Pub Date : 2025-02-13DOI: 10.1016/j.amc.2025.129344
Philip P. Forrier , Joan Gimeno , Àngel Jorba
In this note we study the behavior of the coefficients of the Taylor method when computing the numerical solution of stiff Ordinary Differential Equations. First, we derive an asymptotic formula for the growth of the stability region w.r.t. the order of the Taylor method. Then, we analyze the behavior of the Taylor coefficients of the solution when the equation is stiff. Using jet transport, we show that the coefficients computed with a floating point arithmetic of arbitrary precision have an absolute error that depends on the variational equations of the solution, which can have a dominant exponential growth in stiff problems. This is naturally related to the characterization of stiffness presented by Söderlind et al. [32], and allows to discuss why explicit solvers need a stepsize reduction when dealing with stiff systems. We explore how high-order methods can alleviate this restriction when high precision computations are required. We provide numerical experiments with classical stiff problems and perform extended precision computations to demonstrate this behavior.
{"title":"A note on the local behavior of the Taylor method for stiff ODEs","authors":"Philip P. Forrier , Joan Gimeno , Àngel Jorba","doi":"10.1016/j.amc.2025.129344","DOIUrl":"10.1016/j.amc.2025.129344","url":null,"abstract":"<div><div>In this note we study the behavior of the coefficients of the Taylor method when computing the numerical solution of stiff Ordinary Differential Equations. First, we derive an asymptotic formula for the growth of the stability region w.r.t. the order of the Taylor method. Then, we analyze the behavior of the Taylor coefficients of the solution when the equation is stiff. Using jet transport, we show that the coefficients computed with a floating point arithmetic of arbitrary precision have an absolute error that depends on the variational equations of the solution, which can have a dominant exponential growth in stiff problems. This is naturally related to the characterization of stiffness presented by Söderlind et al. <span><span>[32]</span></span>, and allows to discuss why explicit solvers need a stepsize reduction when dealing with stiff systems. We explore how high-order methods can alleviate this restriction when high precision computations are required. We provide numerical experiments with classical stiff problems and perform extended precision computations to demonstrate this behavior.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129344"},"PeriodicalIF":3.5,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394465","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 : 2025-02-13DOI: 10.1016/j.amc.2025.129359
Wei Tang, Da Xu
In this article, a direct method for the numerical solution of multi-term fractional differential equations is proposed. The method is based on transforming the original equation into an equivalent system of multi-order fractional equations. This system is discretized by fractional derivatives of Riesz spline wavelets and the collocation method. Then the original problem is transformed into a system of algebraic equations and can be easily solved. Finally, several numerical examples and comparisons with other methods are provided to demonstrate the efficiency and accuracy of our approach.
{"title":"Numerical solution of nonlinear multi-term fractional differential equations based on spline Riesz wavelets","authors":"Wei Tang, Da Xu","doi":"10.1016/j.amc.2025.129359","DOIUrl":"10.1016/j.amc.2025.129359","url":null,"abstract":"<div><div>In this article, a direct method for the numerical solution of multi-term fractional differential equations is proposed. The method is based on transforming the original equation into an equivalent system of multi-order fractional equations. This system is discretized by fractional derivatives of Riesz spline wavelets and the collocation method. Then the original problem is transformed into a system of algebraic equations and can be easily solved. Finally, several numerical examples and comparisons with other methods are provided to demonstrate the efficiency and accuracy of our approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129359"},"PeriodicalIF":3.5,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403629","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 : 2025-02-11DOI: 10.1016/j.amc.2025.129347
Yuliang Cai , Youtong Wang , Hanguang Su , Lianyan Fu , Qiang He
This paper addresses the bipartite leader-following consensus problem for general linear multi-agent systems (MASs) with unknown disturbances under directed communication topology. A novel control strategy is proposed to effectively mitigate disturbances and reduce unnecessary triggering actions, thereby conserving resources. The strategy consists of double dynamic event-triggered mechanisms (DDETM) that operate independently: one governs inter-agent communication, while the other determines controller updates. To prevent Zeno behavior, additional constants are introduced into the triggering mechanisms. Moreover, a simplified parameter selection method is developed, eliminating the need for verifying solutions to specific matrix inequalities. Finally, comprehensive simulation experiments are conducted to demonstrate the effectiveness and practicality of the proposed approach.
{"title":"Bipartite leader-following consensus of linear multi-agent systems with unknown disturbances under directed graphs by double dynamic event-triggered mechanism","authors":"Yuliang Cai , Youtong Wang , Hanguang Su , Lianyan Fu , Qiang He","doi":"10.1016/j.amc.2025.129347","DOIUrl":"10.1016/j.amc.2025.129347","url":null,"abstract":"<div><div>This paper addresses the bipartite leader-following consensus problem for general linear multi-agent systems (MASs) with unknown disturbances under directed communication topology. A novel control strategy is proposed to effectively mitigate disturbances and reduce unnecessary triggering actions, thereby conserving resources. The strategy consists of double dynamic event-triggered mechanisms (DDETM) that operate independently: one governs inter-agent communication, while the other determines controller updates. To prevent Zeno behavior, additional constants are introduced into the triggering mechanisms. Moreover, a simplified parameter selection method is developed, eliminating the need for verifying solutions to specific matrix inequalities. Finally, comprehensive simulation experiments are conducted to demonstrate the effectiveness and practicality of the proposed approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129347"},"PeriodicalIF":3.5,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143388414","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 : 2025-02-10DOI: 10.1016/j.amc.2025.129316
Yingxue Hou , Yan-Jun Liu , Shaocheng Tong
This paper is devoted to solving the finite-time fault-tolerant tracking control problem based on event-triggered control (ETC) strategy for multi-input-multi-output (MIMO) switched nonlinear systems, which are simultaneously subject to unknown sensor and actuator faults. A switched state observer with fault estimation is designed to compensate unknown sensor fault parameter and unavailable states online, while fuzzy logic systems (FLSs) are employed to identify the uncertainties. The shortcoming of “explosion of complexity” is mitigated by fusing backstepping control and command filter. To trade off the communication resources and the system performance, a event-triggered finite-time fault-tolerant control (FTC) scheme with adaptive parameter compensation mechanism is developed, which can alleviate the impact of actuator and sensor faults by designing different parameter adaptive laws, and ensures all signals are semiglobal practical finite-time stable (SGPFS). Furthermore, a mass spring damper system is applied to verify the performance of the proposed control method.
{"title":"Event-triggered fault-compensation-based fuzzy finite-time FTC for MIMO switched nonlinear systems","authors":"Yingxue Hou , Yan-Jun Liu , Shaocheng Tong","doi":"10.1016/j.amc.2025.129316","DOIUrl":"10.1016/j.amc.2025.129316","url":null,"abstract":"<div><div>This paper is devoted to solving the finite-time fault-tolerant tracking control problem based on event-triggered control (ETC) strategy for multi-input-multi-output (MIMO) switched nonlinear systems, which are simultaneously subject to unknown sensor and actuator faults. A switched state observer with fault estimation is designed to compensate unknown sensor fault parameter and unavailable states online, while fuzzy logic systems (FLSs) are employed to identify the uncertainties. The shortcoming of “explosion of complexity” is mitigated by fusing backstepping control and command filter. To trade off the communication resources and the system performance, a event-triggered finite-time fault-tolerant control (FTC) scheme with adaptive parameter compensation mechanism is developed, which can alleviate the impact of actuator and sensor faults by designing different parameter adaptive laws, and ensures all signals are semiglobal practical finite-time stable (SGPFS). Furthermore, a mass spring damper system is applied to verify the performance of the proposed control method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129316"},"PeriodicalIF":3.5,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376735","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 : 2025-02-07DOI: 10.1016/j.amc.2025.129337
Wen-Biao Gao
The two-dimensional fractional Fourier transform (FrFT) has very important applications in applied mathematics and signal processing. The polar coordinate form can not only enables the definitions of instantaneous amplitude, instantaneous phase, and the instantaneous frequency of a signal, but also extract some features that cannot be directly observed in the real signal. In this paper, we study the problem of correlation theorem and applications in the FrFT domain based on the polar coordinates. First, shift theorem and product theorem associated with the FrFT are exploited. Then, a correlation theorem of the FrFT is achieved according to the shift theorem. Furthermore, the relationship between the product theorem and the correlation theorem for the FrFT is established. Finally, we explored the possible applications of the obtained results of the FrFT on time-frequency representation, equation solving, and fast algorithm.
{"title":"Correlation theorem and applications associated with the fractional Fourier transform in polar coordinates","authors":"Wen-Biao Gao","doi":"10.1016/j.amc.2025.129337","DOIUrl":"10.1016/j.amc.2025.129337","url":null,"abstract":"<div><div>The two-dimensional fractional Fourier transform (FrFT) has very important applications in applied mathematics and signal processing. The polar coordinate form can not only enables the definitions of instantaneous amplitude, instantaneous phase, and the instantaneous frequency of a signal, but also extract some features that cannot be directly observed in the real signal. In this paper, we study the problem of correlation theorem and applications in the FrFT domain based on the polar coordinates. First, shift theorem and product theorem associated with the FrFT are exploited. Then, a correlation theorem of the FrFT is achieved according to the shift theorem. Furthermore, the relationship between the product theorem and the correlation theorem for the FrFT is established. Finally, we explored the possible applications of the obtained results of the FrFT on time-frequency representation, equation solving, and fast algorithm.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129337"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143242667","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 : 2025-02-07DOI: 10.1016/j.amc.2025.129340
Zhe Liu , Qingyuan Zhang
Remaining useful life (RUL) prediction is one of the key problems in equipment operation and maintenance. In some engineering practices, sufficient degradation observations can not be obtained due to limitations in cost, technology, and time. Under these situations, several degradation models are established using uncertain processes, and based on which the RULs are predicted under belief reliability theory. Although these methods showed advantages in dealing with small sample sizes, they all regarded the failure threshold as a known constant. However, as the system will be used by a diverse range of users, the failure threshold can vary appreciably with different using scenarios. Furthermore, due to the unclear understanding and insufficient collection of the actual operation process by users, the determination of the failure threshold is quite subjective. If the threshold is simply regarded as a known constant, it will cause inaccuracies in the reliability assessment and the scheduling of maintenance, which may further lead to unnecessary losses. Therefore, this work develops a method to estimate RUL with an uncertain failure threshold based on a degradation model constructed by the uncertain differential equation. Unknown parameters in the established degradation model are estimated by the method of moment based on residuals to alleviate the problem in which observation intervals are not close enough. The effectiveness of the proposed methodology is verified through a degradation data set.
{"title":"Remaining useful life estimation considering threshold epistemic uncertainty with uncertain differential equation","authors":"Zhe Liu , Qingyuan Zhang","doi":"10.1016/j.amc.2025.129340","DOIUrl":"10.1016/j.amc.2025.129340","url":null,"abstract":"<div><div>Remaining useful life (RUL) prediction is one of the key problems in equipment operation and maintenance. In some engineering practices, sufficient degradation observations can not be obtained due to limitations in cost, technology, and time. Under these situations, several degradation models are established using uncertain processes, and based on which the RULs are predicted under belief reliability theory. Although these methods showed advantages in dealing with small sample sizes, they all regarded the failure threshold as a known constant. However, as the system will be used by a diverse range of users, the failure threshold can vary appreciably with different using scenarios. Furthermore, due to the unclear understanding and insufficient collection of the actual operation process by users, the determination of the failure threshold is quite subjective. If the threshold is simply regarded as a known constant, it will cause inaccuracies in the reliability assessment and the scheduling of maintenance, which may further lead to unnecessary losses. Therefore, this work develops a method to estimate RUL with an uncertain failure threshold based on a degradation model constructed by the uncertain differential equation. Unknown parameters in the established degradation model are estimated by the method of moment based on residuals to alleviate the problem in which observation intervals are not close enough. The effectiveness of the proposed methodology is verified through a degradation data set.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129340"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349946","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 : 2025-02-07DOI: 10.1016/j.amc.2025.129342
Liuchao Xiao , Minghao Li , Zhenzhen Li , Hongru Chen
In this paper, we consider the implicit Euler scheme of the transient conduction-convection equations. The supercloseness properties and global superconvergence results are derived for two pairs of low order rectangular elements. Firstly, we obtain a prior estimate of finite element solutions. Then using the properties of the Stokes projection and Stokes operator, the derivative transforming skill and the -norm estimate, we deduce the supercloseness properties of the velocity and temperature in -norm, and the pressure in -norm. Next, the global superconvergence results are obtained through the interpolation postprocessing technique. Finally, a numerical example is provided to confirm the theoretical analysis. Compared with previous results, the superconvergence analysis is more concise, a lower regularity of solutions is required, and no time step restriction is needed.
{"title":"The supercloseness property and global superconvergence analysis for the transient conduction-convection equations","authors":"Liuchao Xiao , Minghao Li , Zhenzhen Li , Hongru Chen","doi":"10.1016/j.amc.2025.129342","DOIUrl":"10.1016/j.amc.2025.129342","url":null,"abstract":"<div><div>In this paper, we consider the implicit Euler scheme of the transient conduction-convection equations. The supercloseness properties and global superconvergence results are derived for two pairs of low order rectangular elements. Firstly, we obtain a prior estimate of finite element solutions. Then using the properties of the Stokes projection and Stokes operator, the derivative transforming skill and the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-norm estimate, we deduce the supercloseness properties of the velocity and temperature in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span>-norm, and the pressure in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>-norm. Next, the global superconvergence results are obtained through the interpolation postprocessing technique. Finally, a numerical example is provided to confirm the theoretical analysis. Compared with previous results, the superconvergence analysis is more concise, a lower regularity of solutions is required, and no time step restriction is needed.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129342"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349953","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 : 2025-02-07DOI: 10.1016/j.amc.2025.129338
Tiantian Mu , Jun-e Feng , Biao Wang
This paper exploits bisimulation relations, generated by extracting the concept of morphisms between algebraic structures, to analyze set stabilization of Boolean control networks with lower complexity. First, for two kinds of bisimulation relations, called as weak bisimulation and strong bisimulation relations, a novel verification method is provided by constructing the bisimulation matrices. Then the comparison for set stabilization of BCNs via two kinds of bisimulation methods is presented, which involves the dimensionality of quotient systems and dependency of the control laws on the original system. Moreover, the proposed method is also applied to the analysis of probabilistic Boolean control networks to establish the unified analysis framework of bisimulations. Finally, the validity of the obtained results is verified by the practical example.
{"title":"Set stabilization of Boolean control networks based on bisimulations: A dimensionality reduction approach","authors":"Tiantian Mu , Jun-e Feng , Biao Wang","doi":"10.1016/j.amc.2025.129338","DOIUrl":"10.1016/j.amc.2025.129338","url":null,"abstract":"<div><div>This paper exploits bisimulation relations, generated by extracting the concept of morphisms between algebraic structures, to analyze set stabilization of Boolean control networks with lower complexity. First, for two kinds of bisimulation relations, called as weak bisimulation and strong bisimulation relations, a novel verification method is provided by constructing the bisimulation matrices. Then the comparison for set stabilization of BCNs via two kinds of bisimulation methods is presented, which involves the dimensionality of quotient systems and dependency of the control laws on the original system. Moreover, the proposed method is also applied to the analysis of probabilistic Boolean control networks to establish the unified analysis framework of bisimulations. Finally, the validity of the obtained results is verified by the practical example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129338"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349372","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 : 2025-02-07DOI: 10.1016/j.amc.2025.129339
G. Radojev , M. Brdar , Lj. Teofanov
A new approach to the Durán-type mesh is presented in order to improve the standard definition of this layer-adjusted mesh and eliminate some of its drawbacks. The construction of this graded mesh is provided for an elliptic convection-diffusion problem, a convection-diffusion-reaction problem, a third-order problem, and a convection-diffusion problem with a large shift. Our modification outperforms the standard Durán-type mesh both theoretically and numerically. Furthermore, the modified mesh is unique and allows for a fair comparison of numerical results obtained with other meshes of the Shishkin and Bakhvalov-types.
{"title":"A modification of Durán-type mesh for singularly perturbed problems","authors":"G. Radojev , M. Brdar , Lj. Teofanov","doi":"10.1016/j.amc.2025.129339","DOIUrl":"10.1016/j.amc.2025.129339","url":null,"abstract":"<div><div>A new approach to the Durán-type mesh is presented in order to improve the standard definition of this layer-adjusted mesh and eliminate some of its drawbacks. The construction of this graded mesh is provided for an elliptic convection-diffusion problem, a convection-diffusion-reaction problem, a third-order problem, and a convection-diffusion problem with a large shift. Our modification outperforms the standard Durán-type mesh both theoretically and numerically. Furthermore, the modified mesh is unique and allows for a fair comparison of numerical results obtained with other meshes of the Shishkin and Bakhvalov-types.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129339"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143242666","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 : 2025-02-07DOI: 10.1016/j.amc.2025.129341
Hirofumi Takesue
This study aimed to investigate the evolutionary dynamics of a three-strategy game that combines snowdrift and stag hunt games. This game is motivated by an experimental study, which found that individual solution lowers cooperation levels. Agents adopting this option aim to address a problem to the extent necessary to prevent negative impact on themselves, although they do not free ride on cooperation effort provided by others. This property of the individual solution is similar to that of option defection in the stag hunt. Thus, the role of the interplay of defection in the snowdrift game and individual solution was examined in this study. The well-mixed population has two asymptotically stable rest points, one wherein the individual solution occupies the population, and the other wherein cooperation and defection coexist. The interactions on a square lattice enlarge the parameter region wherein cooperation survives, and the three strategies often coexist. The scrutinization of the evolutionary process shows that multiple mechanisms lead to the coexistence of the three strategies depending on parameter values. Our analysis suggests that considering the individual solution adds complexity to the evolutionary process, which might contribute to our understanding on the evolution of cooperation.
{"title":"Evolution of cooperation in a three-strategy game combining snowdrift and stag hunt games","authors":"Hirofumi Takesue","doi":"10.1016/j.amc.2025.129341","DOIUrl":"10.1016/j.amc.2025.129341","url":null,"abstract":"<div><div>This study aimed to investigate the evolutionary dynamics of a three-strategy game that combines snowdrift and stag hunt games. This game is motivated by an experimental study, which found that individual solution lowers cooperation levels. Agents adopting this option aim to address a problem to the extent necessary to prevent negative impact on themselves, although they do not free ride on cooperation effort provided by others. This property of the individual solution is similar to that of option defection in the stag hunt. Thus, the role of the interplay of defection in the snowdrift game and individual solution was examined in this study. The well-mixed population has two asymptotically stable rest points, one wherein the individual solution occupies the population, and the other wherein cooperation and defection coexist. The interactions on a square lattice enlarge the parameter region wherein cooperation survives, and the three strategies often coexist. The scrutinization of the evolutionary process shows that multiple mechanisms lead to the coexistence of the three strategies depending on parameter values. Our analysis suggests that considering the individual solution adds complexity to the evolutionary process, which might contribute to our understanding on the evolution of cooperation.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129341"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349947","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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