Pub Date : 2026-02-05DOI: 10.1016/j.amc.2026.129997
Xiao-Yan Wang , Yue Long
In this paper, the stability problem dependent on both the time delay and its derivative is analyzed for a class of nonlinear systems with time-varying delays using the T-S fuzzy approach. According to its derivative, is categorized as either monotonically increasing or decreasing, thus modeling it as a switched system. A high-order Wirtinger-type integral inequality is proposed. By introducing double and triple integral terms and combining the techniques of piecewise interval division and relaxation matrix decomposition, the tightness of the lower-bound estimation is improved. Furthermore, a novel mode-dependent Lyapunov-Krasovskii functional is designed, where the matrix terms are time-varying and allow different Lyapunov matrices for different delay variation modes. By using the average dwell time method, a condition for exponential stability of the fuzzy system is derived. Finally, the effectiveness and advantages of the proposed method are verified through a simulation example of a liquid monopropellant rocket engine model.
{"title":"Improved higher-order Wirtinger integral inequality and switching mode design for nonlinear time-delay systems","authors":"Xiao-Yan Wang , Yue Long","doi":"10.1016/j.amc.2026.129997","DOIUrl":"10.1016/j.amc.2026.129997","url":null,"abstract":"<div><div>In this paper, the stability problem dependent on both the time delay and its derivative is analyzed for a class of nonlinear systems with time-varying delays using the T-S fuzzy approach. According to its derivative, is categorized as either monotonically increasing or decreasing, thus modeling it as a switched system. A high-order Wirtinger-type integral inequality is proposed. By introducing double and triple integral terms and combining the techniques of piecewise interval division and relaxation matrix decomposition, the tightness of the lower-bound estimation is improved. Furthermore, a novel mode-dependent Lyapunov-Krasovskii functional is designed, where the matrix terms are time-varying and allow different Lyapunov matrices for different delay variation modes. By using the average dwell time method, a condition for exponential stability of the fuzzy system is derived. Finally, the effectiveness and advantages of the proposed method are verified through a simulation example of a liquid monopropellant rocket engine model.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129997"},"PeriodicalIF":3.4,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134769","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 : 2026-02-05DOI: 10.1016/j.amc.2026.129991
Sergio Amat , Sonia Busquier , David Levin , Juan Ruiz-Álvarez , Dionisio F. Yáñez
In this paper, we introduce a nonlinear subdivision scheme designed to converge to piecewise smooth functions. The scheme is formulated as a convex nonlinear combination of Chaikin-type linear schemes. In regions of regularity, it attains a high level of smoothness and accuracy, comparable to that of the fourth-order linear algorithm that it approximates. Near discontinuities, the scheme successfully avoids Gibbs-type oscillations and does not introduce any artificial intermediate points within the intervals containing the discontinuities. Furthermore, the proposed scheme adaptively responds to discontinuities while utilizing the maximum number of available points within smooth regions, thus ensuring the highest attainable order of accuracy in every case. A set of numerical experiments is provided, illustrating and supporting the theoretical analysis with respect to convergence, stability, accuracy, and regularity across both smooth regions and regions with discontinuities. To the best of our knowledge, this represents the first algorithm capable of simultaneously exhibiting all these desirable properties.
{"title":"On a weighted Chaikin-type subdivision scheme for non-smooth data","authors":"Sergio Amat , Sonia Busquier , David Levin , Juan Ruiz-Álvarez , Dionisio F. Yáñez","doi":"10.1016/j.amc.2026.129991","DOIUrl":"10.1016/j.amc.2026.129991","url":null,"abstract":"<div><div>In this paper, we introduce a nonlinear subdivision scheme designed to converge to piecewise smooth functions. The scheme is formulated as a convex nonlinear combination of Chaikin-type linear schemes. In regions of regularity, it attains a high level of smoothness and accuracy, comparable to that of the <span><math><mrow><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> fourth-order linear algorithm that it approximates. Near discontinuities, the scheme successfully avoids Gibbs-type oscillations and does not introduce any artificial intermediate points within the intervals containing the discontinuities. Furthermore, the proposed scheme adaptively responds to discontinuities while utilizing the maximum number of available points within smooth regions, thus ensuring the highest attainable order of accuracy in every case. A set of numerical experiments is provided, illustrating and supporting the theoretical analysis with respect to convergence, stability, accuracy, and regularity across both smooth regions and regions with discontinuities. To the best of our knowledge, this represents the first algorithm capable of simultaneously exhibiting all these desirable properties.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129991"},"PeriodicalIF":3.4,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134771","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 : 2026-02-05DOI: 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":"2026-02-05","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 : 2026-02-05DOI: 10.1016/j.amc.2026.129993
Huiying Cao , Dengxiu Yu , C. L. Philip Chen
Expanding transport systems have disrupted the geographical boundaries of human mobility, producing intricate patterns of spatiotemporal contagion dynamics. Conventional theoretical models often neglect the memory effect of human mobility and the dynamic evolution of social interactions. To address this problem, we introduce a novel theoretical framework for modeling spatiotemporal contagion dynamics. We first develop a temporal multilayer network that integrates the spatial structure of populations with a non-instantaneous travel process, where infections occur both within layers and during transit, facilitated by time-varying social interactions modeled via activity-driven networks. Second, we formulate the non-Markovian dynamics using quenched mean-field theory and derive an analytical epidemic threshold based on the Next Generation Matrix approach, demonstrating that the onset and progression of epidemics are governed by travel strength (proportion of travelers and hopping rate), interaction density, and travel duration. Third, through extensive experiments and analysis, we find that, compared to Markovian dynamics and analytical SIR-type solutions, non-Markovian dynamics introduce memory-driven delays in the redistribution of effective population size across structural components, capturing realistic multi-wave infection patterns more accurately. Dense travel interactions predominantly drive spatiotemporal contagion dynamics. In highly connected travel environments, stronger travel strength consistently accelerates epidemic spread. In contrast, the impact of travel duration is more complex and depends on transmission rate, reflecting the interplay of infection and recovery during transit. This study offers critical theoretical insights for designing public health interventions, such as travel restrictions and quarantine measures, to mitigate pandemic risks.
{"title":"Spatiotemporal contagion dynamics driven by human mobility in multilayer activity-driven networks","authors":"Huiying Cao , Dengxiu Yu , C. L. Philip Chen","doi":"10.1016/j.amc.2026.129993","DOIUrl":"10.1016/j.amc.2026.129993","url":null,"abstract":"<div><div>Expanding transport systems have disrupted the geographical boundaries of human mobility, producing intricate patterns of spatiotemporal contagion dynamics. Conventional theoretical models often neglect the memory effect of human mobility and the dynamic evolution of social interactions. To address this problem, we introduce a novel theoretical framework for modeling spatiotemporal contagion dynamics. We first develop a temporal multilayer network that integrates the spatial structure of populations with a non-instantaneous travel process, where infections occur both within layers and during transit, facilitated by time-varying social interactions modeled via activity-driven networks. Second, we formulate the non-Markovian dynamics using quenched mean-field theory and derive an analytical epidemic threshold based on the Next Generation Matrix approach, demonstrating that the onset and progression of epidemics are governed by travel strength (proportion of travelers and hopping rate), interaction density, and travel duration. Third, through extensive experiments and analysis, we find that, compared to Markovian dynamics and analytical SIR-type solutions, non-Markovian dynamics introduce memory-driven delays in the redistribution of effective population size across structural components, capturing realistic multi-wave infection patterns more accurately. Dense travel interactions predominantly drive spatiotemporal contagion dynamics. In highly connected travel environments, stronger travel strength consistently accelerates epidemic spread. In contrast, the impact of travel duration is more complex and depends on transmission rate, reflecting the interplay of infection and recovery during transit. This study offers critical theoretical insights for designing public health interventions, such as travel restrictions and quarantine measures, to mitigate pandemic risks.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129993"},"PeriodicalIF":3.4,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134770","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 : 2026-02-05DOI: 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 denotes the graph obtained by joining a new vertex to every vertex in nH. Let and . Hamm, Hazelton, and Thompson (Discrete Appl. Math., 2021) proved that for sufficiently large nh, . Subsequently, Chung and Lin (Adv. Appl. Math., 2025) observed that the proof requires further justification. In this paper, we prove that if , thenOur proof combines the theorem by Andrásfai, Erdős, and Sós (Discrete Math., 1974) with a result by Haxell (Combin. Probab. Comput., 2001) on independent transversals.
{"title":"Ramsey numbers of generalized fans versus multiple cliques","authors":"Ze Wang, Yanbo Zhang","doi":"10.1016/j.amc.2026.129985","DOIUrl":"10.1016/j.amc.2026.129985","url":null,"abstract":"<div><div>Let <em>r</em>(<em>G, H</em>) denote the Ramsey number for two graphs <em>G</em> and <em>H</em>. The notation <em>nH</em> represents the union of <em>n</em> disjoint copies of <em>H</em>, and <span><math><mrow><msub><mi>K</mi><mn>1</mn></msub><mo>+</mo><mi>n</mi><mi>H</mi></mrow></math></span> denotes the graph obtained by joining a new vertex to every vertex in <em>nH</em>. Let <span><math><mrow><mi>h</mi><mo>=</mo><mo>|</mo><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>|</mo></mrow></math></span> and <span><math><mrow><mi>ℓ</mi><mo>=</mo><mi>r</mi><mo>(</mo><msub><mi>K</mi><mi>p</mi></msub><mo>,</mo><mi>H</mi><mo>)</mo></mrow></math></span>. Hamm, Hazelton, and Thompson (<em>Discrete Appl. Math.</em>, 2021) proved that for sufficiently large <em>nh</em>, <span><math><mrow><mi>r</mi><mrow><mo>(</mo><mi>t</mi><msub><mi>K</mi><mi>p</mi></msub><mo>,</mo><msub><mi>K</mi><mn>1</mn></msub><mo>+</mo><mi>n</mi><mi>H</mi><mo>)</mo></mrow><mo>=</mo><mi>n</mi><mi>h</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>t</mi></mrow></math></span>. Subsequently, Chung and Lin (<em>Adv. Appl. Math.</em>, 2025) observed that the proof requires further justification. In this paper, we prove that if <span><math><mrow><mi>n</mi><mo>≥</mo><mi>max</mi><mo>{</mo><mn>6</mn><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>ℓ</mi><mo>+</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>h</mi><mo>,</mo><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>t</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>}</mo></mrow></math></span>, then<span><span><span><math><mrow><mi>r</mi><mrow><mo>(</mo><mi>t</mi><msub><mi>K</mi><mi>p</mi></msub><mo>,</mo><msub><mi>K</mi><mn>1</mn></msub><mo>+</mo><mi>n</mi><mi>H</mi><mo>)</mo></mrow><mo>=</mo><mi>n</mi><mi>h</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>t</mi><mo>.</mo></mrow></math></span></span></span>Our proof combines the theorem by Andrásfai, Erdős, and Sós (<em>Discrete Math.</em>, 1974) with a result by Haxell (<em>Combin. Probab. Comput.</em>, 2001) on independent transversals.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129985"},"PeriodicalIF":3.4,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134776","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 : 2026-02-04DOI: 10.1016/j.amc.2026.129963
Yingli Sang, Zhengqiang Zhang
{"title":"Multivariable state tracking control for uncertain reference model with application to leader–follower consensus problem","authors":"Yingli Sang, Zhengqiang Zhang","doi":"10.1016/j.amc.2026.129963","DOIUrl":"https://doi.org/10.1016/j.amc.2026.129963","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"1 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134775","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}
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.
{"title":"On well-posedness and Euler scheme for regime-switching stochastic differential equations with discontinuous drift coefficient","authors":"Divyanshu Vashistha , Chaman Kumar , Raj Karan Gupta , Tejinder Kumar","doi":"10.1016/j.amc.2026.129992","DOIUrl":"10.1016/j.amc.2026.129992","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129992"},"PeriodicalIF":3.4,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134774","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 : 2026-02-03DOI: 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.
{"title":"Revisiting deterministic evolution: Robustness of cooperation under stochastic mutations and delayed feedback","authors":"Kaipeng Hu , Xiaoqian Zhao , Zhouhong Li , Mahmut Özer , Lei Shi , Matjaž Perc","doi":"10.1016/j.amc.2026.129994","DOIUrl":"10.1016/j.amc.2026.129994","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129994"},"PeriodicalIF":3.4,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110511","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 : 2026-02-02DOI: 10.1016/j.amc.2026.129984
Guo-Jun Liu , Fan Wang , Donghong Hu
This paper addresses the problem of nonfragile fuzzy filtering for continuous-time nonlinear systems with event-triggered and quantized mechanisms. Firstly, the continuous-time nonlinear systems are represented by Takagi-Sugeno fuzzy models. Secondly, the dynamic quantization strategies and event-triggered mechanisms are used to reduce the communication burden and improve resource efficiency. Thirdly, considering the uncertainty of filtering parameters, the analysis and synthesis of nonfragile H∞ filters are carried out using integral Lyapunov functions and decoupled inequality techniques. In addition, the optimization parameter results of three factors including event-triggered mechanisms, dynamic quantization and nonfragile filtering are obtained by using linear matrix inequality. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed method.
{"title":"Nonfragile fuzzy filtering for nonlinear systems with event-triggered and quantized mechanisms","authors":"Guo-Jun Liu , Fan Wang , Donghong Hu","doi":"10.1016/j.amc.2026.129984","DOIUrl":"10.1016/j.amc.2026.129984","url":null,"abstract":"<div><div>This paper addresses the problem of nonfragile fuzzy filtering for continuous-time nonlinear systems with event-triggered and quantized mechanisms. Firstly, the continuous-time nonlinear systems are represented by Takagi-Sugeno fuzzy models. Secondly, the dynamic quantization strategies and event-triggered mechanisms are used to reduce the communication burden and improve resource efficiency. Thirdly, considering the uncertainty of filtering parameters, the analysis and synthesis of nonfragile <em>H</em><sub>∞</sub> filters are carried out using integral Lyapunov functions and decoupled inequality techniques. In addition, the optimization parameter results of three factors including event-triggered mechanisms, dynamic quantization and nonfragile filtering are obtained by using linear matrix inequality. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129984"},"PeriodicalIF":3.4,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110514","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 : 2026-02-02DOI: 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.
{"title":"Performances and correlations of centrality measures in complex networks","authors":"Yilin Bi, Xinshan Jiao, Tao Zhou","doi":"10.1016/j.amc.2026.129972","DOIUrl":"10.1016/j.amc.2026.129972","url":null,"abstract":"<div><div>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 <em>τ</em>). 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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"522 ","pages":"Article 129972"},"PeriodicalIF":3.4,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110513","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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