{"title":"Stability of partially unstable discrete-time switched positive nonlinear systems with delays","authors":"Jinyuan Ni , Yin Sheng , Qiang Xiao , Zhigang Zeng , Tingwen Huang","doi":"10.1016/j.amc.2025.129591","DOIUrl":"10.1016/j.amc.2025.129591","url":null,"abstract":"<div><div>This paper addresses the stability issue of discrete-time switched positive nonlinear systems (SPNSs) characterized by partial unstable subsystems and constant delays. Firstly, we use a parameter to constrain the ratio of active durations of the stable and unstable modes, and derive the exponential stability conditions for SPNSs based on a key function. Then we analyze the relationship between convergence speed and the constant delay. Additionally, we obtain a stability criterion of SPNSs under a particular sequence of switching signals. Finally, we validate the results through a numerical example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129591"},"PeriodicalIF":3.5,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242156","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 source problems for identifying time and space-dependent coefficients in a 2D generalized diffusion equation","authors":"Asim Ilyas , Stefano Serra-Capizzano","doi":"10.1016/j.amc.2025.129597","DOIUrl":"10.1016/j.amc.2025.129597","url":null,"abstract":"<div><div>This article addresses two inverse source problems related to determining a space-dependent source term and a time-dependent coefficient in a two-dimensional generalized diffusion equation. The considered problems are ill-posed in the Hadamard sense, where small perturbations in the data can lead to uncontrolled variations in the solution. The present work also provides existence and uniqueness results for the solutions of these problems under appropriate over-specified and regularity conditions. Special cases of the diffusion equation are examined, focusing on specific selections of the memory kernel involved in the time-fractional derivative. The results are illustrated with several examples, demonstrating the practical implications of the proposed methods for inverse source problems.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129597"},"PeriodicalIF":3.5,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242241","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":"Q-learning driven cooperative evolution with dual-reputation incentive mechanisms","authors":"Qianwei Zhang, Xinran Zhang","doi":"10.1016/j.amc.2025.129590","DOIUrl":"10.1016/j.amc.2025.129590","url":null,"abstract":"<div><div>Reinforcement learning, as a powerful framework for analyzing strategic dynamics in evolutionary games, has gained significant traction in game theory research. In this study, we propose a dual-reputation incentive mechanism that integrates individual and group reputation metrics within the spatial Prisoner's Dilemma paradigm, aiming to elucidate how adaptive Q-learning drives the evolution of cooperation. Our approach combines traditional game payoffs with reputation-based rewards through a novel Q-learning reward function, strategically decomposing reputation into two components: individual rewards (quantifying an agent’s behavioral history) and group rewards (reflecting the collective reputation of their local neighborhood). Simulations demonstrate that when individual reputation rewards are prioritized, agents optimize long-term gains by dynamically adjusting strategies under strong motivational incentives, which ultimately enhances global cooperation levels. Microscopic analysis reveals that individual reputation incentives promote high-density cooperator clusters and facilitate cooperative behavior propagation. Furthermore, when a high weight is assigned to individual reputation rewards, evolutionary analysis demonstrates that cooperative Q-values consistently exceeds defective ones, indicating the emergence of cooperation as an evolutionarily stable strategy. This research provides theoretical insights for designing reputation-aware reinforcement learning systems to foster cooperation in real-world social dilemmas.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129590"},"PeriodicalIF":3.5,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222926","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":"A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations","authors":"Nguyen Van Duc , Thi-Phong Nguyen","doi":"10.1016/j.amc.2025.129567","DOIUrl":"10.1016/j.amc.2025.129567","url":null,"abstract":"<div><div>This paper investigates a Tikhonov-type approach for addressing inverse source problems related to time-space fractional parabolic equations. The method ensures a Hölder-type error estimate for the regularized solution at an optimal order, enabling a fixed parameter choice rule that does not depend on the data. Efficient numerical algorithms are devised for practical implementation, accompanied by numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129567"},"PeriodicalIF":3.5,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222368","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":"Predefined-time Lyapunov stability for nonlinear systems via a dynamic event-triggered control strategy","authors":"Jie Wu , Rongni Yang , Levente Kovacs , Peng Shi","doi":"10.1016/j.amc.2025.129558","DOIUrl":"10.1016/j.amc.2025.129558","url":null,"abstract":"<div><div>In this paper, the predefined-time Lyapunov stability of nonlinear systems is investigated via a dynamic event-triggered control strategy. Specifically, we succeeded in making such systems with local finite-time convergence property admit a larger convergence domain within a predefined instant. As is well known, the presence of finite-time property brings great difficulties in excluding Zeno behavior of event-triggered mechanism. Hence, a possible solution is that the designed event-based controller only works in extended domain, while the convergence of initial domain is generated by system itself. Thus the Zeno behavior is excluded. Meanwhile, sufficient conditions for the predefined-time stability of the resultant closed-loop systems are further established. Finally, two simulation examples including an application to Chua's circuit are presented to illustrate the effectiveness of the proposed theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129558"},"PeriodicalIF":3.5,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222927","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}
Huaiqin Wu , Xueqing Zhao , Lingyan Wang , Jinde Cao
{"title":"Observer-based fixed-time topology identification and synchronization for complex networks via quantized pinning control strategy","authors":"Huaiqin Wu , Xueqing Zhao , Lingyan Wang , Jinde Cao","doi":"10.1016/j.amc.2025.129568","DOIUrl":"10.1016/j.amc.2025.129568","url":null,"abstract":"<div><div>This paper is concerned with observer-based topology identification and synchronization in fixed time for multi-weighted complex networks (MWCNs) with/without output couplings. Firstly, a new fixed-time stability criterion is developed for continuous nonlinear systems by utilizing incomplete beta function and beta function ratio. Secondly, a quantized pinning controller and several topology observers are designed respectively to realize the fixed-time topology identification (FTTI) and the fixed-time synchronization (FTS) objective. Thirdly, by applying Lyapunov functional approach, the proposed stability criteria and the inequality analysis technique, some sufficient conditions with respect to the FTTI and the FTS are addressed in terms of linear matrix inequalities (LMIs). Eventually, the Chua's chaotic circuit and the island micro-grid, as two practical application examples, are given to demonstrate the effectiveness of the designed control strategies and the correctness of the obtained theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129568"},"PeriodicalIF":3.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204350","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":"Asymptotics for the coefficients of the truncated theta series","authors":"Renrong Mao","doi":"10.1016/j.amc.2025.129592","DOIUrl":"10.1016/j.amc.2025.129592","url":null,"abstract":"<div><div>Motivated by the groundbreaking work of Andrews and Merca, truncated theta series are extensively studied in recent years. Recently, Merca made conjectures on the non-negativity of the coefficient of <span><math><msup><mrow><mi>q</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> in truncated series from the Jacobi triple product identity and the quintuple product identity. In this paper, using Wright's Circle Method, we establish asymptotic formulas for the coefficients of these series and prove Merca's conjectures are true for sufficiently large <em>N</em>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129592"},"PeriodicalIF":3.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204349","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":"Decoding rhythmic complexity: A nonlinear dynamics approach via visibility graphs for classifying asymmetrical rhythmic frameworks of Turkish classical music","authors":"Fuat Kaan Mirza , Tunçer Baykaş , Mustafa Hekimoğlu , Önder Pekcan , Gönül Paçacı Tunçay","doi":"10.1016/j.amc.2025.129565","DOIUrl":"10.1016/j.amc.2025.129565","url":null,"abstract":"<div><div>The non-isochronous, hierarchical rhythmic cycles (usuls) of Turkish Classical Music (TCM) exhibit emergent temporal structures that challenge conventional rhythm analysis based on metrical regularity. To address this challenge, this study presents a complexity-oriented framework for usul classification, grounded in nonlinear time series analysis and network-based representations. Rhythmic signals are processed through energy envelope extraction, diffusion entropy analysis, and spectral transformations to capture multiscale temporal dynamics. Visibility graphs (VGs) are constructed from these representations to encode underlying structural complexity and temporal dependencies. Features derived from VG adjacency matrices serve as complexity-sensitive descriptors and enable high-accuracy classification (0.99) across 40 usul classes and 628 compositions. Energy envelope-derived graphs provide the most discriminative information, highlighting the importance of amplitude modulation in encoding rhythmic structure. Beyond classification, the analysis reveals self-organizing patterns and signatures of complexity, such as quasi-periodicity, scale-dependent variability, and entropy saturation, suggesting that usuls function as adaptive, nonlinear systems rather than metrically constrained patterns. The topological features extracted from the resulting graphs align with theoretical constructs from complexity science, such as modularity and long-range temporal correlations. This positions usul as an exemplary case for studying structured temporal complexity in cultural artifacts through the lens of dynamical systems. These findings contribute to computational rhythm analysis by demonstrating the efficacy of complexity measures in characterizing culturally specific rhythmic systems.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129565"},"PeriodicalIF":3.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204039","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":"Rainbow independent triangles in complete split graphs","authors":"Q. Wang, Z.M. Jin","doi":"10.1016/j.amc.2025.129589","DOIUrl":"10.1016/j.amc.2025.129589","url":null,"abstract":"<div><div>For two graphs <em>K</em> and <em>H</em>, where <em>K</em> contains <em>H</em> as a subgraph, the anti-Ramsey number of <em>H</em> in <em>K</em>, denoted by <span><math><mi>A</mi><mi>R</mi><mo>(</mo><mi>K</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></span>, is the largest integer <em>k</em> such that there exists a <em>k</em>-edge-coloring of <em>K</em> containing no rainbow <em>H</em>. Let <span><math><mn>2</mn><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> denote the union of two independent triangles. In this paper we obtain the value of <span><math><mi>A</mi><mi>R</mi><mo>(</mo><mover><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mo>‾</mo></mover><mo>+</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mn>2</mn><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span> for <span><math><mi>s</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>≥</mo><mn>4</mn></math></span> and <span><math><mi>s</mi><mo>+</mo><mi>n</mi><mo>≥</mo><mn>6</mn></math></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129589"},"PeriodicalIF":3.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204351","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":"Application of multiple two-dimensional interpolation methods to bathymetric data on the FVCOM unstructured triangular grid","authors":"Zongli Ruan , Guobing Qian , Yiwei Wang , Jia Xiao","doi":"10.1016/j.amc.2025.129564","DOIUrl":"10.1016/j.amc.2025.129564","url":null,"abstract":"<div><div>In general, the ocean bathymetric dataset is defined on a uniform rectangular grid, whereas FVCOM employs an unstructured triangular grid. Consequently, it is necessary to interpolate the data from the nodes of the rectangular grid onto those of the triangular grid. The nearest neighbor method, bilinear method, and inverse distance weighting (IDW) method are three commonly utilized two-dimensional interpolation techniques, and inverse distance weighted regression (IDWR) represents a more recent interpolation approach. In this study, these methods were applied to interpolate the bathymetric data of the Hormuz Strait and the North Indian Ocean onto the FVCOM triangular grid. The experimental results demonstrate that a very small error in the interpolation of bathymetric data was achieved. Additionally, these methods were compared with the interpolation techniques provided by the MATLAB system. The comparative analysis reveals that the bilinear method can achieve a superior interpolation effect compared to the other three methods.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"507 ","pages":"Article 129564"},"PeriodicalIF":3.5,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196359","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}