Pub Date : 2025-03-03DOI: 10.1016/j.matcom.2025.02.011
Lalchand Verma , Ramakanta Meher , Darshak P. Pandya
This work considers a temporal fractional HIV/AIDS model with fractal dimensions to examine the influence of awareness on the dynamics of HIV/AIDS. It investigates an epidemiological model of the dynamics of HIV/AIDS transmission in India using actual data from 1990 to 2016 to authenticate the proposed model. The Picard–Lindelof approach is employed to demonstrate the uniqueness and existence of the solutions where the stability analysis is done with the disease-free equilibrium point and basic reproduction number . The Adams–Bashforth method employs a two-step Lagrange polynomial in the generalised power-law kernel form to obtain the proposed model’s numerical solution. Finally, the least square curve fitting method is used to estimate the parametric study of the proposed model with the actual data on HIV cases reported in India from 1990 to 2016.
{"title":"Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India","authors":"Lalchand Verma , Ramakanta Meher , Darshak P. Pandya","doi":"10.1016/j.matcom.2025.02.011","DOIUrl":"10.1016/j.matcom.2025.02.011","url":null,"abstract":"<div><div>This work considers a temporal fractional HIV/AIDS model with fractal dimensions to examine the influence of awareness on the dynamics of HIV/AIDS. It investigates an epidemiological model of the dynamics of HIV/AIDS transmission in India using actual data from 1990 to 2016 to authenticate the proposed model. The Picard–Lindelof approach is employed to demonstrate the uniqueness and existence of the solutions where the stability analysis is done with the disease-free equilibrium point and basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. The Adams–Bashforth method employs a two-step Lagrange polynomial in the generalised power-law kernel form to obtain the proposed model’s numerical solution. Finally, the least square curve fitting method is used to estimate the parametric study of the proposed model with the actual data on HIV cases reported in India from 1990 to 2016.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 135-150"},"PeriodicalIF":4.4,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552757","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 : 2025-03-01DOI: 10.1016/j.matcom.2025.02.022
Serigne Daouda Pene , Antoine Picot , Fabrice Gamboa , Nicolas Savy , Christophe Turpin , Amine Jaafar
This article presents a methodology that aims to model and to provide predictive capabilities for the lifetime of Proton Exchange Membrane Fuel Cell (PEMFC). The approach integrates parametric identification, dynamic modeling, and Extended Kalman Filtering (EKF). The foundation is laid with the creation of a representative aging database, emphasizing specific operating conditions. Electrochemical behavior is characterized through the identification of critical parameters. The methodology extends to capture the temporal evolution of the identified parameters. We also address challenges posed by the limiting current density through a differential analysis-based modeling technique and the detection of breakpoints. This approach, involving Monte Carlo simulations, is coupled with an EKF for predicting voltage degradation. The Remaining Useful Life (RUL) is also estimated. The results show that our approach accurately predicts future voltage and RUL with very low relative errors.
{"title":"Aging modeling and lifetime prediction of a proton exchange membrane fuel cell using an extended Kalman filter","authors":"Serigne Daouda Pene , Antoine Picot , Fabrice Gamboa , Nicolas Savy , Christophe Turpin , Amine Jaafar","doi":"10.1016/j.matcom.2025.02.022","DOIUrl":"10.1016/j.matcom.2025.02.022","url":null,"abstract":"<div><div>This article presents a methodology that aims to model and to provide predictive capabilities for the lifetime of Proton Exchange Membrane Fuel Cell (PEMFC). The approach integrates parametric identification, dynamic modeling, and Extended Kalman Filtering (EKF). The foundation is laid with the creation of a representative aging database, emphasizing specific operating conditions. Electrochemical behavior is characterized through the identification of critical parameters. The methodology extends to capture the temporal evolution of the identified parameters. We also address challenges posed by the limiting current density through a differential analysis-based modeling technique and the detection of breakpoints. This approach, involving Monte Carlo simulations, is coupled with an EKF for predicting voltage degradation. The Remaining Useful Life (RUL) is also estimated. The results show that our approach accurately predicts future voltage and RUL with very low relative errors.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 151-168"},"PeriodicalIF":4.4,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577954","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}
Pub Date : 2025-02-28DOI: 10.1016/j.matcom.2025.02.021
Chunru Li , Xuesong Yuan , Yu Gong
The Solow–Swan model, introduced in 1956, is a fundamental framework in macroeconomic theory that models long-term economic growth through capital accumulation and labor force dynamics. This research builds on the original Solow–Swan model by incorporating capital-induced labor migration, which is a significant extension considering modern economic contexts where migration plays a crucial role in regional and national economic dynamics. First, we analyze the existence of the solution of the model. Then, we explore the local asymptotic stability and Turing bifurcation of the positive equilibrium. We then study the nonconstant steady state solution of the model as a branch of solution bifurcation from stationary system. And then we investigate the stability of the nonconstant steady state solution. Finally, we present some numerical simulations to verify our theoretical predictions.
{"title":"Dynamic analysis of a Solow–Swan model with capital-induced labor migration","authors":"Chunru Li , Xuesong Yuan , Yu Gong","doi":"10.1016/j.matcom.2025.02.021","DOIUrl":"10.1016/j.matcom.2025.02.021","url":null,"abstract":"<div><div>The Solow–Swan model, introduced in 1956, is a fundamental framework in macroeconomic theory that models long-term economic growth through capital accumulation and labor force dynamics. This research builds on the original Solow–Swan model by incorporating capital-induced labor migration, which is a significant extension considering modern economic contexts where migration plays a crucial role in regional and national economic dynamics. First, we analyze the existence of the solution of the model. Then, we explore the local asymptotic stability and Turing bifurcation of the positive equilibrium. We then study the nonconstant steady state solution of the model as a branch of solution bifurcation from stationary system. And then we investigate the stability of the nonconstant steady state solution. Finally, we present some numerical simulations to verify our theoretical predictions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 73-85"},"PeriodicalIF":4.4,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534693","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}
Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction–diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewise Dynamic Mode Decomposition (pDMD) to reconstruct them. Moreover, we analyse the predictive performance of the pDMD for moderate time horizons. Our findings show that pDMD is effective at precisely recreating and predicting chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.
{"title":"Patterns in soil organic carbon dynamics: Integrating microbial activity, chemotaxis and data-driven approaches","authors":"Angela Monti , Fasma Diele , Deborah Lacitignola , Carmela Marangi","doi":"10.1016/j.matcom.2025.02.019","DOIUrl":"10.1016/j.matcom.2025.02.019","url":null,"abstract":"<div><div>Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction–diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewise Dynamic Mode Decomposition (pDMD) to reconstruct them. Moreover, we analyse the predictive performance of the pDMD for moderate time horizons. Our findings show that pDMD is effective at precisely recreating and predicting chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 86-101"},"PeriodicalIF":4.4,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552758","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}
Pub Date : 2025-02-26DOI: 10.1016/j.matcom.2025.02.018
Zhijian Wei, Lihui Guo
In this paper, we investigate the non-classical wave for a pressureless hydrodynamic model with the flux perturbed term by the Riemann problem and a singularity formation. All the possible Riemann solutions, the combination of two contact discontinuities , and a delta shock wave , are constructed in fully explicit forms. It should be mentioned that the delta shock wave appears in the solution if and only if the flux perturbed parameter satisfies some specific condition. Due to the particularity of the delta shock wave in the Riemann solutions, we investigate the formation of singularity, namely, the traffic density blowing up under certain data. Moreover, its result gives an example of the conjecture proposed by Majda [Springer New York, 1984]: “If a hyperbolic system of conservation laws is totally linearly degenerate, then the system has smooth global solutions when the initial data are smooth, unless the solution itself blows up in a finite time.” We further explore and discuss their asymptotic behaviors to analyze the effect of , in which the delta shock wave and vacuum state solutions for a pressureless hydrodynamic model can be obtained by as tends to 0. In addition, we offer some typical numerical simulations that are identical well to our theoretical results and provide a more intuitive way to observe the singular wave.
{"title":"The singular wave in a pressureless hydrodynamic model","authors":"Zhijian Wei, Lihui Guo","doi":"10.1016/j.matcom.2025.02.018","DOIUrl":"10.1016/j.matcom.2025.02.018","url":null,"abstract":"<div><div>In this paper, we investigate the non-classical wave for a pressureless hydrodynamic model with the flux perturbed term by the Riemann problem and a singularity formation. All the possible Riemann solutions, the combination of two contact discontinuities <span><math><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, and a delta shock wave <span><math><mrow><mi>δ</mi><mi>S</mi></mrow></math></span>, are constructed in fully explicit forms. It should be mentioned that the delta shock wave appears in the solution if and only if the flux perturbed parameter <span><math><mi>ɛ</mi></math></span> satisfies some specific condition. Due to the particularity of the delta shock wave in the Riemann solutions, we investigate the formation of singularity, namely, the traffic density blowing up under certain data. Moreover, its result gives an example of the conjecture proposed by Majda [Springer New York, 1984]: “<em>If a hyperbolic system of conservation laws is totally linearly degenerate, then the system has smooth global solutions when the initial data are smooth, unless the solution itself blows up in a finite time.</em>” We further explore and discuss their asymptotic behaviors to analyze the effect of <span><math><mi>ɛ</mi></math></span>, in which the delta shock wave and vacuum state solutions for a pressureless hydrodynamic model can be obtained by <span><math><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> as <span><math><mi>ɛ</mi></math></span> tends to 0. In addition, we offer some typical numerical simulations that are identical well to our theoretical results and provide a more intuitive way to observe the singular wave.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 15-30"},"PeriodicalIF":4.4,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519888","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 : 2025-02-25DOI: 10.1016/S0378-4754(25)00065-5
{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00065-5","DOIUrl":"10.1016/S0378-4754(25)00065-5","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Page 505"},"PeriodicalIF":4.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479350","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}
Pub Date : 2025-02-25DOI: 10.1016/S0378-4754(25)00064-3
{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00064-3","DOIUrl":"10.1016/S0378-4754(25)00064-3","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Page 504"},"PeriodicalIF":4.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479349","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 : 2025-02-24DOI: 10.1016/j.matcom.2025.02.020
Yicheng Hao , Yantao Luo , Jianhua Huang , Long Zhang , Zhidong Teng
Considering the effects of commercial heterosexual behavior and environmental noise on the dynamics of HIV/AIDS disease, in this study, we establish a stochastic HIV/AIDS model that combines commercial heterosexual behavior and ln-type Ornstein–Uhlenbeck process. Firstly, for the deterministic model, i.e., the stochastic noise is not taken into account, the local and global asymptotic stability of the equilibria in terms of basic reproduction number are given. Then, for the stochastic model, the uniqueness and existence of global solutions, the existence of stationary distribution under , and the exponential extinction of HIV-positive patients under can all be obtained by constructing suitable random Lyapunov functions. In particular, under certain conditions, specific expression of the probability density function near the quasi-endemic equilibrium of the stochastic system can be obtained. Finally, numerical simulations indicate that controlling noise intensity, as well as commercial heterosexual activities, can help control the transmission of HIV.
{"title":"Analysis of a stochastic HIV/AIDS model with commercial heterosexual activity and Ornstein–Uhlenbeck process","authors":"Yicheng Hao , Yantao Luo , Jianhua Huang , Long Zhang , Zhidong Teng","doi":"10.1016/j.matcom.2025.02.020","DOIUrl":"10.1016/j.matcom.2025.02.020","url":null,"abstract":"<div><div>Considering the effects of commercial heterosexual behavior and environmental noise on the dynamics of HIV/AIDS disease, in this study, we establish a stochastic HIV/AIDS model that combines commercial heterosexual behavior and ln-type Ornstein–Uhlenbeck process. Firstly, for the deterministic model, i.e., the stochastic noise is not taken into account, the local and global asymptotic stability of the equilibria in terms of basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> are given. Then, for the stochastic model, the uniqueness and existence of global solutions, the existence of stationary distribution under <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>S</mi></mrow></msubsup><mo>></mo><mn>1</mn></mrow></math></span>, and the exponential extinction of HIV-positive patients under <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>E</mi></mrow></msubsup><mo><</mo><mn>1</mn></mrow></math></span> can all be obtained by constructing suitable random Lyapunov functions. In particular, under certain conditions, specific expression of the probability density function near the quasi-endemic equilibrium of the stochastic system can be obtained. Finally, numerical simulations indicate that controlling noise intensity, as well as commercial heterosexual activities, can help control the transmission of HIV.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 50-72"},"PeriodicalIF":4.4,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143528696","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 : 2025-02-24DOI: 10.1016/j.matcom.2025.01.028
Elishan Christian Braun , Daniela Mansutti , Kumbakonam R. Rajagopal
Literature confirms the crucial influence on glacier and rock glacier flow of non-viscous deformations together with temperature impact. This observation suggests numerical glaciologists ought to reconsider the established mathematical modeling based on the representation of ice as a power-law viscous fluid and the Glen’s law. Along this line, we propose the numerical solution of a two-dimensional rock-glacier flow model, based on a constitutive law of second grade of complexity two, as just published for a one-dimensional set-up by two of the authors. With the representation of the composition of the rocky ice as a mixture of ice and rock and sand grains, and the inclusion of the local impact of pressure and of thermal effects, this model has allowed the reproduction of borehole measurement data from alpine glacier internal sliding motion via a similarity solution of the flow governing equations. Here, the adopted numerical procedure uses a second order finite difference scheme and imposes the incompressibility constrain up to computer accuracy via the pressure method, that we have extended from Newtonian computational fluid dynamics. This method solves the governing equations for the flow in primitive variables with the advantage that no pre-/post-processing is required; in addition, it avoids splitted solution of the Poisson equation for pressure which might be source of undesired numerical mass unbalancing. The results of a numerical test on the Murtel-Corvatsch alpine glacier flow, reporting satisfactory matching with published on-field observations, are presented.
{"title":"Numerical solution of a two-dimensional rock-glacier flow model via the pressure method","authors":"Elishan Christian Braun , Daniela Mansutti , Kumbakonam R. Rajagopal","doi":"10.1016/j.matcom.2025.01.028","DOIUrl":"10.1016/j.matcom.2025.01.028","url":null,"abstract":"<div><div>Literature confirms the crucial influence on glacier and rock glacier flow of non-viscous deformations together with temperature impact. This observation suggests numerical glaciologists ought to reconsider the established mathematical modeling based on the representation of ice as a power-law viscous fluid and the Glen’s law. Along this line, we propose the numerical solution of a two-dimensional rock-glacier flow model, based on a constitutive law of second grade of complexity two, as just published for a one-dimensional set-up by two of the authors. With the representation of the composition of the rocky ice as a mixture of ice and rock and sand grains, and the inclusion of the local impact of pressure and of thermal effects, this model has allowed the reproduction of borehole measurement data from alpine glacier internal sliding motion via a similarity solution of the flow governing equations. Here, the adopted numerical procedure uses a second order finite difference scheme and imposes the incompressibility constrain up to computer accuracy via the pressure method, that we have extended from Newtonian computational fluid dynamics. This method solves the governing equations for the flow in primitive variables with the advantage that no pre-/post-processing is required; in addition, it avoids splitted solution of the Poisson equation for pressure which might be source of undesired numerical mass unbalancing. The results of a numerical test on the Murtel-Corvatsch alpine glacier flow, reporting satisfactory matching with published on-field observations, are presented.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 102-112"},"PeriodicalIF":4.4,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552759","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}
Pub Date : 2025-02-22DOI: 10.1016/j.matcom.2025.02.015
Mourad Azioune, Mohammed-Salah Abdelouahab
This paper explores the dynamic behavior of a Bertrand duopoly game involving boundedly rational firms and a quadratic cost function. The study delves into the nonlinear and complex dynamics that appear when the Bertrand–Nash equilibrium point loses its stability as both the speed of adjustment and the differentiation measure between the products increase, characterized by a period-doubling bifurcation. Subsequently, the system exhibits chaos and mixed-mode oscillations with unpredictable patterns through a sequence of flip bifurcations, as demonstrated by numerical analyses. The application of state feedback control successfully stabilizes the system at the Bertrand–Nash equilibrium point. This control method defines three stability boundaries, outlining a triangular region in parameters space. Each line corresponds to specific scenarios influencing overall stability, with intersections indicating the stability region.
{"title":"Controlling chaos and mixed mode oscillations in a Bertrand duopoly game with homogeneous expectations and quadratic cost functions","authors":"Mourad Azioune, Mohammed-Salah Abdelouahab","doi":"10.1016/j.matcom.2025.02.015","DOIUrl":"10.1016/j.matcom.2025.02.015","url":null,"abstract":"<div><div>This paper explores the dynamic behavior of a Bertrand duopoly game involving boundedly rational firms and a quadratic cost function. The study delves into the nonlinear and complex dynamics that appear when the Bertrand–Nash equilibrium point loses its stability as both the speed of adjustment and the differentiation measure between the products increase, characterized by a period-doubling bifurcation. Subsequently, the system exhibits chaos and mixed-mode oscillations with unpredictable patterns through a sequence of flip bifurcations, as demonstrated by numerical analyses. The application of state feedback control successfully stabilizes the system at the Bertrand–Nash equilibrium point. This control method defines three stability boundaries, outlining a triangular region in parameters space. Each line corresponds to specific scenarios influencing overall stability, with intersections indicating the stability region.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 553-566"},"PeriodicalIF":4.4,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488240","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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