Pub Date : 2025-11-18DOI: 10.1016/j.matcom.2025.11.020
Ziyad AlSharawi , Jose S. Cánovas
In this paper, we focus on finding one-dimensional maps that detect global stability in multidimensional maps. We consider various local and global stability techniques in discrete-time dynamical systems and discuss their advantages and limitations. Specifically, we navigate through the embedding technique, the expansion strategy, the dominance condition technique, and the enveloping technique to establish a unifying approach to global stability. We introduce the concept of strong local asymptotic stability (SLAS), then integrate what we call the expansion strategy with the enveloping technique to develop the enveloping technique for two-dimensional maps, which allows to give novel global stability results. Our results make it possible to verify global stability geometrically for two-dimensional maps. We provide several illustrative examples to elucidate our concepts, bolster our theory, and demonstrate its application.
{"title":"Integrating the enveloping technique with the expansion strategy to establish stability","authors":"Ziyad AlSharawi , Jose S. Cánovas","doi":"10.1016/j.matcom.2025.11.020","DOIUrl":"10.1016/j.matcom.2025.11.020","url":null,"abstract":"<div><div>In this paper, we focus on finding one-dimensional maps that detect global stability in multidimensional maps. We consider various local and global stability techniques in discrete-time dynamical systems and discuss their advantages and limitations. Specifically, we navigate through the embedding technique, the expansion strategy, the dominance condition technique, and the enveloping technique to establish a unifying approach to global stability. We introduce the concept of strong local asymptotic stability (SLAS), then integrate what we call the expansion strategy with the enveloping technique to develop the enveloping technique for two-dimensional maps, which allows to give novel global stability results. Our results make it possible to verify global stability geometrically for two-dimensional maps. We provide several illustrative examples to elucidate our concepts, bolster our theory, and demonstrate its application.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 1-15"},"PeriodicalIF":4.4,"publicationDate":"2025-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145555218","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 : 2025-11-17DOI: 10.1016/j.matcom.2025.11.004
Rakesh Kumar Dhiman
In this work, we investigate the turning points where the model’s behavior diverges significantly from other points within the domain. These points play a crucial role in shaping the overall dynamics and characteristics of the system. We provide a comprehensive study of turning points in optical waveguides with three-layer constant step-index profiles, addressing both their mathematical and physical aspects.
A general mathematical formula is introduced to determine the exact locations of all possible turning points for different TE and TM modes in one-dimensional straight and bent waveguides. The number and positions of these turning points depend on parameters such as the bent radius, refractive index profiles, and mode properties, which are analyzed in detail.
{"title":"Analysis and computation of turning points in optical straight and bent waveguides","authors":"Rakesh Kumar Dhiman","doi":"10.1016/j.matcom.2025.11.004","DOIUrl":"10.1016/j.matcom.2025.11.004","url":null,"abstract":"<div><div>In this work, we investigate the turning points where the model’s behavior diverges significantly from other points within the domain. These points play a crucial role in shaping the overall dynamics and characteristics of the system. We provide a comprehensive study of turning points in optical waveguides with three-layer constant step-index profiles, addressing both their mathematical and physical aspects.</div><div>A general mathematical formula is introduced to determine the exact locations of all possible turning points for different TE and TM modes in one-dimensional straight and bent waveguides. The number and positions of these turning points depend on parameters such as the bent radius, refractive index profiles, and mode properties, which are analyzed in detail.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 84-95"},"PeriodicalIF":4.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580120","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 : 2025-11-15DOI: 10.1016/j.matcom.2025.11.017
Silajit Kar , Dilip Kumar Maiti , Atasi Patra Maiti
Model Framework:
This study introduces a new HIV/AIDS model utilizing the Caputo fractional-order derivative to capture disease dynamics under realistic conditions. The model incorporates media-driven awareness and local communication to inform susceptible populations, while accounting for how psychological anxiety impacts infection rates among aware individuals. We incorporated both fixed and periodic disease transmission rates into our model. It also includes a diagnostic process for identifying CD4+ T cell count in asymptomatic cases, alongside treatment functions that consider medical resource limitations to enhance real-world applicability. An individual’s economic status for accessing treatment is also taken into account. Both sides of the model equations are dimensionally balanced.
Analytical-Numerical Experiments:
Analytical results show a unique positive solution with both HIV/AIDS-free and infected equilibria. The fractional-order dependent basic reproduction number is derived using the next-generation matrix, and the Routh–Hurwitz criterion confirms the local stability of the infected equilibrium. Numerical simulations with the Adams–Bashforth-Moulton method validate these findings, demonstrating how variations in , diagnosis rate, awareness delay, psychological anxiety, individual’s economic status, resource availability, and periodic disease transmission rate affect system dynamics.
Fractional Order, Memory Tracing, and Periodic Transmission on Disease Dynamics:
The study analyzes how the fractional order and memory kernel influence system dynamics and disease transmission control during transitional phases. Spectral analysis reveals periodic instabilities from oscillations in transmission rates, showing that increased transmission can stabilize the system but also raises secondary infections and . The study examines the effects of and oscillation period on system behavior. Using the scheme, memory evolution is visualized, showing that memory trace decreases as increases from 0 to 1 and diminishes at 1, highlighting distinctions between integer and non-integer order derivatives. These insights aid in understanding outbreaks and improving future forecasts and mitigation strategies.
{"title":"Memory tracing in fractional-order modeling of HIV/AIDS: Analyzing periodic transmission, anxiety, economic constraints, and treatment barriers","authors":"Silajit Kar , Dilip Kumar Maiti , Atasi Patra Maiti","doi":"10.1016/j.matcom.2025.11.017","DOIUrl":"10.1016/j.matcom.2025.11.017","url":null,"abstract":"<div><h3>Model Framework:</h3><div>This study introduces a new HIV/AIDS model utilizing the Caputo fractional-order derivative to capture disease dynamics under realistic conditions. The model incorporates media-driven awareness and local communication to inform susceptible populations, while accounting for how psychological anxiety impacts infection rates among aware individuals. We incorporated both fixed and periodic disease transmission rates into our model. It also includes a diagnostic process for identifying CD4+ T cell count in asymptomatic cases, alongside treatment functions that consider medical resource limitations to enhance real-world applicability. An individual’s economic status for accessing treatment is also taken into account. Both sides of the model equations are dimensionally balanced.</div></div><div><h3>Analytical-Numerical Experiments:</h3><div>Analytical results show a unique positive solution with both HIV/AIDS-free and infected equilibria. The fractional-order dependent basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is derived using the next-generation matrix, and the Routh–Hurwitz criterion confirms the local stability of the infected equilibrium. Numerical simulations with the Adams–Bashforth-Moulton method validate these findings, demonstrating how variations in <span><math><mi>α</mi></math></span>, diagnosis rate, awareness delay, psychological anxiety, individual’s economic status, resource availability, and periodic disease transmission rate affect system dynamics.</div></div><div><h3>Fractional Order, Memory Tracing, and Periodic Transmission on Disease Dynamics:</h3><div>The study analyzes how the fractional order <span><math><mi>α</mi></math></span> and memory kernel influence system dynamics and disease transmission control during transitional phases. Spectral analysis reveals periodic instabilities from oscillations in transmission rates, showing that increased transmission can stabilize the system but also raises secondary infections and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. The study examines the effects of <span><math><mi>α</mi></math></span> and oscillation period on system behavior. Using the <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> scheme, memory evolution is visualized, showing that memory trace decreases as <span><math><mi>α</mi></math></span> increases from 0 to 1 and diminishes at 1, highlighting distinctions between integer and non-integer order derivatives. These insights aid in understanding outbreaks and improving future forecasts and mitigation strategies.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 199-229"},"PeriodicalIF":4.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624689","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 : 2025-11-15DOI: 10.1016/j.matcom.2025.11.013
M. Fardi, B. Raeisi, M. Ahmadi Darani
This paper presents a novel numerical method using radial basis functions (RBFs) to solve two-dimensional multi-term time-fractional partial integro-differential equations with multi-term weakly singular kernels. The spatial discretization is based on an RBF-generated finite difference method, combined with geometrically optimal point selection for efficient stencil design. The key contribution of this study is the development of a greedy algorithm that constructs quasi-uniform point sets by balancing the fill distance and separation distance, thereby ensuring asymptotically optimal domain coverage. By generating weights with desirable properties, the method significantly enhances stability. A series of numerical experiments has been conducted to evaluate the efficiency and accuracy of the proposed method. The results, presented through detailed tables and figures, confirm the method’s effectiveness in accurately solving the target equations. Furthermore, performance evaluations using various examples highlight the method’s superiority and reliability.
{"title":"An RBF-based method with optimal point selection for solving two-dimensional multi-term time-fractional PIDEs with weakly singular kernels","authors":"M. Fardi, B. Raeisi, M. Ahmadi Darani","doi":"10.1016/j.matcom.2025.11.013","DOIUrl":"10.1016/j.matcom.2025.11.013","url":null,"abstract":"<div><div>This paper presents a novel numerical method using radial basis functions (RBFs) to solve two-dimensional multi-term time-fractional partial integro-differential equations with multi-term weakly singular kernels. The spatial discretization is based on an RBF-generated finite difference method, combined with geometrically optimal point selection for efficient stencil design. The key contribution of this study is the development of a greedy algorithm that constructs quasi-uniform point sets by balancing the fill distance and separation distance, thereby ensuring asymptotically optimal domain coverage. By generating weights with desirable properties, the method significantly enhances stability. A series of numerical experiments has been conducted to evaluate the efficiency and accuracy of the proposed method. The results, presented through detailed tables and figures, confirm the method’s effectiveness in accurately solving the target equations. Furthermore, performance evaluations using various examples highlight the method’s superiority and reliability.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 96-120"},"PeriodicalIF":4.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580119","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 : 2025-11-15DOI: 10.1016/j.matcom.2025.11.014
Zichen Yao , Zhanwen Yang , Mingying Sun
In this paper, we investigate the numerical analysis of fractional Fisher–KPP equation with Neumann boundary conditions. We rigorously establish key analytical properties of the exact solution, including positivity, boundedness, asymptotic stability, and regularity. A finite element method combined with an -implicit–explicit scheme is proposed to solve the equation. Building upon the diagonally positive-definite structure of the mass matrix, it is shown that both the semi-discrete and fully discrete schemes preserve the qualitative properties of the solution, i.e., the numerical solution remains positive for positive initial data, bounded for bounded initial data, and stable for when the exact solution is stable. We further derive the spatial error estimates by exploiting the boundedness and regularity of the exact solution. Our scheme extends effectively to irregular domains while maintaining these properties. Numerical experiments illustrate and complement the theoretical results.
{"title":"Numerical analysis of a positivity-preserving finite element method for fractional Fisher–KPP equation","authors":"Zichen Yao , Zhanwen Yang , Mingying Sun","doi":"10.1016/j.matcom.2025.11.014","DOIUrl":"10.1016/j.matcom.2025.11.014","url":null,"abstract":"<div><div>In this paper, we investigate the numerical analysis of fractional Fisher–KPP equation with Neumann boundary conditions. We rigorously establish key analytical properties of the exact solution, including positivity, boundedness, asymptotic stability, and regularity. A finite element method combined with an <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span>-implicit–explicit scheme is proposed to solve the equation. Building upon the diagonally positive-definite structure of the mass matrix, it is shown that both the semi-discrete and fully discrete schemes preserve the qualitative properties of the solution, i.e., the numerical solution remains positive for positive initial data, bounded for bounded initial data, and stable for when the exact solution is stable. We further derive the spatial error estimates by exploiting the boundedness and regularity of the exact solution. Our scheme extends effectively to irregular domains while maintaining these properties. Numerical experiments illustrate and complement the theoretical results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 35-50"},"PeriodicalIF":4.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571200","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 : 2025-11-15DOI: 10.1016/j.matcom.2025.11.018
Shan Chen , Yuanzhao Ding
It is essential to comprehend and forecast animal migratory paths. Only with this knowledge will scientists be able to help conserve animals and better safeguard their habitats. Using the zebra migration as an example, this research simulates and interprets the evolution of zebra migration patterns using a revolutionary genetic algorithm method. With this technique, we discover that only when the zebra population size is quite large and the mutation rate is moderate does migratory route evolution go more smoothly. Future efforts to conserve animals will be greatly impacted by this paper's demonstration of the viability of employing a genetic algorithm to comprehend and enhance animal migration pathways.
{"title":"Feasibility study of using artificial intelligence to explore the process of zebra migration","authors":"Shan Chen , Yuanzhao Ding","doi":"10.1016/j.matcom.2025.11.018","DOIUrl":"10.1016/j.matcom.2025.11.018","url":null,"abstract":"<div><div>It is essential to comprehend and forecast animal migratory paths. Only with this knowledge will scientists be able to help conserve animals and better safeguard their habitats. Using the zebra migration as an example, this research simulates and interprets the evolution of zebra migration patterns using a revolutionary genetic algorithm method. With this technique, we discover that only when the zebra population size is quite large and the mutation rate is moderate does migratory route evolution go more smoothly. Future efforts to conserve animals will be greatly impacted by this paper's demonstration of the viability of employing a genetic algorithm to comprehend and enhance animal migration pathways.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 74-83"},"PeriodicalIF":4.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580116","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 : 2025-11-14DOI: 10.1016/j.matcom.2025.11.015
Yangrong Li, Zhiqiang Wang, Xiaowen Tang
Discrete-time Klein–Gordon–Schrödinger lattice equations are established according to implicit Euler schemes, while a family of numerical attractors is obtained when time-sizes belong to an existing interval. The continuity-set of numerical attractors under the Hausdorff distance is shown to be a dense IOD-type (Intersection of countably many Open Dense sets) in the existing interval, moreover, this continuity-set has the continuum cardinality. A common bound of all numerical attractors is provided and leads to the continuous convergence of numerical attractors as two external forces tend to zero. Finally, the global attractor of the original continuous-time system is approximated by numerical attractors in the sense of upper semicontinuity. Forward invariant sets, recursive tails estimates and Taylor’s remainders play key roles in the proofs.
{"title":"IOD-type continuity-sets and bounds of numerical attractors for discrete Klein–Gordon–Schrödinger equations","authors":"Yangrong Li, Zhiqiang Wang, Xiaowen Tang","doi":"10.1016/j.matcom.2025.11.015","DOIUrl":"10.1016/j.matcom.2025.11.015","url":null,"abstract":"<div><div>Discrete-time Klein–Gordon–Schrödinger lattice equations are established according to implicit Euler schemes, while a family of numerical attractors is obtained when time-sizes belong to an existing interval. The continuity-set of numerical attractors under the Hausdorff distance is shown to be a dense IOD-type (Intersection of countably many Open Dense sets) in the existing interval, moreover, this continuity-set has the continuum cardinality. A common bound of all numerical attractors is provided and leads to the continuous convergence of numerical attractors as two external forces tend to zero. Finally, the global attractor of the original continuous-time system is approximated by numerical attractors in the sense of upper semicontinuity. Forward invariant sets, recursive tails estimates and Taylor’s remainders play key roles in the proofs.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 19-35"},"PeriodicalIF":4.4,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532420","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}
The main innovation of this work is proposing a lifespan economic assessment for resistive superconducting faults current limiter (rSFCL) and a sizing methodology for the rSFCL impedance in railways DC substations. In the presence of short-circuit fault, the current can reach up to 30 times its nominal value. A sizing methodology for rSFCL is developed and applied in the presence of faults. Optimization of REBCO tapes is proposed through heat exchange using MATLAB and EMTP-RV, followed by application for fault limitation. Finally, an investigation of several rSFCL positions is conducted to determine the optimal location for better sizing of the circuit breakers. A cost assessment of the system is conducted. A case study is conducted using three DC substations with a fault current value of 120 kA. The results show that the rSFCL can limit up to 66.7% the fault current and reduce the size of the circuit breaker by 50%. The substation with the rSFCL offers a minimum total expenditure (TOTEX), comprising CAPEX (capital expenditure) and OPEX (operational expenditure), profitability of 15.5% compared to a traditional substation.
{"title":"Sizing methodology and optimal location of superconducting fault current limiter in DC substations for railways applications","authors":"Willy Magloire Nkounga , Khaled Almaksour , Arnaud Allais , Hervé Caron , Christophe Saudemont , Benoit Robyns","doi":"10.1016/j.matcom.2025.11.010","DOIUrl":"10.1016/j.matcom.2025.11.010","url":null,"abstract":"<div><div>The main innovation of this work is proposing a lifespan economic assessment for resistive superconducting faults current limiter (rSFCL) and a sizing methodology for the rSFCL impedance in railways DC substations. In the presence of short-circuit fault, the current can reach up to 30 times its nominal value. A sizing methodology for rSFCL is developed and applied in the presence of faults. Optimization of REBCO tapes is proposed through heat exchange using MATLAB and EMTP-RV, followed by application for fault limitation. Finally, an investigation of several rSFCL positions is conducted to determine the optimal location for better sizing of the circuit breakers. A cost assessment of the system is conducted. A case study is conducted using three <span><math><mrow><mn>1500</mn><mspace></mspace><mtext>V-</mtext><mn>4</mn><mspace></mspace><mtext>kA</mtext></mrow></math></span> DC substations with a fault current value of 120 kA. The results show that the rSFCL can limit up to 66.7% the fault current and reduce the size of the circuit breaker by 50%. The substation with the rSFCL offers a minimum total expenditure (TOTEX), comprising CAPEX (capital expenditure) and OPEX (operational expenditure), profitability of 15.5% compared to a traditional substation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 1-18"},"PeriodicalIF":4.4,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532421","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 : 2025-11-14DOI: 10.1016/j.matcom.2025.11.016
Subarna Roy , Dina Sultan AL-Jaf , Ashraf Adnan Thirthar , Pankaj Kumar Tiwari
In this study, we investigate the complex interplay between prey and predators under varying human-mediated influences. Theoretical analyses explore the solution’s non-negativity and boundedness, existence of feasible equilibria and their stability behaviors, and various bifurcations including saddle–node and Hopf. Using a detailed numerical exploration, we identified distinct population distribution, demonstrating how different factors shape ecological systems in non-trivial ways. The results suggest that human interventions, whether through direct shielding of prey or indirect effects on predator–prey interactions, can significantly disrupt ecological dynamics. Our findings highlight the importance of sustainable strategies that conserve prey populations while supporting predators to maintain ecosystem balance. Furthermore, by adding seasonal changes to some key parameters, we extend our autonomous system to a nonautonomous framework. Simple periodic oscillations, higher periodic oscillations, bursting patterns, and the extinction of predators are observed due to seasonal changes in the parameters.
{"title":"The impact of human shields in autonomous and non-autonomous prey–predator models with modified Cosner functional response","authors":"Subarna Roy , Dina Sultan AL-Jaf , Ashraf Adnan Thirthar , Pankaj Kumar Tiwari","doi":"10.1016/j.matcom.2025.11.016","DOIUrl":"10.1016/j.matcom.2025.11.016","url":null,"abstract":"<div><div>In this study, we investigate the complex interplay between prey and predators under varying human-mediated influences. Theoretical analyses explore the solution’s non-negativity and boundedness, existence of feasible equilibria and their stability behaviors, and various bifurcations including saddle–node and Hopf. Using a detailed numerical exploration, we identified distinct population distribution, demonstrating how different factors shape ecological systems in non-trivial ways. The results suggest that human interventions, whether through direct shielding of prey or indirect effects on predator–prey interactions, can significantly disrupt ecological dynamics. Our findings highlight the importance of sustainable strategies that conserve prey populations while supporting predators to maintain ecosystem balance. Furthermore, by adding seasonal changes to some key parameters, we extend our autonomous system to a nonautonomous framework. Simple periodic oscillations, higher periodic oscillations, bursting patterns, and the extinction of predators are observed due to seasonal changes in the parameters.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 54-73"},"PeriodicalIF":4.4,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532418","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 : 2025-11-11DOI: 10.1016/j.matcom.2025.11.011
Jingjing Song , Yanqing He , Qi Li
We propose a new phase-field vesicle model that rigorously enforces physical constraints and admits efficient, energy-stable numerical discretizations. The model couples a conserved Allen–Cahn gradient flow, which guarantees exact preservation of the enclosed volume, with a single Lagrange multiplier that imposes the global surface area constraint. Based on this formulation, we design two classes of numerical schemes. The first is a linear SAV-based framework that is simple to implement and reduces each time step to constant-coefficient linear solves. The second is a new Lagrange multiplier scheme that retains the efficiency of SAV while exactly preserving the physical constraints and strictly dissipating the original free energy, requiring only two inexpensive nonlinear solves per step. For both schemes, we establish discrete energy dissipation laws, provide implementation details, and validate their performance through extensive 2D and 3D simulations. Numerical results confirm accuracy, unconditional stability, exact constraint preservation, and computational efficiency, demonstrating the effectiveness of the proposed approaches for simulating vesicle dynamics.
{"title":"Efficient energy-stable numerical methods for phase-field vesicle membrane models with strict volume and surface area constraints","authors":"Jingjing Song , Yanqing He , Qi Li","doi":"10.1016/j.matcom.2025.11.011","DOIUrl":"10.1016/j.matcom.2025.11.011","url":null,"abstract":"<div><div>We propose a new phase-field vesicle model that rigorously enforces physical constraints and admits efficient, energy-stable numerical discretizations. The model couples a conserved Allen–Cahn gradient flow, which guarantees exact preservation of the enclosed volume, with a single Lagrange multiplier that imposes the global surface area constraint. Based on this formulation, we design two classes of numerical schemes. The first is a linear SAV-based framework that is simple to implement and reduces each time step to constant-coefficient linear solves. The second is a new Lagrange multiplier scheme that retains the efficiency of SAV while exactly preserving the physical constraints and strictly dissipating the original free energy, requiring only two inexpensive nonlinear solves per step. For both schemes, we establish discrete energy dissipation laws, provide implementation details, and validate their performance through extensive 2D and 3D simulations. Numerical results confirm accuracy, unconditional stability, exact constraint preservation, and computational efficiency, demonstrating the effectiveness of the proposed approaches for simulating vesicle dynamics.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 36-53"},"PeriodicalIF":4.4,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532419","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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