Mathematics and Computers in Simulation最新文献

英文中文

Nonlinear study of interacting population with increasing functional response: The significance of fear and movement 与功能反应增加的相互作用人群的非线性研究：恐惧和运动的意义

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-11 DOI: 10.1016/j.matcom.2025.11.009

R.P. Gupta , Harinand Singh , Roberto Barrio , Arun Kumar

The study of hunting cooperation and fear effects is emerging as important ecological factors in population dynamics. These two features are analyzed independently in the literature by several researchers in detail. It is observed that both effects are important but poorly understood mechanisms that mediate the way predators organize ecosystems. The literature suggests that the outcomes of predator–prey interactions and their impact on ecosystems can be influenced together by these two factors. Therefore, we review the expanding body of research that integrates hunting cooperation and/or the effect of fear phenomena into the ecology of predator–prey. Our aim is to provide a framework for examining how the increasing type of functional response is affected by fear factor. The temporal dynamics, including the stability and bifurcation analysis of the system, is discussed briefly. Various parametric planes are analyzed to identify the regions of stability, instability, and bistability, along with some invariant manifolds in the phase plane that divide the basins of attraction. The temporal model is extended to the spatiotemporal framework to capture the movements of populations, and the conditions for Turing instability are derived, revealing spatial dynamics that produce various Turing patterns (spots, stripes, and mixed type) in response to the changes in fear effect and diffusion coefficients. Extensive numerical simulations are also performed to illustrate the dynamics of the model in temporal and spatio-temporal contexts.

狩猎合作和恐惧效应的研究正在成为种群动态的重要生态因素。这两个特征在一些研究者的文献中分别进行了详细的分析。据观察，这两种影响都很重要，但人们对调节捕食者组织生态系统的方式的机制知之甚少。文献表明，捕食者-猎物相互作用的结果及其对生态系统的影响可能受到这两个因素的共同影响。因此，我们回顾了将狩猎合作和/或恐惧现象的影响纳入捕食者-猎物生态学的不断扩大的研究机构。我们的目的是提供一个框架来研究如何增加类型的功能反应是受恐惧因素的影响。简要讨论了系统的时间动力学，包括系统的稳定性和分岔分析。分析了不同的参数平面，以识别稳定、不稳定和双稳定区域，以及相平面中划分吸引力盆地的一些不变流形。将时间模型扩展到时空框架来捕捉种群的运动，并推导出图灵不稳定的条件，揭示了随着恐惧效应和扩散系数的变化而产生各种图灵模式（斑点型、条纹型和混合型）的空间动力学。还进行了广泛的数值模拟，以说明该模型在时间和时空背景下的动态。

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引用次数: 0

Approximation of piecewise smooth functions by nonuniform nonlinear quadratic and cubic spline quasi-interpolants 用非均匀非线性二次和三次样条拟插值逼近分段光滑函数

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-11 DOI: 10.1016/j.matcom.2025.11.008

Francesc Aràndiga , Sara Remogna

This paper presents new nonlinear quadratic and cubic spline quasi-interpolants for approximating piecewise smooth functions on nonuniform knot partitions. By incorporating WENO techniques in the quasi-interpolant definition, our method avoids Gibbs phenomenon near discontinuities while maintaining high-order accuracy in smooth regions. The construction extends previous research by considering nonuniform knot distributions, offering enhanced flexibility in function reconstruction. Numerical experiments validate the method’s superior performance compared to linear approaches.

本文提出了一种新的非线性二次样条和三次样条拟插值法，用于逼近非均匀结分区上的分段光滑函数。通过在准插值定义中引入WENO技术，我们的方法避免了不连续附近的吉布斯现象，同时保持了光滑区域的高阶精度。该结构通过考虑非均匀结分布扩展了先前的研究，为功能重建提供了增强的灵活性。数值实验验证了该方法优于线性方法的性能。

引用次数: 0

Dynamic stability of Stackelberg equilibrium in mixed oligopolies: The role of social responsibility, marginal costs, and market structure 混合寡头市场中Stackelberg均衡的动态稳定性：社会责任、边际成本和市场结构的作用

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-11 DOI: 10.1016/j.matcom.2025.11.012

Jing Ren, Hao Sun, Panfei Sun

This paper investigates how corporate social responsibility, marginal costs, and market structure affect the stability of the Stackelberg equilibrium in mixed oligopolies. To achieve this, we develop dynamic mixed duopoly and triopoly models, showing that the Stackelberg equilibrium is locally asymptotically stable when the adjustment speed is below a threshold. The stability of the equilibrium is enhanced by increased marginal costs, stronger commitment to social responsibility, and the presence of a sophisticated follower in the triopoly setting. However, when the adjustment speed exceeds the threshold and the equilibrium becomes unstable, we introduce a control term into the dynamic model to restore stability. The implications of our analysis highlight the importance of firms avoiding excessive cost cutting in favor of innovation driven competition. Additionally, fostering social responsibility and moderate market competition plays a critical role in sustaining stable markets over the long term.

本文研究了混合寡头市场中企业社会责任、边际成本和市场结构对Stackelberg均衡稳定性的影响。为了实现这一点，我们建立了动态混合双寡头和三寡头模型，表明当调整速度低于阈值时，Stackelberg均衡是局部渐近稳定的。增加的边际成本、更强的社会责任承诺，以及在三足鼎立的环境中存在成熟的追随者，都会增强均衡的稳定性。然而，当调整速度超过阈值，平衡变得不稳定时，我们在动态模型中引入控制项以恢复稳定。我们分析的含义强调了企业避免过度削减成本以支持创新驱动竞争的重要性。此外，培育社会责任和适度的市场竞争对维持市场长期稳定起着至关重要的作用。

引用次数: 0

Use of Ishikawa and Picard–Ishikawa iterations with s-convexity in the generation of Mandelbrot and Julia sets: A comparative analysis 使用Ishikawa和Picard-Ishikawa迭代与s-凸在生成Mandelbrot和Julia集：比较分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-10 DOI: 10.1016/j.matcom.2025.11.007

Subhadip Roy , Krzysztof Gdawiec , Parbati Saha , Binayak S. Choudhury

In this paper, we consider a two-step Ishikawa iteration and a three-step Picard–Ishikawa iteration extended with

s

-convexity for complex polynomials of the form

z^{p + 1} + c

for the generation of sequences in the complex plane which lead to the formation of Mandelbrot and Julia sets. Various patterns that emerge from these processes of generation are displayed, analyzed and their variations with the change in the various parameters of the iteration processes are discussed. The outcomes highlight the notable differences in the images obtained by the two iterations. Additionally, we examine the relationship between the iteration parameters and two numerical measures, the average escape time, and the non-escaping area index. The numerical examples demonstrate that this dependency is nonlinear and often differs significantly between the two iterations.

在本文中，我们考虑了对于zp+1+c形式的复数多项式的两步Ishikawa迭代和具有s-凸扩展的三步Picard-Ishikawa迭代，用于在复平面上生成导致Mandelbrot集和Julia集形成的序列。对这些生成过程中出现的各种模式进行了显示和分析，并讨论了它们随迭代过程各参数变化的变化。结果突出了两次迭代得到的图像的显著差异。此外，我们还研究了迭代参数与两个数值度量，即平均逃逸时间和非逃逸区域指数之间的关系。数值算例表明，这种依赖关系是非线性的，并且在两次迭代之间往往存在显著差异。

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引用次数: 0

A numerical method for the solution of the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators 涉及Riesz空间-分数算子的二维时间-分数阶分布阶索方程的数值解法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-10 DOI: 10.1016/j.matcom.2025.11.002

M.H. Derakhshan , H.R. Marasi , Pushpendra Kumar

In this paper, we propose an efficient hybrid numerical approach to obtain approximate solutions to the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators. This combined numerical approach includes two numerical approaches in time and space directions. The weighted and shifted Grünwald difference numerical method is used to approximate the fractional problem in the time direction, and the fractional compact numerical method is applied in the direction of the space variable. The stability and convergence analyses are studied for the proposed numerical approach. To show the effectiveness of the presented numerical method, some numerical examples are given, and the numerical results for these examples are plotted. Also, this numerical approach is compared with other methods.

本文提出了一种有效的混合数值方法来求解包含Riesz空间-分数算子的二维分布阶时间-分数索方程的近似解。该组合数值方法包括时间和空间两个方向的数值方法。在时间方向上采用加权移位grnwald差分数值方法逼近分数阶问题，在空间变量方向上采用分数阶紧化数值方法逼近。对该数值方法进行了稳定性和收敛性分析。为了说明所提出的数值方法的有效性，给出了一些数值算例，并绘制了这些算例的数值结果。并与其他数值方法进行了比较。

引用次数: 0

Exploring the impact of healthcare capacity and time delays in SIR epidemic model 探讨SIR流行病模型中医疗保健能力和时间延迟的影响

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-07 DOI: 10.1016/j.matcom.2025.11.001

Agnieszka Kowalewska , Joanna Krawczyk , Marek Bodnar , María Vela-Pérez

In this paper, we analyze a compartmental model for the spread of COVID-19 that incorporates the capacity of the healthcare system. The model is governed by a set of delayed differential equations, with a focus on a healthcare capacity function inversely proportional to the size of the infectious compartment. While the properties of the model with constant healthcare capacity have been studied before in Krawczyk et al., (2022), we extend this analysis to the dynamic case. We establish conditions for the global asymptotic stability of the disease-free equilibrium using a Lyapunov functional and investigate how the system’s trajectories depend on various time delay values. Additionally, we fit the model’s infectious compartment dynamics to Polish governmental data from autumn 2021.

在本文中，我们分析了包含医疗保健系统能力的COVID-19传播的分区模型。该模型由一组延迟微分方程控制，重点关注与感染室大小成反比的医疗保健能力函数。虽然在Krawczyk等人（2022）之前已经研究了具有恒定医疗保健能力的模型的属性，但我们将此分析扩展到动态情况。我们利用Lyapunov泛函建立了无病平衡点全局渐近稳定的条件，并研究了系统的轨迹如何依赖于不同的时滞值。此外，我们将模型的感染室动力学与波兰2021年秋季的政府数据拟合。

引用次数: 0

An element-free Galerkin method for linear and nonlinear delay-reaction-diffusion equations 线性和非线性延迟-反应-扩散方程的无单元伽辽金方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-06 DOI: 10.1016/j.matcom.2025.11.003

Yanxia Zhang , Xiaolin Li

In this paper, an element-free Galerkin (EFG) method is proposed for solving delay-reaction–diffusion (DRD) equations. A fully discrete EFG system is developed by integrating a second-order time discretization with a penalized EFG spatial discretization. The unconditional stability of the time semi-discrete system is analyzed, and then the theoretical error of the meshless fully discrete system is derived. Finally, through numerical experiments, the validity of the method is verified and the theoretical result is confirmed.

本文提出了一种求解延迟-反应-扩散方程的无单元伽辽金法。将二阶时间离散化与惩罚型空间离散化相结合，建立了一个完全离散的脑电信号系统。分析了时间半离散系统的无条件稳定性，推导了无网格全离散系统的理论误差。最后通过数值实验验证了该方法的有效性，并对理论结果进行了验证。

引用次数: 0

Secure consensus of nonlinear multi-layer multi-agent systems under sequential scaling attacks 非线性多层多智能体系统在顺序缩放攻击下的安全一致性

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-04 DOI: 10.1016/j.matcom.2025.10.036

Zhengxin Wang , Yimei Tao , Min Xiao , Yuanzhen Feng , Cong Zheng , Mei Hong

In the article, secure consensus of nonlinear multi-layer multi-agent systems under sequential scaling attacks is investigated by using an asynchronous event-triggered scheme. For a nonlinear multi-layer multi-agent system, a distributed event-triggered protocol is designed to solve consensus under sequential scaling attacks. To minimize unnecessary controller updates and enhance the autonomy of agents, a fully asynchronous protocol is adopted. Apparently, the triggering instants are related to both the specific agent and the layer. By analyzing the relationship between the event-triggered parameters and systems matrices, sufficient criteria are established to ensure that consensus is reached. Besides, different scaling factors of sequential scaling attacks are analyzed. Furthermore, it is proved that no Zeno behavior occurs. At the end, an example is given to illustrate the effectiveness of the derived theorems and results.

本文采用异步事件触发方案，研究了非线性多层多智能体系统在顺序缩放攻击下的安全一致性问题。针对非线性多层多智能体系统，设计了一种分布式事件触发协议，以解决连续扩容攻击下的一致性问题。为了减少不必要的控制器更新和增强代理的自主性，采用了全异步协议。显然，触发时刻与特定的介质和层都有关。通过分析事件触发参数与系统矩阵之间的关系，建立了充分的准则以确保达成共识。此外，还分析了顺序缩放攻击的不同缩放因子。进一步证明了不存在芝诺行为。最后，通过一个算例说明了所得定理和结果的有效性。

引用次数: 0

A study on the convergence and efficiency of a novel seventh-order iterative method to solve systems of nonlinear equations with electrical engineering applications 一种新颖的求解非线性方程组的七阶迭代方法的收敛性和效率研究

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-11-01 DOI: 10.1016/j.matcom.2025.10.035

Raziyeh Erfanifar, Masoud Hajarian

In this paper, we present a numerical approach for solving nonlinear differential equations by combining finite difference methods with an efficient three-step iterative method. First, the nonlinear differential equations are discretized and transformed into a system of nonlinear algebraic equations using finite difference approximations. This system is then solved using a novel three-step iterative method designed to enhance computational efficiency. A key feature of the proposed iterative method is that each full iteration requires only one evaluation of the Jacobian matrix of the function and computation of its inverse. This significantly reduces the computational cost, resulting in a higher efficiency index compared to existing techniques. To validate the effectiveness of the method, we provide numerical experiments on several nonlinear differential equations. The results demonstrate the superior accuracy and computational efficiency of the proposed approach, highlighting its advantages over conventional methods.

本文提出了一种将有限差分法与有效的三步迭代法相结合的求解非线性微分方程的数值方法。首先，将非线性微分方程离散化，利用有限差分近似将其转化为非线性代数方程组。然后采用一种新颖的三步迭代方法来求解该系统，以提高计算效率。所提出的迭代方法的一个关键特点是每次完整迭代只需要对函数的雅可比矩阵求一次值并计算其逆。这大大降低了计算成本，与现有技术相比，产生了更高的效率指数。为了验证该方法的有效性，我们对几个非线性微分方程进行了数值实验。结果表明，该方法具有较高的精度和计算效率，与传统方法相比具有明显的优势。

引用次数: 0

Dynamics of a phytoplankton–zooplankton model with three-dimensional patch under the impacts of hydrodynamic conditions 三维斑块浮游植物-浮游动物模型在水动力条件影响下的动力学

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-10-31 DOI: 10.1016/j.matcom.2025.10.034

Milton Mondal , Ch. Srinivasa Rao , Tonghua Zhang

In this paper, we propose and study a mathematical model for phytoplankton–zooplankton interaction, considering the impact of hydrodynamic conditions. We investigate the impact of flow-induced hydrodynamic disturbance on the predation of phytoplankton by zooplankton and its consequent effect on the overall plankton dynamics through a mathematical modeling framework. In the model, we have incorporated the ability of phytoplankton to form patches and release toxins into the aquatic environment and also taken into account environmental toxin-induced plankton mortality. Moreover, to capture system dynamics more realistically, we have studied the corresponding seasonally forced model by introducing seasonality in some relevant model parameters. An in-depth mathematical analysis has been carried out for both autonomous and nonautonomous systems, with numerical simulations delving into the diverse dynamics exhibited by each system. We have established the existence of positive periodic solution in the seasonally forced system by using the continuation theorem in coincidence degree theory and also proved its global attractiveness by defining a suitable Lyapunov functional.

本文提出并研究了考虑水动力条件影响的浮游植物-浮游动物相互作用的数学模型。通过一个数学模型框架，研究了水流诱导的水动力扰动对浮游动物捕食浮游植物的影响及其对整体浮游生物动力学的影响。在模型中，我们纳入了浮游植物形成斑块和向水生环境释放毒素的能力，并考虑了环境毒素引起的浮游生物死亡率。此外，为了更真实地捕捉系统动力学，我们通过在一些相关模型参数中引入季节性，研究了相应的季节强迫模型。对自治系统和非自治系统进行了深入的数学分析，并通过数值模拟深入研究了每个系统所表现出的不同动力学。利用重合度理论中的延拓定理，建立了季节性强迫系统正周期解的存在性，并通过定义一个合适的Lyapunov泛函证明了它的全局吸引性。

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引用次数: 0

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