Mathematics and Computers in Simulation最新文献

英文中文

Spatiotemporal dynamics in a diffusive eco-epidemiological system with spatial memory and fear effect 具有空间记忆和恐惧效应的弥漫性生态流行病学系统的时空动态

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-17 DOI: 10.1016/j.matcom.2026.01.020

Jia Liu , Hongyong Zhao

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.

本文提出并分析了一种新的延迟扩散模型来研究生态流行病学系统的复杂时空动态。该模型的特点是同时整合了四种关键的生态机制：抑制猎物繁殖的恐惧效应、猎物种群内的疾病传播、标准扩散和基于记忆的反捕食者定向，其中猎物根据过去的信息主动避开捕食者。严格的数学分析建立了系统的适定性，揭示了复杂的稳定动力学。我们证明了猎物的反捕食者出租车可以触发图灵不稳定性，导致静止空间模式的形成。至关重要的是，这种不稳定效应被恐惧机制所抵消，恐惧机制通过扩大同质共存的参数域而起到空间稳定器的作用。此外，我们的分析确定了猎物反应的时间延迟是时间不稳定的有力驱动因素，通过Hopf分岔诱导持续的种群振荡。除了局部分岔外，我们还利用Lyapunov泛函方法推导了无感染平衡点和共存平衡点全局渐近稳定的充分条件。数值模拟不仅证实了我们的分析预测，而且揭示了在二维空间中出现的丰富多样的复杂空间结构，包括斑点、条纹和混合模式。总之，我们的研究结果强调了恐惧、记忆和运动之间复杂的相互作用可以深刻地改变系统的稳定性，并产生不同的时空异质性，为自然生态系统中控制群落结构和疾病动态的机制提供了重要的见解。

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引用次数: 0

Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains 方形域上顶帽核函数Holling-Tanner模型的模式形成

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-21 DOI: 10.1016/j.matcom.2026.01.025

Daifeng Duan , Biao Liu , Junjie Wei

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.

研究了周期边界条件对定义在方形域上的非局部Holling-Tanner模型的影响。采用有限支持的顶帽核函数来描述非局部相互作用，并进一步适应周期边界条件。随后，我们推导了图灵和时空Hopf分岔曲线，并在这些曲线所描绘的参数范围内进行了数值模拟。我们的研究结果表明，方形域与一维情况下的时空模式存在显著差异，包括正方形、条纹、混合状态、不规则点状六边形模式以及三条纹和斑点共存状态。这些观察到的模式与化学实验结果和鱼类皮肤色素沉着模式具有显著的一致性，从而为理解化学和生物系统的时空模式提供了有价值的理论见解和预测框架。

引用次数: 0

Multistability of equilibria for Clifford-valued Cohen–Grossberg neural networks with discontinuous activation functions and time delays 具有不连续激活函数和时滞的clifford -value Cohen-Grossberg神经网络平衡点的多重稳定性

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2025-12-24 DOI: 10.1016/j.matcom.2025.12.015

Qiuyan Yang , Yuanhua Qiao , Lijuan Duan , Jun Miao

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

{(\prod_{A} (4 K_{A} + 1))}^{n}

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

{(\prod_{A} (2 K_{A} + 1))}^{n}

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.

研究了具有时变时滞和不连续激活函数的clifford -value Cohen-Grossberg神经网络（cgnn）模型的多重稳定性问题。首先探讨了平衡点的存在性，通过推导出若干充分条件和中间值定理，发现了π (4KA+1)n个平衡点的存在性，并给出了正不变量；接下来，我们研究了这些多个平衡点（EPs）的局部稳定性，这表明存在∏A(2KA+1)n个局部渐近稳定平衡点。此外，对cgnn中稳定EPs的吸引盆地进行了估计和放大。最后，通过数值算例验证了所得结果的有效性。

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引用次数: 0

A generalized Caputo fractional jerk equation with Caputo antiperiodic boundary conditions: Existence of solutions, stability and numerical simulations 一类具有Caputo反周期边界条件的广义Caputo分数阶jerk方程：解的存在性、稳定性及数值模拟

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-12 DOI: 10.1016/j.matcom.2026.01.005

Zeeshan Ali , Sandra Pinelas

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

α

and

β

using MATLAB. A special case of the proposed system is also discussed in the conclusion.

研究一类具有分数阶反周期边界条件的广义分数阶jerk方程的解的存在性、稳定性和数值模拟。该模型在方程和边界条件中具有非整数阶导数，从而产生更一般的公式。利用不动点理论建立了存在唯一性的充分条件，得到了新的结果。进一步分析了Ulam-Hyers稳定性及其广义形式，以保证解的鲁棒性。通过实例验证了理论结果的适用性，并用MATLAB分析了系统在不同分数阶α和β下的行为和稳定性。结论部分还讨论了该系统的一个特例。

引用次数: 0

Modeling a delay-driven eco-epidemiological system with fear and migration under ratio-dependent predation 比例依赖捕食条件下具有恐惧和迁移的延迟驱动生态流行病学系统建模

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-12 DOI: 10.1016/j.matcom.2026.01.002

Kahuwa Kuwali Barman , Ankur Jyoti Kashyap , Hemanta Kumar Sarmah

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.

本研究调查了一个生态流行病学捕食者-猎物模型，该模型结合了易感猎物的恐惧驱动行为变化以及猎物和捕食者种群的迁移。对受感染猎物的捕食通过比率依赖的功能反应建模，并引入传输延迟来表示感染的非瞬时性质，为框架增加了新颖性。我们研究了非延迟系统的局部稳定性和全局稳定性，并分析了跨临界分岔和Hopf分岔的发生。结果表明，恐惧效应和易感猎物迁移可能会破坏生态系统的稳定，而较高的被感染猎物生物量转化率则有利于生态系统的稳定共存。延迟引起的分岔分析进一步揭示了增加传输延迟会破坏内部平衡，数值模拟支持了这些分析结果。

引用次数: 0

Spherical fuzzy Bézier curve approximation for efficient lane-changing trajectories under uncertain data 不确定数据下有效变道轨迹的球面模糊bsamizier曲线逼近

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-08 DOI: 10.1016/j.matcom.2026.01.006

Bushra Aqil , Rakib Mustafa , Ghulam Mustafa

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 (

S_{f} BC

) 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,

S_{f} BC

employs spherical fuzzy point relations and control point relations are defined using fuzzy set theory to achieve superior uncertainty modeling and adaptability. An

S_{f} BC

, illustrated in a lane-changing scenario, produces adaptive, obstacle-avoiding trajectories that outperform crisp Bézier models. Visualization of spherical fuzzy Bézier surfaces (

S_{f} BS

) 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.

在现实世界的问题中，获取精确的信息可能具有挑战性，因为数据点经常表现出模糊、不精确或不确定性。由于信息不完整，处理不确定数据的过程十分复杂，这给处理不确定数据带来了困难。本文提出了一种用于计算机辅助几何设计（CAGD）的球面模糊bsamizier曲线（SfBC）模型，以处理不确定数据，特别是车辆变道轨迹。与现有方法假设精确数据而忽略障碍或不确定性不同，SfBC采用球面模糊点关系，控制点关系采用模糊集理论定义，具有优越的不确定性建模和适应性。在变道场景中，SfBC产生了自适应的避障轨迹，其性能优于清晰的bsamzier模型。本文还提供了球面模糊bsamizier曲面的可视化。de Casteljau算法有效地计算曲线点，动态轨迹规划方法提高了适应性。该模型与传统的清晰bsamzier方法相比表现出优越的性能，为汽车设计、3D建模和动画提供了有价值的解决方案。

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引用次数: 0

A two-grid spectral deferred correction method for the generalized multi-order fractional differential equations 广义多阶分数阶微分方程的两网格谱延迟校正方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-05 DOI: 10.1016/j.matcom.2025.12.021

Quen-Yi Lin, Ming-Cheng Shiue

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.

光谱延迟校正（SDC）方法是一类通过迭代应用低阶方法实现任意高阶精度的数值格式。这些方法具有较高的精度和较低的计算成本，对微分方程的数值求解具有很大的吸引力。本文研究了广义多阶分数阶微分方程的显式两网格SDC方法及其理论分析。分析表明，在时间步长足够小的条件下，所提出的方案是稳定的，并且在相同的条件下实现了高阶收敛。数值实验对理论结果进行了验证和说明。

引用次数: 0

Two-step optimization of knots in B-spline curve approximation b样条曲线近似中结点的两步优化

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-08 DOI: 10.1016/j.matcom.2026.01.004

Xiao Guo , Chengzhi Liu

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.

本文提出了曲线拟合中b样条结点位置优化的框架。我们表明，在去除结期间引入的扰动随着去除结处的导数跳变幅度的增加而增加。基于这一观察，我们采用多项式趋势滤波来检测样本数据的高阶离散导数的突变，从而指导有效的结选择。提出的框架包括两个主要步骤：(1)从密集放置的初始结向量开始，使用广义lasso模型优化0度b样条的系数。与选定顺序的离散导数的显著变化相对应的节被识别为活动；(2)然后利用这些活动结点构造一个高阶b样条近似。在保持近似质量的同时迭代地去除冗余结点。我们在几个函数和参数曲线拟合任务上验证了该方法。结果表明，所提出的方法产生的b样条近似具有与现有方法相似的节点数量，同时达到相当或提高的精度。

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引用次数: 0

Algorithms for American XVA and free boundary calculations with stochastic counterparty default intensity 美国XVA算法及随机交易对手违约强度下的自由边界计算

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2025-12-29 DOI: 10.1016/j.matcom.2025.12.018

Yuwei Chen, Christina C. Christara

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.

作为巴塞尔协议III框架下风险管理的一部分，信贷和总估值调整（CVA和XVA）在股票市场中具有重要意义。此外，依赖路径的衍生品，如美国式衍生品，在市场上大量交易。因此，准确、高效地计算美式衍生品的估值调整是非常重要的。本文在假设交易对手违约风险服从均值回归随机过程，而自身违约风险为常数的情况下，导出了包含XVA在内的美式衍生品定价的二维空间偏微分方程（PDE）。我们将时间相关的二维非线性偏微分方程重新表述为包含两个非线性源项的惩罚形式。我们对二维偏微分方程采用双罚迭代来解决两个非线性项，而我们使用有限差分格式进行空间离散，并使用Crank-Nicolson-Rannacher时间步进。我们介绍了精确计算自由边界的算法。我们还制定了一种渐进逼近技术，类似于为欧洲案例问题开发的技术，但针对美国看跌期权问题进行了调整。关键的一步是推导美式看跌期权自由边界的渐近逼近。为了研究二维偏微分方程和渐近逼近的准确性和有效性，我们进行了数值实验。

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引用次数: 0

Global dynamics of a SARS-CoV-2 infection model with interferons, spatial heterogeneity and nonlocal diffusion 具有干扰素、空间异质性和非局部扩散的SARS-CoV-2感染模型的全球动力学

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-14 DOI: 10.1016/j.matcom.2026.01.012

Jiangxue Xu , Toshikazu Kuniya , Guihong Fan , Zhen Jin , Haitao Song

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

(ℛ_{0})

of the system is defined. We then analyze global dynamics of the system based on

ℛ_{0}

: when

ℛ_{0} < 1

, infection-free steady state is globally asymptotically stable; the system is uniformly persistent when

ℛ_{0} > 1

. In addition, for a special case, an appropriate Lyapunov function is constructed to prove global asymptotic stability of the unique infection steady state for

ℛ_{0} > 1

. 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

ℛ_{0}

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.

严重急性呼吸综合征冠状病毒-2 （SARS-CoV-2）的全球大流行突出表明，迫切需要了解其在宿主内的复杂动态。为了研究干扰素（ifn）、空间异质性和非局部扩散在SARS-CoV-2感染中的作用，我们提出了一个包含这些因素的新的宿主内动力学模型。首先证明了该系统的适定性，并定义了该系统的基本再现数。然后，我们分析了系统的全局动力学特性：当条件为1时，无感染稳态是全局渐近稳定的；当条件为1时，系统是一致持久的。此外，对于一个特殊情况，构造了一个适当的Lyapunov函数，证明了唯一感染稳态的全局渐近稳定性。数值模拟验证了我们的理论发现，并揭示了增强ifn的抗病毒效力和维持抗病毒状态是在SARS-CoV-2感染早期限制其感染的有效策略。此外，我们的研究结果表明，增加细胞和病毒的扩散速率可以降低贡献率并控制病毒传播，其中有效感染的细胞和病毒的扩散尤为重要。我们的研究为设计抗病毒疗法和理解SARS-CoV-2的持久性提供了理论见解。

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