Applied Mathematics and Computation最新文献

{"title":"Symmetry and the Buchanan-Lillo conjecture: A resolution of the mixed feedback case","authors":"Elena Braverman ,&nbsp;John Ioannis Stavroulakis","doi":"10.1016/j.amc.2025.129376","DOIUrl":"10.1016/j.amc.2025.129376","url":null,"abstract":"<div><div>Buchanan and Lillo both conjectured that oscillatory solutions of the first-order delay differential equation with positive feedback <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi><mo>(</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><mi>t</mi><mo>≥</mo><mn>0</mn></math></span>, where <span><math><mn>0</mn><mo>≤</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span>, <span><math><mn>0</mn><mo>≤</mo><mi>t</mi><mo>−</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>≤</mo><mn>2.75</mn><mo>+</mo><mi>ln</mi><mo>⁡</mo><mn>2</mn><mo>,</mo><mi>t</mi><mo>∈</mo><mi>R</mi></math></span>, are asymptotic to a shifted multiple of a unique periodic solution. This special solution can also be described from the more general perspective of the mixed feedback case (sign-changing <em>p</em>), thanks to its symmetry (antiperiodicity). The analogue of this conjecture for negative feedback, <span><math><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>≤</mo><mn>0</mn></math></span>, was resolved by Lillo, and the mixed feedback analog was recently set as an open problem. In this paper, we resolve the case of mixed feedback, obtaining results in support of the conjecture of Buchanan and Lillo, underlining its link to the symmetry of the periodic solution. In particular, we obtain and describe the optimal estimates on the necessary delay for existence of periodic (more generally, nonvanishing) solutions, with respect to the period (oscillation speed). These apply to almost any first-order delay system, as we consider the general nonautonomous case, under minimal assumptions of measurability of the parameters. We furthermore discuss and elucidate the relations between the periodic and the nonautonomous case.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129376"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experience-driven learning and interactive rules under link weight adjustment promote cooperation in spatial prisoner's dilemma game","authors":"Shounan Lu ,&nbsp;Yang Wang","doi":"10.1016/j.amc.2025.129381","DOIUrl":"10.1016/j.amc.2025.129381","url":null,"abstract":"<div><div>Drawing on social learning theory, which emphasizes the dual influence of direct and indirect experience on behavior, this study extends the Spatial Prisoner's Dilemma game framework through three key innovations. First, we develop a link weight adjustment mechanism that incorporates tolerance, a previously neglected factor. Second, we extend the interaction probability model by integrating both direct and indirect link weights. Third, we design a strategy update rule where behavioral adaptation depends on combined experience learning. Simulation results show that our approach significantly outperforms traditional models in promoting cooperation. In particular, we identify an inverse relationship between tolerance and cooperation levels, with reduced defection sensitivity effectively protecting cooperators from exploitation. Furthermore, indirect experiences prove more powerful than direct interactions in sustaining cooperation. Together, these mechanisms increase cooperators' payoffs and competitive advantage. Integrating both direct and indirect experiences into policy updates offers a more comprehensive approach to addressing complex social challenges, as it enables decision-makers to leverage both personal insights and collective wisdom for more effective solutions.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129381"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511599","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":"Bounded consensus in second-order uncertain nonlinear multiagent systems: A distributed neural network control approach","authors":"Chaoyang Li ,&nbsp;Shidong Zhai ,&nbsp;Yuanshi Zheng","doi":"10.1016/j.amc.2025.129369","DOIUrl":"10.1016/j.amc.2025.129369","url":null,"abstract":"<div><div>This paper explores the consensus issue in second-order generalized nonlinear multiagent systems (MAS) that involve uncertain nonlinear dynamics and external disturbances from the system. Suppose that the uncertain nonlinear terms can be approximated by neural networks with nonlinear residues. Through the incorporation of localized adaptive observer and disturbance observer for each agent, we propose a distributed adaptive protocol to promote bounded consensus (BC) in the network. Due to the use of saturated functions and adaptive gains in the protocol, the chattering phenomenon is weakened. Finally, two simulation examples verify the results of the fully distributed adaptive bounded consensus protocol.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129369"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527310","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":"How predator harvesting affects prey-predator dynamics in deterministic and stochastic environments?","authors":"Bapin Mondal ,&nbsp;Sayan Mandal ,&nbsp;Pankaj Kumar Tiwari ,&nbsp;Ranjit Kumar Upadhyay","doi":"10.1016/j.amc.2025.129380","DOIUrl":"10.1016/j.amc.2025.129380","url":null,"abstract":"<div><div>This study investigates the dynamics of predator-prey interactions in both deterministic and stochastic environments, with a focus on the ecological implications of predator harvesting. Theoretical and numerical analyses explore local stability, bifurcations, and bionomic equilibria to identify sustainable harvesting strategies. Our findings reveal that increasing predator harvesting rates can induce up to four interior equilibrium points via saddle-node bifurcations, including catastrophic transitions that destabilize the system. At high harvesting rates, the predator-free equilibrium becomes globally stable, while low and intermediate rates result in bistability or tristability, allowing coexistence of prey and predator populations. For the stochastic model, we derive conditions for species persistence and extinction, using the confidence ellipse method to quantify threshold noise intensities that trigger critical transitions between stable states. At low noise levels, predator and prey populations fluctuate around stable equilibria, but higher noise intensities can drive shifts to alternate states or predator extinction. The key factors influencing system dynamics include the predator's intrinsic growth rate, alternative food sources, and harvesting intensity. Our analysis underscores the vulnerability of ecological systems to stochastic disturbances and emphasizes the importance of carefully managed harvesting practices. These findings contribute to the development of strategies that balance ecological stability with economic objectives, ensuring the long-term sustainability of predator-prey populations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129380"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526704","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":"Finite element hybridization of port-Hamiltonian systems","authors":"Andrea Brugnoli ,&nbsp;Ramy Rashad ,&nbsp;Yi Zhang ,&nbsp;Stefano Stramigioli","doi":"10.1016/j.amc.2025.129377","DOIUrl":"10.1016/j.amc.2025.129377","url":null,"abstract":"<div><div>In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al. (2023) <span><span>[16]</span></span>] to port-Hamiltonian systems describing linear wave propagation phenomena. To this aim, a dual field mixed Galerkin discretization is introduced, in which one variable is approximated via conforming finite element spaces, whereas the second is completely local. The mixed formulation is then hybridized to obtain an equivalent formulation that can be more efficiently solved using a static condensation procedure in discrete time. The size reduction achieved thanks to the hybridization is greater than the one obtained for the Hodge Laplacian as the final system only contains the globally coupled traces of one variable. Numerical experiments on the 3D wave and Maxwell equations illustrate the convergence of the method and the size reduction achieved by the hybridization.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129377"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527309","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":"Catalyst strategy for the evolution of cooperation in indirect reciprocity","authors":"Ji Quan ,&nbsp;Yixin Feng ,&nbsp;Jiacheng Nie ,&nbsp;Xianjia Wang","doi":"10.1016/j.amc.2025.129379","DOIUrl":"10.1016/j.amc.2025.129379","url":null,"abstract":"<div><div>Indirect reciprocity, as a primary mechanism for cooperation between unrelated individuals, evaluates individuals' behavior and assigns reputation labels based on social norms. Since evaluating reputation is challenging in practice, unlike previous studies, we do not introduce the reputation evaluation rule but only record two recent action information as individuals' labels, including the most recent actions of the individual and his partner. A new type of strategy set is constructed, in which each strategy is represented by a quadruplet, with each element corresponding to an action when facing a different label partner. We explore the invasion and competition of these strategies in a population when playing donor games in both noiseless and noisy scenarios. By conducting pairwise invasion simulations between all sixteen strategies, we find that in the noiseless case, cooperative strategies with evolutionary stability can identify reasonable cooperative behaviors, tolerate unreasonable cooperative behaviors, and adopt a harsh attitude toward unreasonable defection. In the noisy case, tolerant cooperative strategies that can distinguish unreasonable defection are evolutionary stable. Furthermore, by simulating multiple strategy combinations, we find a key strategy which we call the catalyst strategy that can act as a refuge for cooperators. Although the strategy is not evolutionary stable, it can help conditional cooperative strategies resist the intrusion of defection and help the system reach a fully cooperative steady state. We also verify that the system's evolutionary outcome is robust to noise intensity and that the presence of noise cannot lead to qualitative changes in the system. Action errors have a greater impact on the average cooperation rate and average payoff of the population relative to label errors. In addition, we find that the catalytic potential of the key strategy is fully realized in larger populations. Conversely, smaller population sizes diminish the efficacy of the catalyst strategy in promoting cooperation, and this detrimental effect is exacerbated in the noisy scenario.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129379"},"PeriodicalIF":3.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511600","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":"Nash equilibria in the Showcase Showdown game with unlimited spins","authors":"L. Bayón ,&nbsp;P. Fortuy Ayuso ,&nbsp;J.M. Grau ,&nbsp;A.M. Oller-Marcén ,&nbsp;M.M. Ruiz","doi":"10.1016/j.amc.2025.129368","DOIUrl":"10.1016/j.amc.2025.129368","url":null,"abstract":"<div><div>The game of <em>Showcase Showdown</em> with unlimited spins is investigated as an <em>n</em>-players continuous game, and the Nash Equilibrium strategies for the players are obtained. The sequential game with information on the results of the previous players is studied, as well as three variants: no information, possibility of draw, and different modalities of winner payoff.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129368"},"PeriodicalIF":3.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508831","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":"Synchronization of short memory fractional coupled neural networks with higher-order interactions via novel intermittent control","authors":"Dongsheng Yang ,&nbsp;Hu Wang ,&nbsp;Guojian Ren ,&nbsp;Yongguang Yu ,&nbsp;Xiao-Li Zhang","doi":"10.1016/j.amc.2025.129363","DOIUrl":"10.1016/j.amc.2025.129363","url":null,"abstract":"<div><div>Due to the fact that higher-order interactions in neural networks significantly enhance the accuracy and depth of network modeling and analysis, this paper investigates the synchronization problem in such networks by employing a novel intermittent control method. Firstly, higher-order interactions in the fractional coupled neural network model are considered, extending the traditional understanding of neural network structures. Based on a designed threshold function, a flexible intermittent controller is introduced. Furthermore, sufficient conditions for achieving network synchronization are provided, ensuring the network reaches a synchronized state under the proposed control method. Alongside these conditions, synchronization criteria are presented to strictly control the synchronization error within a predetermined decay range, guaranteeing the performance meets specific accuracy requirements. Finally, the effectiveness of our innovative intermittent control strategy is demonstrated through two numerical simulations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129363"},"PeriodicalIF":3.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479508","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":"Reconstruction of micro-dynamics characterizing human decision-making behavior in repeated social dilemmas","authors":"Luhe Yang ,&nbsp;Yongpeng Ning ,&nbsp;Lianzhong Zhang","doi":"10.1016/j.amc.2025.129367","DOIUrl":"10.1016/j.amc.2025.129367","url":null,"abstract":"<div><div>Exploring evolutionary updating rules more consistent with individual cognitive processes is crucial to the study of human cooperation. A considerable number of dynamic models describing human decision-making behavior lack empirical evidence. We have conducted a behavioral experiment and proposed a hypothesis that human players make decisions based on proportional change rather than absolute difference of payoffs. Thus we can reconstruct the micro-dynamics, namely individual strategy updating rules, with a singular function considering the individual's choice to cooperate and defect separately. We find the micro-dynamics evolve over time and our dynamic model can well predict the evolution of cooperation. Furthermore, combined with the conception “elasticity” commonly used in economics, we reveal the relationship between the intrinsic property of population and players’ subjective decision intentions. Our findings provide a novel framework for measuring human decision-making behavior with bounded rationality in repeated social dilemmas.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129367"},"PeriodicalIF":3.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479509","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":"Input-to-state stabilization of nonlinear systems with impulsive disturbance via event-triggered impulsive control","authors":"Wenjun Sun ,&nbsp;Mingzhu Wang ,&nbsp;Jianwei Xia ,&nbsp;Xiaodi Li","doi":"10.1016/j.amc.2025.129365","DOIUrl":"10.1016/j.amc.2025.129365","url":null,"abstract":"<div><div>This paper investigates the input-to-state stabilization (ISS) problem for nonlinear impulsive systems under event-triggered impulsive control (ETIC), encompassing comprehensive considerations of external continuous and impulsive disturbances. Some flexible design criteria of ETIC strategies are proposed for ISS of addressed systems based on Lyapunov theory without Zeno behavior, which can effectively overcome the negative effects caused by the double disturbances. Moreover, a relationship between event-triggered mechanism (ETM), impulsive control strength, and two kinds of external disturbances is established. Compared with the existing results on ISS of nonlinear systems based on ETIC, our proposed ETIC strategies can be applied to the practical applications involving impulsive disturbance with stronger robustness. Finally, the proposed results are further validated through the presentation of two numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"497 ","pages":"Article 129365"},"PeriodicalIF":3.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479510","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}