Applied Mathematics and Computation最新文献

{"title":"Numerical approximation for a stochastic time-fractional cable equation","authors":"Qimin Li ,&nbsp;Yubin Yan ,&nbsp;Leijie Qiao ,&nbsp;Yu Zhang","doi":"10.1016/j.amc.2025.129709","DOIUrl":"10.1016/j.amc.2025.129709","url":null,"abstract":"<div><div>An efficient numerical method is proposed to address a stochastic time-fractional cable equation driven by fractionally integrated additive noise. Under the reasonable assumptions, we rigorously establish for the first time, the existence, uniqueness, and regularity of the mild solution for this equation. For spatial discretization, a semi-discrete scheme is constructed employing the Galerkin FEM, and the optimal spatial error estimate is derived based on the semigroup approach. In temporal discretization, a piecewise constant function is introduced to approximate the noise, leading to the formulation of a regularized stochastic time-fractional cable equation. A detailed proof of the temporal error estimates is provided via the semigroup approach. Numerical experiments demonstrate that the temporal convergence order attains <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>τ</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> for initial data of either smooth or non-smooth type. The order is independent of the parameters <span><math><mrow><msub><mi>α</mi><mn>1</mn></msub><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><msub><mi>α</mi><mn>2</mn></msub><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, and <span><math><mrow><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> in the equation. These results perfectly align with the theoretical predictions.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"511 ","pages":"Article 129709"},"PeriodicalIF":3.4,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145103905","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":"Optimal information spreading strategy for containing epidemic spreading on higher-order multiplex networks","authors":"Jiayi Song ,&nbsp;Wenjie Li ,&nbsp;Yunzhu Xiao ,&nbsp;Ling Chen ,&nbsp;Chun Yang ,&nbsp;Li Qi ,&nbsp;Wei Wang","doi":"10.1016/j.amc.2025.129725","DOIUrl":"10.1016/j.amc.2025.129725","url":null,"abstract":"<div><div>When an epidemic spreads through a population, related information also spreads concurrently, prompting individuals to adopt protective behaviours (e.g., washing hands). Collective behaviour has been shown to play a critical role in shaping the dynamics of epidemic spreading, and higher-order networks offer a natural framework to describe such group interactions in social contact networks. Yet, the interplay between epidemic and information dynamics on higher-order structures is not fully understood, further limiting our understanding of the optimal information spreading strategy for containing epidemic spreading.In this study, we first construct a higher-order multiplex network framework based on simplicial complexes. Then, a coevolutionary spreading model is proposed, integrating epidemic spreading and information spreading on simplicial complexes. The epidemic spreads through both lower-order (pairwise) and higher-order (group) interactions, while information spreads through lower-order interactions in a degree-preferential manner. Using an extended Microscopic Markov Chain Approach, we analytically derive the dynamical equations of the system and compute the basic reproduction number using the next-generation matrix method. Finally, we conduct extensive numerical simulations of the spreading process across various parameter regimes. Our results demonstrate the role of higher-order infections in promoting epidemics. Although information spreading generally suppresses the spread of most epidemics, it can paradoxically enhance the spread of certain epidemics with a very low spreading capacity. Increases in the recovery probabilities of both the disease and the information can weaken the promoting effect of higher-order infection and enhance the suppressive effect of the information. For certain epidemics with weak spreading capabilities but strong recovery capabilities, the spread of information can completely suppress the outbreak of the disease, while the enhancement of higher-order infections can promote the outbreak of these diseases. By analysing the effects of different information spreading strategies on epidemic spreading, we find that the optimal strategy for containing the epidemic is to allow information to spread without degree preference.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"511 ","pages":"Article 129725"},"PeriodicalIF":3.4,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145103892","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":"Equilibrium analysis of edge-heterogeneous binary network games","authors":"Jiawen Wang ,&nbsp;Yangyang Luan ,&nbsp;Xiaoqun Wu","doi":"10.1016/j.amc.2025.129723","DOIUrl":"10.1016/j.amc.2025.129723","url":null,"abstract":"<div><div>Recent studies on the equilibrium of binary network games have primarily focused on scenarios characterized by agent heterogeneity, where agents exhibit unique attributes but their interactions with different neighbors remain uniform. In this paper, we investigate the edge-heterogeneous binary network game, a more general framework that incorporates heterogeneity into agent interactions. We establish two sufficient equilibrium conditions under asynchronous best-response dynamics from different perspectives. The first condition requires underlying symmetry in interactions between neighboring agents, integrating and generalizing three classical convergence situations in binary network games. The second condition focuses on network balance, positing that equilibrium is achievable if the coordination value network of a game is structurally balanced. Additionally, for games meeting this condition, we develop a method to predict the final state based on initial state information. These results reveal factors that steer edge-heterogeneous binary network games towards equilibrium, providing valuable insights for controlling such highly nonlinear systems. Lastly, we extend the analysis to higher-order network games and propose an equilibrium condition for edge-heterogeneous 2-order network games.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"511 ","pages":"Article 129723"},"PeriodicalIF":3.4,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145103890","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":"Switching event-triggered control for mean-square exponential synchronization of complex-valued delayed memristive neural networks under hybrid attacks","authors":"Shuai Xiao ,&nbsp;Zhen Wang ,&nbsp;Hongjue Wang ,&nbsp;Yueying Liu ,&nbsp;Xia Huang","doi":"10.1016/j.amc.2025.129715","DOIUrl":"10.1016/j.amc.2025.129715","url":null,"abstract":"<div><div>This paper investigates the mean-square exponential synchronization (MSES) of complex-valued delayed memristive neural networks (CVDMNNs) under complex-valued hybrid attacks. Considering the discontinuous right-hand sides of CVDMNNs, the systems are analyzed based on Filippov differential inclusion theory, and the interval matrix method is used to handle the memristive connection weights, thereby constructing error systems that are amenable to analysis. To utilize limited communication resources, a complex-valued switching event-triggered mechanism is introduced. Furthermore, to mitigate the effects of complex-valued hybrid attacks, consisting of complex-valued replay attacks and deception attacks following the Bernoulli distribution, a secure controller is designed that can simultaneously counteract the interference caused by residual terms in the error systems. On this basis, a piecewise Lyapunov functional is constructed, and the sufficient condition for achieving MSES under complex-valued hybrid attacks is derived using Lyapunov stability theory and inequality techniques. Based on the derived synchronization criterion, algorithms are proposed to determine the maximum allowable replay and deception attack rates of the system. Finally, a numerical example is provided to validate the effectiveness and superiority of the proposed scheme.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129715"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048467","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":"The chromatic number of {P2∪P3,banner}-free graphs","authors":"Jiali Long ,&nbsp;Kaiyang Lan ,&nbsp;Yan Wang","doi":"10.1016/j.amc.2025.129707","DOIUrl":"10.1016/j.amc.2025.129707","url":null,"abstract":"<div><div>Borodin and Kostochka conjectured that for any graph <span><math><mi>G</mi></math></span> with maximum degree <span><math><mrow><mstyle><mi>Δ</mi></mstyle><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>9</mn></mrow></math></span>, the chromatic number satisfies <span><math><mrow><mi>χ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>max</mi><mo>{</mo><mstyle><mi>Δ</mi></mstyle><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mn>1</mn><mo>,</mo><mi>ω</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>}</mo></mrow></math></span>, where <span><math><mrow><mi>ω</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></math></span> denotes the clique number. While this conjecture remains open for general graphs, we prove its validity for the class of <span><math><mrow><mo>{</mo><msub><mi>P</mi><mn>2</mn></msub><mo>∪</mo><msub><mi>P</mi><mn>3</mn></msub><mo>,</mo><mtext>banner</mtext><mo>}</mo></mrow></math></span>-free graphs. Here, <span><math><mrow><msub><mi>P</mi><mn>2</mn></msub><mo>∪</mo><msub><mi>P</mi><mn>3</mn></msub></mrow></math></span> represents the disjoint union of a two-vertex path and a three-vertex path, and a <em>banner</em> refers to the graph formed by attaching a pendant vertex to a cycle with four vertices. Our result extends the recent work of Lan and Lin [1], establishing the conjecture for a strictly larger class of graphs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129707"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048465","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":"Theory and numerics of subspace approximation of eigenvalue problems","authors":"Siu Wun Cheung ,&nbsp;Youngsoo Choi ,&nbsp;Seung Whan Chung ,&nbsp;Jean-Luc Fattebert ,&nbsp;Coleman Kendrick ,&nbsp;Daniel Osei-Kuffuor","doi":"10.1016/j.amc.2025.129722","DOIUrl":"10.1016/j.amc.2025.129722","url":null,"abstract":"<div><div>Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. We provide general error estimates under non-simple eigenvalue conditions, establishing some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"511 ","pages":"Article 129722"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057345","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":"Research on the resilience of reputation mechanism to the cooperative environment in the face of external shocks","authors":"Jiaoyuan Wang,&nbsp;Yanlong Yang","doi":"10.1016/j.amc.2025.129713","DOIUrl":"10.1016/j.amc.2025.129713","url":null,"abstract":"<div><div>Social development is changing rapidly, and the assumed stability of the cooperative environment is only an ideal state. In the majority of prior research concerning evolutionary games, it is commonly posited that external influences are absent, thereby allowing for an exclusive examination of the system’s intrinsic evolution. However, the situation in the real world is complex, dynamic, and unstable. Therefore, this paper proposes introducing an external shock that compels a change in the rate of cooperation during the evolutionary process. This approach aims to simulate environmental changes in the real world and to observe how these changes impact the rate of cooperation. When facing external shocks, the reputation mechanism has a certain degree of recovery ability, which provides certain support for the reputation theory. This paper also adds the mechanism of learning from historical strategies to the traditional reputation model, optimizing the resilience of the reputation mechanism in the face of external shocks. Simulation results show that history learning can promote the recovery of a cooperative environment faster and more stably, short memory length strengthens the role of temptation to defect, long memory amplifies the impact of the initial state, and the joint effect of history learning rate and memory length is complex.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129713"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048469","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":"Evolutionary multigame with perception competition between conformists and imitators","authors":"Tianbo An ,&nbsp;Ran Zhang ,&nbsp;Jian Zhao ,&nbsp;Huizhen Zhang ,&nbsp;Zhen Wang","doi":"10.1016/j.amc.2025.129712","DOIUrl":"10.1016/j.amc.2025.129712","url":null,"abstract":"<div><div>Perceptual heterogeneity reflects individuals’ different perspectives on the same thing, and competition among individuals with different perceptions of either social dilemmas or payoffs can independently promote cooperation. In this article, we construct a coupled competition mechanism to explore the impact of competition between the two types of perceptions. Specifically, individuals’ differing perceptions of social dilemmas are modeled by the snowdrift game (<span><math><mrow><mi>S</mi><mi>D</mi><mi>G</mi></mrow></math></span>) and the prisoner’s dilemma game (<span><math><mrow><mi>P</mi><mi>D</mi><mi>G</mi></mrow></math></span>), differing perceptions of payoffs are captured by conformists and imitators. Extensive simulations show that the coupled competition mechanism markedly promotes cooperation. <span><math><mrow><mi>P</mi><mi>D</mi><mi>G</mi></mrow></math></span> players are substantially less competitive than <span><math><mrow><mi>S</mi><mi>D</mi><mi>G</mi></mrow></math></span> players, which dominate the population. Conformists act as an amplifier, inclined to choose cooperation when cooperators are dominant, thus further promoting cooperation levels. When defectors are dominant, conformists may temporarily choose to defect in the short term, but defection is unsustainable due to lower average accumulated payoffs. We further find that intensified competition among imitators weakens the competitiveness of conformists and diminishes their positive impact on cooperation. Finally, we demonstrate the impact of different proportions of conformists, network structures, and noise levels on the main results to verify the robustness of the model.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129712"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048468","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":"Neuro-adaptive optimized control for stochastic systems with state constraints: The non-affine faults case","authors":"Tong Zhang,&nbsp;Yiyan Han,&nbsp;Ling Wang,&nbsp;Xin Wang","doi":"10.1016/j.amc.2025.129720","DOIUrl":"10.1016/j.amc.2025.129720","url":null,"abstract":"<div><div>This paper addresses the issue of neuro-adaptive optimal control for stochastic nonlinear systems with state constraints under the presence of non-affine faults. The presence of non-affine faults poses considerable challenges to the stability and performance of the system. To address these challenges, in this article, an adaptive neural network (NN) control scheme is devised within the identifier-critic-actor architecture, enabling the approximation of unknown dynamics and the design of both virtual and actual optimal controllers. In addition, Barrier Lyapunov Functions (BLFs) are utilized to ensure stability while handling state constraints, and a Butterworth low-pass filter is introduced to compensate for high-frequency noise and non-affine nonlinear faults, enhancing system robustness. Furthermore, a novel hybrid event-triggered control (HETC) strategy is proposed to reduce communication and computation demands while optimizing resource utilization. The suggested control strategy guarantees the boundedness of closed-loop signals and keeps all state variables within predefined compact sets. Lastly, the efficacy of the proposed optimal control method is demonstrated through simulation results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129720"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048466","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":"An entropy stable and well-balanced scheme for an augmented blood flow model with variable geometrical and mechanical properties","authors":"Raimund Bürger ,&nbsp;Andrés Guerra ,&nbsp;Carlos A. Vega","doi":"10.1016/j.amc.2025.129719","DOIUrl":"10.1016/j.amc.2025.129719","url":null,"abstract":"<div><div>The flow of blood through a vessel can be described by a hyperbolic system of balance equations for the cross-sectional area and averaged velocity as functions of axial spatial position and time. The variable arterial wall rigidity and the equilibrium cross-sectional area are incorporated within the so-called tube law that gives rise to an internal pressure term. This system can be written as a conservative hyperbolic system for five unknowns. An entropy stable scheme for this augmented one-dimensional blood flow model is developed based on entropy conservative numerical flux. It is proved that the proposed scheme is well-balanced in the sense that it preserves both trivial (zero velocity) and non-trivial (non-zero velocity) steady-state solutions. Several demanding numerical tests show that the scheme can handle various kinds of shocks and preserves stationary solutions when geometrical and mechanical properties of the vessel are variable.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129719"},"PeriodicalIF":3.4,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048470","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}