhan","doi":"10.1016/j.amc.2026.129961","DOIUrl":"10.1016/j.amc.2026.129961","url":null,"abstract":"<div><div>The Richards’ equation (RE), a non-linear elliptic-parabolic partial differential equation, is extensively used to simulate the flow processes in the unsaturated porous medium. This equation’s coefficients include two highly non-linear functions associated with unsaturated hydraulic conductivity, soil water potential, and soil water content. Various standard models are available in the literature to express these non-linear functions, potentially leading to significantly different outcomes in unsaturated flow problems. van Genuchten model is most widely used to express these non-linear functions for measuring accurate moisture content profiles. This paper presents the numerical results of a mixed form of RE based on this model using the Crank-Nicolson finite difference scheme. We compare the obtained numerical results with the available analytical and experimental results to verify the model. Accurate numerical results are also presented by comparing them with those obtained from Hydrus-1D, a widely used numerical tool for solving the RE. Notwithstanding, the numerical results are extended in 2D and 3D.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129961"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-15Epub Date: 2026-01-20DOI: 10.1016/j.amc.2026.129956
Jingchu Jia , Luhe Yang , Duoxing Yang , Lianzhong Zhang
Empirically grounded bounded rationality decision-making, when information exchange is lacking, can be abstracted as an aspiration-driven dynamic mechanism within anonymous evolutionary games. Prospect Theory, meanwhile, provides a behavioral economics-based qualitative description for such decision-making. Therefore, we establish a micro-dynamic model based on Prospect Theory, incorporating psychological reference point dynamics, heterogeneous memory mechanisms, and asymmetric strategy updating dynamics. We systematically examine the influence of individual cognitive and behavioral parameters on the evolution of cooperation. Through Monte Carlo simulations and asynchronous update mechanisms, it reveals the complex interaction among factors such as memory capacity, decision preference, strategy updating sensitivity, synergy factor, and initial cooperation proportion. Findings indicate that the effect of memory capacity on cooperation strongly depends on decision preferences, long memory significantly promotes cooperation only when individuals exhibit more greedy as defectors. Strategy updating sensitivity can either enhance group steady-state cooperation level or compromise system stability. The synergy factor forms positive synergy with the memory mechanism by amplifying cooperation payoffs. Additionally, group steady-state cooperation levels are independent of initial conditions. These findings emphasize the condition-dependent nature of cooperation promotion. We suggest that future research should pay more attention to the important role of bounded rationality in modeling human decision-making behavior.
{"title":"Memory capacity and decision preference co-shape cooperation in public goods games","authors":"Jingchu Jia , Luhe Yang , Duoxing Yang , Lianzhong Zhang","doi":"10.1016/j.amc.2026.129956","DOIUrl":"10.1016/j.amc.2026.129956","url":null,"abstract":"<div><div>Empirically grounded bounded rationality decision-making, when information exchange is lacking, can be abstracted as an aspiration-driven dynamic mechanism within anonymous evolutionary games. Prospect Theory, meanwhile, provides a behavioral economics-based qualitative description for such decision-making. Therefore, we establish a micro-dynamic model based on Prospect Theory, incorporating psychological reference point dynamics, heterogeneous memory mechanisms, and asymmetric strategy updating dynamics. We systematically examine the influence of individual cognitive and behavioral parameters on the evolution of cooperation. Through Monte Carlo simulations and asynchronous update mechanisms, it reveals the complex interaction among factors such as memory capacity, decision preference, strategy updating sensitivity, synergy factor, and initial cooperation proportion. Findings indicate that the effect of memory capacity on cooperation strongly depends on decision preferences, long memory significantly promotes cooperation only when individuals exhibit more greedy as defectors. Strategy updating sensitivity can either enhance group steady-state cooperation level or compromise system stability. The synergy factor forms positive synergy with the memory mechanism by amplifying cooperation payoffs. Additionally, group steady-state cooperation levels are independent of initial conditions. These findings emphasize the condition-dependent nature of cooperation promotion. We suggest that future research should pay more attention to the important role of bounded rationality in modeling human decision-making behavior.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129956"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-15Epub Date: 2026-01-24DOI: 10.1016/j.amc.2026.129958
Yan Jiang , Zhijun Zeng , Wuyue Yang , Liu Hong , Pipi Hu , Yi Zhu
Revealing hidden stochastic dynamics from observation data is of great importance in applications. Traditional methods usually require a large number of independent trajectories to obtain the probability distributions at several time snapshots. This paper proposes a fast and accurate regression method to obtain the stochastic dynamics from a single trajectory. If the stochastic system possesses a stationary distribution, we can utilize the ergodicity and the Weak Collocation Regression method, which is a fast method based on the weak form and sparse regression to solve inverse problems of partial differential equations related to probability density functions, to extract the score function of the stationary distribution from the single trajectory data without high cost. Then a novel expression of the drift term in terms of the score function and the diffusion term can be established, based on which we can extract the drift and diffusion terms through the Weak Collocation Regression method again. Our method has a high efficiency and low requirements for the trajectory data. Its outstanding performance has been verified through extensive numerical experiments, including non-gradient drift, multi-scale and high-dimensional problems.
{"title":"STWCR: Weak collocation regression for revealing hidden stochastic dynamics from single trajectory data","authors":"Yan Jiang , Zhijun Zeng , Wuyue Yang , Liu Hong , Pipi Hu , Yi Zhu","doi":"10.1016/j.amc.2026.129958","DOIUrl":"10.1016/j.amc.2026.129958","url":null,"abstract":"<div><div>Revealing hidden stochastic dynamics from observation data is of great importance in applications. Traditional methods usually require a large number of independent trajectories to obtain the probability distributions at several time snapshots. This paper proposes a fast and accurate regression method to obtain the stochastic dynamics from a single trajectory. If the stochastic system possesses a stationary distribution, we can utilize the ergodicity and the Weak Collocation Regression method, which is a fast method based on the weak form and sparse regression to solve inverse problems of partial differential equations related to probability density functions, to extract the score function of the stationary distribution from the single trajectory data without high cost. Then a novel expression of the drift term in terms of the score function and the diffusion term can be established, based on which we can extract the drift and diffusion terms through the Weak Collocation Regression method again. Our method has a high efficiency and low requirements for the trajectory data. Its outstanding performance has been verified through extensive numerical experiments, including non-gradient drift, multi-scale and high-dimensional problems.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"521 ","pages":"Article 129958"},"PeriodicalIF":3.4,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-01-11DOI: 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.
{"title":"Evolutionary dynamics of cooperation in two-layer lattice networks with a leader-follower hierarchy: integrating dominant strategy and time cost","authors":"Bolin Yang , Guanghui Yang","doi":"10.1016/j.amc.2026.129951","DOIUrl":"10.1016/j.amc.2026.129951","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"520 ","pages":"Article 129951"},"PeriodicalIF":3.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-07-01Epub Date: 2026-01-21DOI: 10.1016/j.amc.2026.129957
Shuangfei Yin , Xiuxia Yin , Zhiwei Gao
This article is centered on event-triggered prescribed-time bipartite output consensus issue for matrix-weighted heterogeneous multi-agent systems under asynchronous DoS attacks, where the dependencies between adjacent agents are characterized by the matrix weights of the edges within the network. First, the system suffering from invalid attack is considered as a switching system. Then, by limiting the duration of the valid attack, a novel prescribed-time bipartite compensator with a static event-triggered mechanism is introduced to track the leader’s state for this category of generalized networks. In order to reduce communication between agents to a greater extent, we introduce a prescribed-time bipartite compensator with a dynamic event-triggered mechanism. Moreover, we demonstrate that neither mechanism exhibits Zeno behavior. Then, through compensator, a distributed state-feedback control protocol and an output-feedback control protocol are designed to achieve prescribed-time bipartite output consensus. Finally, simulation examples are presented to validate the validity of the main results.
{"title":"Dynamic event-triggered prescribed time bipartite consensus for matrix-weighted HMASs under asynchronous attacks","authors":"Shuangfei Yin , Xiuxia Yin , Zhiwei Gao","doi":"10.1016/j.amc.2026.129957","DOIUrl":"10.1016/j.amc.2026.129957","url":null,"abstract":"<div><div>This article is centered on event-triggered prescribed-time bipartite output consensus issue for matrix-weighted heterogeneous multi-agent systems under asynchronous DoS attacks, where the dependencies between adjacent agents are characterized by the matrix weights of the edges within the network. First, the system suffering from invalid attack is considered as a switching system. Then, by limiting the duration of the valid attack, a novel prescribed-time bipartite compensator with a static event-triggered mechanism is introduced to track the leader’s state for this category of generalized networks. In order to reduce communication between agents to a greater extent, we introduce a prescribed-time bipartite compensator with a dynamic event-triggered mechanism. Moreover, we demonstrate that neither mechanism exhibits Zeno behavior. Then, through compensator, a distributed state-feedback control protocol and an output-feedback control protocol are designed to achieve prescribed-time bipartite output consensus. Finally, simulation examples are presented to validate the validity of the main results.</div><div><strong>Key words:</strong> Asynchronous DoS attacks; Prescribed-time consensus; Matrix-weighted networks; Dynamic event-triggered mechanism; Bipartite consensus.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"520 ","pages":"Article 129957"},"PeriodicalIF":3.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"A nonstandard finite difference scheme for an SEIQR epidemiological PDE model","authors":"Achraf Zinihi , Matthias Ehrhardt , Moulay Rchid Sidi Ammi","doi":"10.1016/j.amc.2026.129953","DOIUrl":"10.1016/j.amc.2026.129953","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"520 ","pages":"Article 129953"},"PeriodicalIF":3.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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