Pub Date : 2026-04-15Epub Date: 2025-11-22DOI: 10.1016/j.amc.2025.129853
Qiufu Wang, Zhanshan Wang, Tianyuan Jia
This paper investigates the finite-time bipartite consensus (FTBC) for nonlinear multi-agent systems (MASs) with input saturation and noncooperative leader, where the leader’s input is not obtainable for followers. Firstly, to ensure that followers can obtain the leader state, a distributed adaptive bipartite leader state estimator (DABLSE) is proposed based on the estimation of leader’s input bound. This method overcomes the limitation of requiring knowledge of leader’s input bound for all followers and relaxes the constraint on leader’s input. Then, a smooth approximation function is applied to handle the input saturation in MASs. Subsequently, for achieving FTBC of MASs, a new adaptive controller is designed based on DABLSE by introducing sign vector and hyperbolic tangent function of error. This design reduces the controller chattering caused by direct compensation using the error’s sign vector in existing literature. Finally, the effectiveness of proposed FTBC strategy is validated by a simulation.
{"title":"DABLSE-based adaptive finite-time bipartite consensus for multi-agent systems with noncooperative leader","authors":"Qiufu Wang, Zhanshan Wang, Tianyuan Jia","doi":"10.1016/j.amc.2025.129853","DOIUrl":"10.1016/j.amc.2025.129853","url":null,"abstract":"<div><div>This paper investigates the finite-time bipartite consensus (FTBC) for nonlinear multi-agent systems (MASs) with input saturation and noncooperative leader, where the leader’s input is not obtainable for followers. Firstly, to ensure that followers can obtain the leader state, a distributed adaptive bipartite leader state estimator (DABLSE) is proposed based on the estimation of leader’s input bound. This method overcomes the limitation of requiring knowledge of leader’s input bound for all followers and relaxes the constraint on leader’s input. Then, a smooth approximation function is applied to handle the input saturation in MASs. Subsequently, for achieving FTBC of MASs, a new adaptive controller is designed based on DABLSE by introducing sign vector and hyperbolic tangent function of error. This design reduces the controller chattering caused by direct compensation using the error’s sign vector in existing literature. Finally, the effectiveness of proposed FTBC strategy is validated by a simulation.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129853"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145575487","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 : 2026-04-15Epub Date: 2025-11-25DOI: 10.1016/j.amc.2025.129819
Yan-Jiao Liu, Jian-Hua Yin
The maximum number of copies of a complete subgraph Ks in any H-free graph on n vertices is defined to be the generalized Turán number ex(n, Ks, H). Let the disjoint union of k copies of Sℓ be denoted kSℓ, where Sℓ is the star graph with vertices. For ℓ ≥ 1 and n ≥ 1, Gan et al. and Chase determined ex(n, Ks, Sℓ) for s ≥ 3, Liu and Yin determined ex(n, Ks, 2Sℓ) for s ≥ 4 and ex(n, Ks, 3Sℓ) for s ≥ 5. In this paper, we further determine ex(n, Ks, 4Sℓ) for all s ≥ 6.
{"title":"The generalized Turán number of 4Sℓ","authors":"Yan-Jiao Liu, Jian-Hua Yin","doi":"10.1016/j.amc.2025.129819","DOIUrl":"10.1016/j.amc.2025.129819","url":null,"abstract":"<div><div>The maximum number of copies of a complete subgraph <em>K<sub>s</sub></em> in any <em>H</em>-free graph on <em>n</em> vertices is defined to be the generalized Turán number <em>ex</em>(<em>n, K<sub>s</sub>, H</em>). Let the disjoint union of <em>k</em> copies of <em>S</em><sub>ℓ</sub> be denoted <em>kS</em><sub>ℓ</sub>, where <em>S</em><sub>ℓ</sub> is the star graph with <span><math><mrow><mi>ℓ</mi><mo>+</mo><mn>1</mn></mrow></math></span> vertices. For ℓ ≥ 1 and <em>n</em> ≥ 1, Gan et al. and Chase determined <em>ex</em>(<em>n, K<sub>s</sub>, S</em><sub>ℓ</sub>) for <em>s</em> ≥ 3, Liu and Yin determined <em>ex</em>(<em>n, K<sub>s</sub></em>, 2<em>S</em><sub>ℓ</sub>) for <em>s</em> ≥ 4 and <em>ex</em>(<em>n, K<sub>s</sub></em>, 3<em>S</em><sub>ℓ</sub>) for <em>s</em> ≥ 5. In this paper, we further determine <em>ex</em>(<em>n, K<sub>s</sub></em>, 4<em>S</em><sub>ℓ</sub>) for all <em>s</em> ≥ 6.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129819"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145592978","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}
Central high-resolution schemes usually consider continuous variation inside cells. Hence, capturing of a possible discontinuity inside a cell would be an open research area. Here, it is tried to capture a (stationary) discontinuity inside a cell by the concept of the discontinuous radial basis functions (RBFs) in the reconstruction stage of central high-resolution schemes. As the formulations of central high-resolution schemes are in the framework of the Godunov method, firstly the concept of the point-wise interpolating discontinuous RBFs is extended to average interpolating discontinuous RBFs. At the next stage, by using this special reconstruction (by considering a discontinuity inside a cell), the formulation of the fully-discrete form is derived. Corresponding semi-discrete form is then obtained in the limiting state, as the time step, Δt approaches zero. In the reconstruction stage, for a cell with a possible discontinuity inside the cell, discontinuous RBFs with C0 continuity feature are used and for other cells (without inner discontinuities), smooth RBFs with C2 continuity property are utilized. Here, the Wendland family of 1-D RBFs is considered with different continuity properties. This central formulation would be useful for problems with stationary discontinuities. Finally, different 1-D and 2-D benchmarks with stationary discontinuities are examined including stress wave propagation problems in layered media. The benchmarks and examples include conservation laws with space-dependent flux functions.
{"title":"Central high resolution schemes capturing discontinuities inside cells via average-interpolating discontinuous radial basis functions: Applications to wave propagation in layered media","authors":"Hassan Yousefi , Iradj Mahmoudzadeh Kani , Timon Rabczuk","doi":"10.1016/j.amc.2025.129838","DOIUrl":"10.1016/j.amc.2025.129838","url":null,"abstract":"<div><div>Central high-resolution schemes usually consider continuous variation inside cells. Hence, capturing of a possible discontinuity inside a cell would be an open research area. Here, it is tried to capture a (stationary) discontinuity inside a cell by the concept of the discontinuous radial basis functions (RBFs) in the <em>reconstruction</em> stage of central high-resolution schemes. As the formulations of central high-resolution schemes are in the framework of the Godunov method, firstly the concept of the point-wise interpolating discontinuous RBFs is extended to <em>average interpolating</em> discontinuous RBFs. At the next stage, by using this special reconstruction (by considering a discontinuity inside a cell), the formulation of the fully-discrete form is derived. Corresponding semi-discrete form is then obtained in the limiting state, as the time step, Δ<em>t</em> approaches zero. In the reconstruction stage, for a cell with a possible discontinuity inside the cell, discontinuous RBFs with <em>C</em><sup>0</sup> continuity feature are used and for other cells (without inner discontinuities), smooth RBFs with <em>C</em><sup>2</sup> continuity property are utilized. Here, the Wendland family of 1-D RBFs is considered with different continuity properties. This central formulation would be useful for problems with stationary discontinuities. Finally, different 1-D and 2-D benchmarks with stationary discontinuities are examined including stress wave propagation problems in layered media. The benchmarks and examples include conservation laws with space-dependent flux functions.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129838"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145567379","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 : 2026-04-15Epub Date: 2025-11-21DOI: 10.1016/j.amc.2025.129849
Zihan Wang, Qing Yang, Hao Shen
In this paper, a value iteration (VI) scheme considering the guaranteed state convergence rate (GSCR) is proposed for multi-input singularly perturbed systems (MISPSs) with unknown system dynamics. Unlike traditional reduced-order methods, a full-order modeling approach is adopted for MISPSs, thereby avoiding the suboptimality of reduction techniques. In contrast to classical differential games, this work explicitly considers the state convergence rate under multiple interacting inputs. Specifically, the control policy design is formulated as solving a guaranteed game algebraic Riccati equation (GGARE). To solve GGARE, an online model-free VI algorithm is developed, which obtains the solutions to Nash equilibrium in real-time using measured state and input data. Compared to existing algorithms, the proposed algorithm offers three key advantages: i) No initial stable control gain is needed; ii) Rapid state convergence is achieved; iii) The information on system dynamics is not required. Finally, the effectiveness of the proposed method is validated through an RC ladder circuit example.
{"title":"A learning-based value iteration scheme for singularly perturbed systems and its application in RC ladder circuit","authors":"Zihan Wang, Qing Yang, Hao Shen","doi":"10.1016/j.amc.2025.129849","DOIUrl":"10.1016/j.amc.2025.129849","url":null,"abstract":"<div><div>In this paper, a value iteration (VI) scheme considering the guaranteed state convergence rate (GSCR) is proposed for multi-input singularly perturbed systems (MISPSs) with unknown system dynamics. Unlike traditional reduced-order methods, a full-order modeling approach is adopted for MISPSs, thereby avoiding the suboptimality of reduction techniques. In contrast to classical differential games, this work explicitly considers the state convergence rate under multiple interacting inputs. Specifically, the control policy design is formulated as solving a guaranteed game algebraic Riccati equation (GGARE). To solve GGARE, an online model-free VI algorithm is developed, which obtains the solutions to Nash equilibrium in real-time using measured state and input data. Compared to existing algorithms, the proposed algorithm offers three key advantages: i) No initial stable control gain is needed; ii) Rapid state convergence is achieved; iii) The information on system dynamics is not required. Finally, the effectiveness of the proposed method is validated through an RC ladder circuit example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129849"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145555389","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 : 2026-04-01Epub Date: 2025-11-17DOI: 10.1016/j.amc.2025.129836
Xianhao Meng , Yuwan Zhang , Weichen Zhao
The Wiener index W(D) of a digraph D is defined as the sum of distances between all ordered pairs of vertices. In directed graphs, a specific convention is adopted: when there exists no directed path connecting vertex a to vertex b, the distance d(a, b) is defined as 0. Notably, this particular stipulation has been put forward independently in a number of research works focusing on directed graphs. In this paper, we obtain the maximum Wiener index of the oriented fan graphs and wheel graphs.
{"title":"The maximum Wiener index of some oriented graphs","authors":"Xianhao Meng , Yuwan Zhang , Weichen Zhao","doi":"10.1016/j.amc.2025.129836","DOIUrl":"10.1016/j.amc.2025.129836","url":null,"abstract":"<div><div>The Wiener index <em>W(D)</em> of a digraph <em>D</em> is defined as the sum of distances between all ordered pairs of vertices. In directed graphs, a specific convention is adopted: when there exists no directed path connecting vertex <em>a</em> to vertex <em>b</em>, the distance <em>d</em>(<em>a, b</em>) is defined as 0. Notably, this particular stipulation has been put forward independently in a number of research works focusing on directed graphs. In this paper, we obtain the maximum Wiener index of the oriented fan graphs and wheel graphs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"514 ","pages":"Article 129836"},"PeriodicalIF":3.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145553800","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 : 2026-04-01Epub Date: 2025-11-06DOI: 10.1016/j.amc.2025.129818
Yaser Alizadeh , Sandi Klavžar , Javaher Langari
For a positive integer , a graph is -stepwise irregular (-SI graph) if the degrees of every pair of adjacent vertices differ by exactly . Such graphs are necessarily bipartite. Using graph products it is demonstrated that for any and any there exists a -SI graph of diameter . A sharp upper bound for the maximum degree of a -SI graph of a given order is proved. The size of -SI graphs is bounded in general and in the special case when . Along the way the degree complexity of a graph is introduced and used.
{"title":"Extremal results on k-stepwise irregular graphs","authors":"Yaser Alizadeh , Sandi Klavžar , Javaher Langari","doi":"10.1016/j.amc.2025.129818","DOIUrl":"10.1016/j.amc.2025.129818","url":null,"abstract":"<div><div>For a positive integer <span><math><mi>k</mi></math></span>, a graph <span><math><mi>G</mi></math></span> is <span><math><mi>k</mi></math></span>-stepwise irregular (<span><math><mi>k</mi></math></span>-SI graph) if the degrees of every pair of adjacent vertices differ by exactly <span><math><mi>k</mi></math></span>. Such graphs are necessarily bipartite. Using graph products it is demonstrated that for any <span><math><mrow><mi>k</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and any <span><math><mrow><mi>d</mi><mo>≥</mo><mn>2</mn></mrow></math></span> there exists a <span><math><mi>k</mi></math></span>-SI graph of diameter <span><math><mi>d</mi></math></span>. A sharp upper bound for the maximum degree of a <span><math><mi>k</mi></math></span>-SI graph of a given order is proved. The size of <span><math><mi>k</mi></math></span>-SI graphs is bounded in general and in the special case when <span><math><mrow><mi>gcd</mi><mo>(</mo><mstyle><mi>Δ</mi></mstyle><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>k</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></math></span>. Along the way the degree complexity of a graph is introduced and used.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"514 ","pages":"Article 129818"},"PeriodicalIF":3.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145449026","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 : 2026-04-01Epub Date: 2025-11-11DOI: 10.1016/j.amc.2025.129820
Chunfeng Cui , Liqun Qi
An M-eigenvalue of a nonnegative biquadratic tensor is referred to as an M-eigenvalue if it has a pair of nonnegative M-eigenvectors. If furthermore that pair of M-eigenvectors is positive, then that M-eigenvalue is called an M-eigenvalue. A nonnegative biquadratic tensor has at least one M eigenvalue, and the largest M-eigenvalue is both the largest M-eigenvalue and the M-spectral radius. For irreducible nonnegative biquadratic tensors, all the M-eigenvalues are M-eigenvalues. Although the M-eigenvalues of irreducible nonnegative biquadratic tensors are not unique in general, we establish a sufficient condition to ensure their uniqueness. For an irreducible nonnegative biquadratic tensor, the largest M-eigenvalue has a max-min characterization, while the smallest M-eigenvalue has a min-max characterization. A Collatz algorithm for computing the largest M-eigenvalues is proposed. Numerical results are reported.
{"title":"Nonnegative biquadratic tensors","authors":"Chunfeng Cui , Liqun Qi","doi":"10.1016/j.amc.2025.129820","DOIUrl":"10.1016/j.amc.2025.129820","url":null,"abstract":"<div><div>An M-eigenvalue of a nonnegative biquadratic tensor is referred to as an M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalue if it has a pair of nonnegative M-eigenvectors. If furthermore that pair of M-eigenvectors is positive, then that M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalue is called an M<span><math><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></math></span>-eigenvalue. A nonnegative biquadratic tensor has at least one M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span> eigenvalue, and the largest M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalue is both the largest M-eigenvalue and the M-spectral radius. For irreducible nonnegative biquadratic tensors, all the M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalues are M<span><math><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></math></span>-eigenvalues. Although the M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalues of irreducible nonnegative biquadratic tensors are not unique in general, we establish a sufficient condition to ensure their uniqueness. For an irreducible nonnegative biquadratic tensor, the largest M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalue has a max-min characterization, while the smallest M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalue has a min-max characterization. A Collatz algorithm for computing the largest M<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-eigenvalues is proposed. Numerical results are reported.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"514 ","pages":"Article 129820"},"PeriodicalIF":3.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145509286","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 : 2026-04-01Epub Date: 2025-11-15DOI: 10.1016/j.amc.2025.129847
Yupin Wang , Tengda Wei , Feifei Du , Hui Li , Shutang Liu
In this paper, fractional Julia sets are constructed through fractional difference equations defined on time scale . The influence of memory and scale within the fractional (q, h)-difference system on its fractal dynamics is elucidated through an exploration of how memory, geometric, and algebraic parameters shape the resulting Julia sets. Numerical investigations using box-counting dimension analysis and symmetry criteria uncover intricate properties of these sets, such as their resilience to perturbations, while their central symmetry in a particular scenario is established.
{"title":"Fractional Julia sets on time scales","authors":"Yupin Wang , Tengda Wei , Feifei Du , Hui Li , Shutang Liu","doi":"10.1016/j.amc.2025.129847","DOIUrl":"10.1016/j.amc.2025.129847","url":null,"abstract":"<div><div>In this paper, fractional Julia sets are constructed through fractional difference equations defined on time scale <span><math><msub><mi>T</mi><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></mrow></msub></math></span>. The influence of memory and scale within the fractional (<em>q, h</em>)-difference system on its fractal dynamics is elucidated through an exploration of how memory, geometric, and algebraic parameters shape the resulting Julia sets. Numerical investigations using box-counting dimension analysis and symmetry criteria uncover intricate properties of these sets, such as their resilience to perturbations, while their central symmetry in a particular scenario is established.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"514 ","pages":"Article 129847"},"PeriodicalIF":3.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535835","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 : 2026-04-01Epub Date: 2025-11-18DOI: 10.1016/j.amc.2025.129837
Zhifang Li, Xiaojie Chen
In recent years, the evolutionary dynamics of opinions on social networks have attracted considerable attention. Evolutionary game theory has been employed to explore the mechanisms underlying opinion evolution. However, most prior works usually ignore the stochastic effects, such as decision-making errors, and thus far few studies have investigated how to promote the emergence of opinions within this context. In this study, we develop a game-theoretic model to investigate the dynamics of opinion evolution with decision errors on social networks. Inspired by previous research, we assume that individuals make decisions on opinion choices according to the global public knowledge and local interaction feedback. Using the method of coalescing random walks, we derive the average fraction of two opinions and determine the mathematical condition for the emergence of one opinion in the limit of rare errors. Our findings show that this critical condition depends on the network topology, the basic score of each opinion, and feedback scores. It is noteworthy that our theoretical analysis can be applied to any network structure. Moreover, we perform simulations on different types of networks, including regular, scale-free, and small-world networks, to validate our theoretical results. All simulation outcomes confirm the corresponding theoretical predictions. We further show that the emergence condition for one opinion, established under rare error limit, is robust across all levels of error. Specifically, when one opinion is favored over the other in the limit of rare errors, it remains favored for all error rate values, although its average fraction decreases as the error rate increases. Conversely, when the opinion is disfavored in the limit of rare errors, the average fraction increases with error rate, yet it never becomes favored even in the extreme case of high error rates.
{"title":"Evolutionary dynamics of binary opinions with decision errors on social networks","authors":"Zhifang Li, Xiaojie Chen","doi":"10.1016/j.amc.2025.129837","DOIUrl":"10.1016/j.amc.2025.129837","url":null,"abstract":"<div><div>In recent years, the evolutionary dynamics of opinions on social networks have attracted considerable attention. Evolutionary game theory has been employed to explore the mechanisms underlying opinion evolution. However, most prior works usually ignore the stochastic effects, such as decision-making errors, and thus far few studies have investigated how to promote the emergence of opinions within this context. In this study, we develop a game-theoretic model to investigate the dynamics of opinion evolution with decision errors on social networks. Inspired by previous research, we assume that individuals make decisions on opinion choices according to the global public knowledge and local interaction feedback. Using the method of coalescing random walks, we derive the average fraction of two opinions and determine the mathematical condition for the emergence of one opinion in the limit of rare errors. Our findings show that this critical condition depends on the network topology, the basic score of each opinion, and feedback scores. It is noteworthy that our theoretical analysis can be applied to any network structure. Moreover, we perform simulations on different types of networks, including regular, scale-free, and small-world networks, to validate our theoretical results. All simulation outcomes confirm the corresponding theoretical predictions. We further show that the emergence condition for one opinion, established under rare error limit, is robust across all levels of error. Specifically, when one opinion is favored over the other in the limit of rare errors, it remains favored for all error rate values, although its average fraction decreases as the error rate increases. Conversely, when the opinion is disfavored in the limit of rare errors, the average fraction increases with error rate, yet it never becomes favored even in the extreme case of high error rates.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"514 ","pages":"Article 129837"},"PeriodicalIF":3.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145553798","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 : 2026-04-01Epub Date: 2025-11-17DOI: 10.1016/j.amc.2025.129841
Aoxue Xiang , Xinyuan Zhao , Ruicheng Ma
This paper studies the optimal herdability control for a class of hierarchical linear multi-agent systems (MASs). Unlike existing work, the finite-horizon herdability problem is presented of hierarchical MASs, which is an extension of classical controllability. Firstly, agents perform local actions in the lower layer, which are integrated into the overall system through connections between agents in the upper layer. Using this hierarchical system structure, a sufficient condition can be constructed to constrain the lower bound of all agents. Then, based on this sufficient condition, an optimal herdability controller is designed to achieve finite-horizon herdability for the hierarchical MASs. The optimal herdability control algorithms for hierarchical MASs are proposed in both discrete-time and continuous-time cases, respectively. Finally, three examples are provided to show the effectiveness of the proposed results.
{"title":"Finite-horizon optimal herdability control for hierarchical linear multi-agent systems with signed weighted graphs","authors":"Aoxue Xiang , Xinyuan Zhao , Ruicheng Ma","doi":"10.1016/j.amc.2025.129841","DOIUrl":"10.1016/j.amc.2025.129841","url":null,"abstract":"<div><div>This paper studies the optimal herdability control for a class of hierarchical linear multi-agent systems (MASs). Unlike existing work, the finite-horizon herdability problem is presented of hierarchical MASs, which is an extension of classical controllability. Firstly, agents perform local actions in the lower layer, which are integrated into the overall system through connections between agents in the upper layer. Using this hierarchical system structure, a sufficient condition can be constructed to constrain the lower bound of all agents. Then, based on this sufficient condition, an optimal herdability controller is designed to achieve finite-horizon herdability for the hierarchical MASs. The optimal herdability control algorithms for hierarchical MASs are proposed in both discrete-time and continuous-time cases, respectively. Finally, three examples are provided to show the effectiveness of the proposed results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"514 ","pages":"Article 129841"},"PeriodicalIF":3.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145554291","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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