Applied Mathematics and Computation最新文献

{"title":"A class of generalized shift-splitting preconditioners for double saddle point problems","authors":"Sk. Safique Ahmad,&nbsp;Pinki Khatun","doi":"10.1016/j.amc.2025.129658","DOIUrl":"10.1016/j.amc.2025.129658","url":null,"abstract":"<div><div>In this paper, we propose a generalized shift-splitting (GSS) preconditioner, along with its two relaxed variants to solve the double saddle point problem (DSPP). The convergence of the associated GSS iterative method is analyzed, and sufficient conditions for its convergence are established. Spectral analyses are performed to derive sharp bounds for the eigenvalues of the preconditioned matrices. Numerical experiments based on examples arising from the PDE-constrained optimization problem and the leaky lid driven cavity problem demonstrate the effectiveness and robustness of the proposed preconditioners compared with existing state-of-the-art preconditioners.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"509 ","pages":"Article 129658"},"PeriodicalIF":3.5,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144711803","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}

{"title":"On (k,g)-graphs without (g + 1)-cycles","authors":"Leonard Chidiebere Eze ,&nbsp;Robert Jajcay ,&nbsp;Jorik Jooken","doi":"10.1016/j.amc.2025.129645","DOIUrl":"10.1016/j.amc.2025.129645","url":null,"abstract":"<div><div>A <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span>-graph is a <em>k</em>-regular graph of girth <em>g</em> which does not contain cycles of length <span><math><mi>g</mi><mo>+</mo><mn>1</mn></math></span>. Such graphs are known to exist for all parameter pairs <span><math><mi>k</mi><mo>≥</mo><mn>3</mn><mo>,</mo><mi>g</mi><mo>≥</mo><mn>3</mn></math></span>, and we focus on determining the orders <span><math><mi>n</mi><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span> of the smallest <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span>-graphs. This problem can be viewed as a special case of the previously studied <em>Girth Pair Problem</em>, the problem of finding the order of a smallest <em>k</em>-regular graph in which the length of a smallest even length cycle and the length of a smallest odd length cycle are prescribed. When considering the case of an odd girth <em>g</em>, this problem also yields results towards the <em>Cage Problem</em>, the problem of finding the order of a smallest <em>k</em>-regular graph of girth <em>g</em>. We establish the monotonicity of the function <span><math><mi>n</mi><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span> with respect to increasing <em>g</em>, and present universal lower bounds for the values <span><math><mi>n</mi><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span>. We propose an algorithm for generating all <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span>-graphs on <em>n</em> vertices, use this algorithm to determine several of the smaller values <span><math><mi>n</mi><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span>, and discuss various approaches to finding smallest <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>,</mo><munder><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow><mo>_</mo></munder><mo>)</mo></math></span>-graphs within several classes of highly symmetrical graphs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129645"},"PeriodicalIF":3.5,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687374","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}

{"title":"Inverse optimal incremental control of nonlinear jump-diffusion systems","authors":"Yuanhong Ren ,&nbsp;Dingli Hua ,&nbsp;Mingxuan Shen ,&nbsp;Guangchen Zhang","doi":"10.1016/j.amc.2025.129643","DOIUrl":"10.1016/j.amc.2025.129643","url":null,"abstract":"<div><div>In this study, we address the challenge of solving the inverse optimal incremental control problem for nonlinear jump-diffusion systems by proposing an innovative inverse optimal incremental controller framework. A pivotal aspect of our approach lies in the novel utilization of an auxiliary incremental controller as a cornerstone for constructing the inverse optimal controller. This design not only ensures that the resultant controller is optimal in the sense of minimizing a meaningful cost functional but also imparts upon the closed-loop jump-diffusion system the property of incremental global <span><math><msub><mrow><mi>K</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-exponential stability. This dual capability of achieving optimality and robust stability underscores the significance and novelty of our proposed controller design. Leveraging our inverse incremental controller design, we derive a comprehensive set of conditions that guarantee the inverse incremental <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> control of nonlinear jump-diffusion systems. Simultaneously, we develop a methodology for estimating the incremental Hamilton-Jacobi inequality (iHJI), which serves as a cornerstone for validating the controller's performance. We present two illustrative engineering examples, showcasing the practical implications and robustness of our approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129643"},"PeriodicalIF":3.5,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687373","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}

{"title":"Applications of Schur-Cohn matrix and matrix pencil methods in studying the stability of high-dimensional neutral delay differential equations","authors":"Jian Ma ,&nbsp;Yixue Ma ,&nbsp;Qiuxia Fu","doi":"10.1016/j.amc.2025.129639","DOIUrl":"10.1016/j.amc.2025.129639","url":null,"abstract":"<div><div>This note will provide a novel method for figuring out when and where the generic high-dimensional neutral delay differential equations can keep stable. Using the Schur-Cohn matrices, matrix pencils, and generalized eigenvalues, all imaginary axis eigenvalues will be presented and the critical delays will be determined in a straightforward manner. Additionally, a simple MATLAB-based algorithm will be presented. The main contribution of this paper is that we provide a computational method for determining imaginary axis eigenvalues and minimal delay margin on general high-dimensional neutral delay differential equations with real coefficients.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129639"},"PeriodicalIF":3.5,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687372","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}

{"title":"Sliding mode control for T-S fuzzy delayed systems via event-triggered round-robin protocol","authors":"Zhiyuan Zuo ,&nbsp;Jun Hu ,&nbsp;Hongxu Zhang ,&nbsp;Hao Liu ,&nbsp;Guangchen Zhang","doi":"10.1016/j.amc.2025.129633","DOIUrl":"10.1016/j.amc.2025.129633","url":null,"abstract":"<div><div>This study addresses the sliding mode control (SMC) issue for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay, which takes the access constrained communication network into account. Firstly, a new event-triggered round-robin (ETRR) protocol is designed to reduce the communication burden. Subsequently, according to the ETRR protocol, a new fuzzy mode-dependent SMC law is constructed, where the controller's membership functions (MFs) depend on the compromised triggered state. Furthermore, sufficient conditions related to the event-triggered mechanism are provided to ensure the stability of the controlled system with satisfactory <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> performance and the reachability of the sliding surface by constructing a token-dependent Lyapunov functional. In addition, an optimization problem is established to solve the optimal <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> performance level. Finally, the usefulness of the proposed SMC approach and the superiority of the ETRR protocol are displayed by comparative simulation experiments.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129633"},"PeriodicalIF":3.5,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680656","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}

{"title":"Quasi-synchronization of multiplex networks under deception attacks via event-triggered impulsive protocol","authors":"Xin Jin ,&nbsp;Xiaojie Chen ,&nbsp;Zhengxin Wang","doi":"10.1016/j.amc.2025.129635","DOIUrl":"10.1016/j.amc.2025.129635","url":null,"abstract":"<div><div>In our work, we provide a novel mathematical model for heterogeneous multiplex networks under deception attacks to analyze synchronization behaviors of the nodes. We introduce a leader and design a static event-triggered impulsive protocol. In addition, to further save control costs, we then design a dynamic event-triggered impulsive protocol. By utilizing the Lyapunov stability method and average impulsive interval method, for both static and dynamic event-triggered impulsive protocols, the sufficient synchronization conditions guaranteeing that all follower nodal states finally converge to a bounded region are derived, and the value of upper bound of the convergence region is also determined. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129635"},"PeriodicalIF":3.5,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680658","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}

{"title":"Tridiagonal M-matrices with tridiagonal Moore-Penrose inverse","authors":"M.I. Bueno ,&nbsp;Susana Furtado ,&nbsp;K. Kranthi Priya ,&nbsp;K.C. Sivakumar","doi":"10.1016/j.amc.2025.129640","DOIUrl":"10.1016/j.amc.2025.129640","url":null,"abstract":"<div><div>In this paper, we characterize the singular tridiagonal <em>M</em>-matrices whose Moore-Penrose inverse is tridiagonal, extending the recent result (Barreras and Peña, 2019) describing the nonsingular tridiagonal M-matrices whose inverse is tridiagonal.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129640"},"PeriodicalIF":3.5,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680657","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}

{"title":"Fast finite-time consensus protocol for high-order nonlinear multi-agent systems based on event-triggered communication scheme","authors":"Junsheng Zhao ,&nbsp;Haina Zhao ,&nbsp;Ying Song ,&nbsp;Zong-Yao Sun ,&nbsp;Dengxiu Yu","doi":"10.1016/j.amc.2025.129631","DOIUrl":"10.1016/j.amc.2025.129631","url":null,"abstract":"<div><div>This paper proposes an adaptive fast finite-time tracking consensus protocol for high-order nonlinear multi-agent systems. To overcome the limitation of finite-time stability, where the convergence speed slows down when the initial state is far from the origin, the fast finite-time stability theory is incorporated into the multi-agent systems to ensure rapid convergence of the tracking error. Furthermore, the power integrator technique is integrated into the backstepping framework to address the inherent singularity issues in high-order systems. Meanwhile, neural networks are used as online approximators to model unknown nonlinear functions, with the <span><math><mi>t</mi><mi>a</mi><mi>n</mi><mi>h</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></math></span> function adopted to mitigate the impact of approximation errors effectively. The developed dynamic event-triggered controller can reduce the frequency of control updates, effectively saving communication resources. Finally, two simulation examples demonstrate the effectiveness of the proposed strategy.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129631"},"PeriodicalIF":3.5,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670445","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}

{"title":"SEIAR rumor spreading model with antagonistic states in hypernetworks","authors":"Peng-Yue Li ,&nbsp;Feng Hu ,&nbsp;Fa-Xu Li ,&nbsp;You-Feng Zhao ,&nbsp;Yu-Rong Song","doi":"10.1016/j.amc.2025.129637","DOIUrl":"10.1016/j.amc.2025.129637","url":null,"abstract":"<div><div>Rumors pose serious harm to society, often affecting public safety and social stability as they spread. Most existing studies on rumor propagation models are based on binary relationships within ordinary graphs, constructing complex network information propagation models. However, these models struggle to capture the multi-dimensional, multi-attribute, and multi-relational complex interaction characteristics of real-world social networks. This paper proposes an SEIAR (Susceptible-Exposed-Informed-Antagonistic-Removed) rumor propagation model, built upon hypergraph theory, which effectively captures complex interaction relationships. The model builds on the SEIR framework by introducing a debunking state, enabling a more comprehensive reflection of the dynamic characteristics of rumor propagation and debunking behavior. Using mean-field theory, the dynamic equations of the SEIAR model are derived, along with an analytical expression for its basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, and a stability analysis is conducted. The study shows that when <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></math></span>, the rumor-free equilibrium state of the model is locally and globally stable, ultimately leading to the disappearance of the rumor. When <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></math></span>, the rumor persists and continues to spread. Numerical simulations using the Runge-Kutta method were performed to validate the effectiveness of the theoretical findings. Subsequently, the model was validated using actual rumor datasets, and the results showed that the model can effectively simulate the rumor propagation process in real social networks. In addition, this paper systematically analyzes the impact of factors such as the influence of debunkers, information control strength and control time, individual interests, information timeliness, and network structure on rumor propagation, and compares the propagation characteristics of different models through simulation. The model presented in this paper broadens the perspective of information propagation research, providing a detailed depiction of the rumor propagation mechanism that includes a debunking state, and offers significant theoretical support for developing rumor control strategies.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129637"},"PeriodicalIF":3.5,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670446","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}

{"title":"Time-varying dynamic event-triggered-based prescribed-time leader-following consensus for multi-agent systems with input saturation","authors":"Meilin Li ,&nbsp;Yue Long ,&nbsp;Kai Zhang ,&nbsp;Tieshan Li","doi":"10.1016/j.amc.2025.129630","DOIUrl":"10.1016/j.amc.2025.129630","url":null,"abstract":"<div><div>This paper is concerned with prescribed-time leader-following consensus tracking for multi-agent systems subject to input saturation and limited resources under directed topology. A time-varying dynamic event-triggered-based prescribed-time approach is proposed to realize the consensus tracking in preset time. First, a novel dynamic event-triggered mechanism based on time-varying parameter is designed to further reduce actuator losses and computational resource usage. Second, a bounded protocol based on prescribed-time is proposed to ensure consensus tracking of the controlled system within the preset time, while keeping the control input within the saturation threshold. Third, the expression of the minimum inter-event time is derived based on the special properties of the parametric Lyapunov equation. The derived expression exhibits a straightforward and clear relationship with the system matrix, and no Zeno phenomenon occurs in the closed-system. Finally, the validity of the design method is verified by several inverted pendulum systems.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129630"},"PeriodicalIF":3.5,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657229","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}