Mathematics and Computers in Simulation最新文献

{"title":"Spatiotemporal dynamics in a diffusive eco-epidemiological system with spatial memory and fear effect","authors":"Jia Liu ,&nbsp;Hongyong Zhao","doi":"10.1016/j.matcom.2026.01.020","DOIUrl":"10.1016/j.matcom.2026.01.020","url":null,"abstract":"<div><div>This paper proposes and analyzes a novel delayed diffusive model to investigate the complex spatiotemporal dynamics of an eco-epidemiological system. The model is distinguished by its simultaneous integration of four critical ecological mechanisms: a fear effect that suppresses prey reproduction, disease transmission within the prey population, standard diffusion, and a memory-based anti-predator taxis, wherein prey actively avoid predators based on past information. Rigorous mathematical analysis establishes the system’s well-posedness and reveals intricate stability dynamics. We demonstrate that the prey’s anti-predator taxis can trigger a Turing instability, leading to the formation of stationary spatial patterns. Crucially, this destabilizing effect is counteracted by the fear mechanism, which acts as a spatial stabilizer by expanding the parameter domain for homogeneous coexistence. Furthermore, our analysis identifies the time delay in the prey’s response as a potent driver of temporal instability, inducing sustained population oscillations via a Hopf bifurcation. Beyond local bifurcations, we also derive sufficient conditions for the global asymptotic stability of both the infection-free and coexistence equilibria using Lyapunov functional methods. Numerical simulations not only corroborate our analytical predictions but also unveil the emergence of a rich variety of complex spatial structures in two dimensions, including spots, stripes, and mixed-mode patterns. In summary, our findings highlight that the sophisticated interplay between fear, memory, and movement can profoundly alter system stability and generate diverse spatiotemporal heterogeneity, offering significant insights into the mechanisms governing community structure and disease dynamics in natural ecosystems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 275-294"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038829","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":"Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains","authors":"Daifeng Duan ,&nbsp;Biao Liu ,&nbsp;Junjie Wei","doi":"10.1016/j.matcom.2026.01.025","DOIUrl":"10.1016/j.matcom.2026.01.025","url":null,"abstract":"<div><div>We investigate the effects of periodic boundary conditions on a nonlocal Holling–Tanner model defined on a square domain. A top-hat kernel function with finite support is employed to characterize nonlocal interactions, which we further adapt to accommodate periodic boundary conditions. Subsequently, we derive the Turing and spatiotemporal Hopf bifurcation curves and conduct numerical simulations across the parameter ranges delineated by these curves. Our findings demonstrate substantial differences in spatiotemporal patterns between the square domain and the one-dimensional case, including squares, stripes, mixed states, irregular spot-like hexagonal patterns, and coexistence states of three-stripes and spots. These observed patterns exhibit remarkable consistency with both chemical experimental results and the skin pigmentation patterns of fish, thereby offering valuable theoretical insights and predictive frameworks for understanding spatiotemporal patterns in chemical and biological systems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 366-383"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038823","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":"Multistability of equilibria for Clifford-valued Cohen–Grossberg neural networks with discontinuous activation functions and time delays","authors":"Qiuyan Yang ,&nbsp;Yuanhua Qiao ,&nbsp;Lijuan Duan ,&nbsp;Jun Miao","doi":"10.1016/j.matcom.2025.12.015","DOIUrl":"10.1016/j.matcom.2025.12.015","url":null,"abstract":"<div><div>In this paper, the multistability of Clifford-valued Cohen–Grossberg neural networks(CGNNs) model with time-varying delays and discontinuous activation function is investigated. Firstly, the existence of equilibrium points is explored, and it is found that there exist <span><math><msup><mrow><mfenced><mrow><msub><mrow><mo>∏</mo></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mn>4</mn><msub><mrow><mi>K</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></msup></math></span> equilibrium points by deriving some sufficient conditions and Intermediate Value Theorem, and then the positive invariant is given. Next, we investigate the local stability of those multiple equilibrium points (EPs), which shows that there are <span><math><msup><mrow><mfenced><mrow><msub><mrow><mo>∏</mo></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mn>2</mn><msub><mrow><mi>K</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></msup></math></span> locally asymptotically stable equilibrium points. Moreover, the attraction basins of the stable EPs in CGNNs are estimated and enlarged. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 428-446"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189576","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":"A generalized Caputo fractional jerk equation with Caputo antiperiodic boundary conditions: Existence of solutions, stability and numerical simulations","authors":"Zeeshan Ali ,&nbsp;Sandra Pinelas","doi":"10.1016/j.matcom.2026.01.005","DOIUrl":"10.1016/j.matcom.2026.01.005","url":null,"abstract":"<div><div>This paper investigates the existence of solutions, stability, and numerical simulations for a generalized fractional jerk equation with fractional antiperiodic boundary conditions, both involving Caputo derivatives. The model features non-integer order derivatives in the equation and boundary conditions, resulting in a more general formulation. Fixed-point theory is employed to establish sufficient conditions for the existence and uniqueness, leading to novel results. Furthermore, Ulam-Hyers stability and its generalized form are analyzed to ensure robustness of the solutions. Examples are presented to demonstrate the applicability of the theoretical findings, with the system’s behavior and stability analyzed for various fractional orders <span><math><mi>α</mi></math></span> and <span><math><mi>β</mi></math></span> using MATLAB. A special case of the proposed system is also discussed in the conclusion.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 79-94"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980216","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":"Modeling a delay-driven eco-epidemiological system with fear and migration under ratio-dependent predation","authors":"Kahuwa Kuwali Barman ,&nbsp;Ankur Jyoti Kashyap ,&nbsp;Hemanta Kumar Sarmah","doi":"10.1016/j.matcom.2026.01.002","DOIUrl":"10.1016/j.matcom.2026.01.002","url":null,"abstract":"<div><div>This study investigates an eco-epidemiological predator–prey model that incorporates fear-driven behavioral changes in susceptible prey along with migration in both prey and predator populations. Predation on infected prey is modeled through a ratio-dependent functional response, and a transmission delay is introduced to represent the non-instantaneous nature of infection, adding novelty to the framework. We examine the local and global stability of the non-delayed system, and analyze the occurrence of transcritical and Hopf bifurcations. The results show that fear effects and susceptible prey migration may destabilize the system, whereas a higher conversion rate of infected prey biomass promotes stable coexistence. Delay-induced bifurcation analysis further reveals that increasing the transmission delay destabilizes the interior equilibrium, and numerical simulations support these analytical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 114-142"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980288","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":"Spherical fuzzy Bézier curve approximation for efficient lane-changing trajectories under uncertain data","authors":"Bushra Aqil ,&nbsp;Rakib Mustafa ,&nbsp;Ghulam Mustafa","doi":"10.1016/j.matcom.2026.01.006","DOIUrl":"10.1016/j.matcom.2026.01.006","url":null,"abstract":"<div><div>In real-world problems, acquiring precise information can be challenging, as data points often exhibit vagueness, imprecision, or uncertainty. Dealing with uncertain data, which involves intricate processes due to incomplete information, poses difficulties. This paper presents a spherical fuzzy Bézier curve (<span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BC</mi></mrow></math></span>) model for computer-aided geometric design (CAGD) to tackle uncertain data, especially in the context of vehicle lane-changing trajectories. Unlike existing methods that assume exact data and overlook obstacles or uncertainty, <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BC</mi></mrow></math></span> employs spherical fuzzy point relations and control point relations are defined using fuzzy set theory to achieve superior uncertainty modeling and adaptability. An <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BC</mi></mrow></math></span>, illustrated in a lane-changing scenario, produces adaptive, obstacle-avoiding trajectories that outperform crisp Bézier models. Visualization of spherical fuzzy Bézier surfaces (<span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BS</mi></mrow></math></span>) is also provided in this paper. The de Casteljau algorithm efficiently calculates curve points, and a dynamic method for trajectory planning improves adaptability. This model demonstrates superior performance compared to traditional crisp Bézier methods, providing valuable solutions for automotive design, 3D modeling, and animation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 65-78"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980287","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":"A two-grid spectral deferred correction method for the generalized multi-order fractional differential equations","authors":"Quen-Yi Lin,&nbsp;Ming-Cheng Shiue","doi":"10.1016/j.matcom.2025.12.021","DOIUrl":"10.1016/j.matcom.2025.12.021","url":null,"abstract":"<div><div>Spectral deferred correction (SDC) methods constitute a class of numerical schemes that achieve arbitrarily high-order accuracy by iteratively applying a low-order method. These methods combine high accuracy with low computational cost, making them attractive for numerically solving differential equations. In this paper, the explicit two-grid SDC method for the generalized multi-order fractional differential equations and its theoretical analysis are studied. The analysis demonstrates that the proposed scheme is stable, provided that the time step size is sufficiently small, and that it achieves high-order convergence under the same condition. Numerical experiments are provided to validate and illustrate the theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 1-20"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145904148","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":"Two-step optimization of knots in B-spline curve approximation","authors":"Xiao Guo ,&nbsp;Chengzhi Liu","doi":"10.1016/j.matcom.2026.01.004","DOIUrl":"10.1016/j.matcom.2026.01.004","url":null,"abstract":"<div><div>This paper presents a framework for optimizing B-spline knot placement in curve fitting. We show that the perturbation introduced during knot removal increases with the magnitude of the derivative jumps at the removed knots. Based on this observation, we employ polynomial trend filtering to detect abrupt changes in the higher-order discrete derivatives of the sample data, which in turn guides effective knot selection. The proposed framework consists of two main steps: (1) Starting from a densely placed initial knot vector, we optimize the coefficients of the 0-degree B-splines using a generalized lasso model. Knots corresponding to significant changes in discrete derivatives of a selected order are identified as active; (2) A higher-order B-spline approximation is then constructed using these active knots. Redundant knots are iteratively removed while maintaining the approximation quality. We validate the method on several functions and parameter curve fitting tasks. Results show that the proposed approach yields B-spline approximations with a similar number of knots as existing methods, while achieving comparable or improved accuracy.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 53-64"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929184","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":"Algorithms for American XVA and free boundary calculations with stochastic counterparty default intensity","authors":"Yuwei Chen,&nbsp;Christina C. Christara","doi":"10.1016/j.matcom.2025.12.018","DOIUrl":"10.1016/j.matcom.2025.12.018","url":null,"abstract":"<div><div>Credit and total valuation adjustments (CVA and XVA) are significant in equity markets, as parts of the risk management under Basel III framework. In addition, path-dependent derivatives, such as American-type ones, are heavily traded in markets. Therefore, it is important to accurately and efficiently compute valuation adjustments for American-type derivatives. In this paper, we derive a two-dimensional (2D) in space partial differential equation (PDE) for pricing American-type derivatives including the XVA, assuming the counterparty default risk follows a mean reversion stochastic process, while the self-party has constant default risk. We reformulate the time-dependent, 2D nonlinear PDE into penalty form, which includes two nonlinear source terms. We employ the double-penalty iteration for the 2D PDE to resolve the two nonlinear terms, while we use a finite difference scheme for the spatial discretization, and Crank–Nicolson-Rannacher timestepping. We introduce algorithms for the accurate calculation of the free boundary. We also formulate an asymptotic approximation technique, similar to the one developed for the European case problem, but adjusted for the American put option problem. A key step is to derive the asymptotic approximation to the free boundary for the American put option. We present numerical experiments in order to study the accuracy and effectiveness of the 2D PDE and asymptotic approximations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 21-34"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929185","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":"Global dynamics of a SARS-CoV-2 infection model with interferons, spatial heterogeneity and nonlocal diffusion","authors":"Jiangxue Xu ,&nbsp;Toshikazu Kuniya ,&nbsp;Guihong Fan ,&nbsp;Zhen Jin ,&nbsp;Haitao Song","doi":"10.1016/j.matcom.2026.01.012","DOIUrl":"10.1016/j.matcom.2026.01.012","url":null,"abstract":"<div><div>The global pandemic of the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) highlights the critical need to understand its complex within-host dynamics. To investigate the roles of interferons (IFNs), spatial heterogeneity, and nonlocal diffusion in SARS-CoV-2 infection, we propose a novel within-host dynamics model incorporating these factors. The well-posedness of the system is first proved, and the basic reproduction number <span><math><mrow><mo>(</mo><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></math></span> of the system is defined. We then analyze global dynamics of the system based on <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>: when <span><math><mrow><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span>, infection-free steady state is globally asymptotically stable; the system is uniformly persistent when <span><math><mrow><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>. In addition, for a special case, an appropriate Lyapunov function is constructed to prove global asymptotic stability of the unique infection steady state for <span><math><mrow><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>. Numerical simulations validate our theoretical findings and reveal that enhancing the antiviral potency of IFNs and maintaining the antiviral state are effective strategies to limit SARS-CoV-2 infection in its early stages. Moreover, our findings suggest that increasing the diffusion rates of cells and viruses can reduce <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and control viral transmission, with the diffusion of productively infected cells and viruses being particularly crucial. Our study provides theoretical insights for designing antiviral therapies and understanding SARS-CoV-2 persistence.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 212-241"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038826","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}