Communications in Nonlinear Science and Numerical Simulation最新文献_第2页

Existence of global attractor in reaction–diffusion model of obesity-induced Alzheimer’s disease and its control strategies 肥胖诱发阿尔茨海默病的反应-扩散模型中全局吸引子的存在及其控制策略

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-18 DOI: 10.1016/j.cnsns.2024.108396

Ranjit Kumar Upadhyay , Debasish Pradhan , Rana D. Parshad , Parimita Roy

Evidence suggests that obesity, diabetes, and aging notably increase susceptibility to dementia-related conditions such as Alzheimer’s disease (AD). This article explores the correlations between obesity, diabetes, and AD. It introduces a diffusion-driven model encompassing variables like glucose dynamics, insulin levels, beta cells, microglia, cytokines, amyloid-

β

plaques, neurofibrillary tangles (

τ

plaques), neurodegeneration, and cognitive decline. The study includes stability analysis (local and global), examining boundedness and long-time behavior via showing the existence of a global attractor for the diffusion-driven model. A global sensitivity analysis, utilizing the Partial Rank Correlation Coefficient (PRCC), identifies factors sensitively impacting

A_{β}

plaque growth,

τ

plaques, and neurodegeneration. The deterministic model solution illustrates spatiotemporal dynamics, revealing a link between obesity and Alzheimer’s, which is characterized by distinct patchy patterns. While Alzheimer’s has no cure, employing optimal control techniques can help alleviate its effects and enhance affected individuals’ quality of life. An optimal control problem for AD management is developed, optimizing multiple aspects of disease management. The study highlights the efficacy of long-term healthy lifestyle practices and customized anti-amyloid therapy in significantly delaying obesity-induced AD progression. This research sheds light on the connection between obesity and Alzheimer’s, underscoring the negative impact of pro-inflammatory microglia on cognitive decline while proposing control strategies.

有证据表明，肥胖、糖尿病和衰老会明显增加患老年痴呆症（如阿尔茨海默病）等痴呆症相关疾病的易感性。本文探讨了肥胖、糖尿病和老年痴呆症之间的相关性。文章介绍了一个扩散驱动模型，其中包含葡萄糖动态、胰岛素水平、β细胞、小胶质细胞、细胞因子、淀粉样蛋白-β斑块、神经纤维缠结（τ斑块）、神经变性和认知能力下降等变量。该研究包括稳定性分析（局部和全局），通过显示扩散驱动模型存在全局吸引子来检验有界性和长期行为。利用部分等级相关系数（PRCC）进行的全局敏感性分析确定了对 Aβ 斑块生长、τ 斑块和神经退化产生敏感影响的因素。确定性模型解决方案展示了时空动态，揭示了肥胖与阿尔茨海默氏症之间的联系，阿尔茨海默氏症的特征是明显的斑块模式。虽然阿尔茨海默氏症无法治愈，但采用优化控制技术有助于减轻其影响，提高患者的生活质量。研究提出了一个针对阿兹海默症管理的最优控制问题，优化了疾病管理的多个方面。该研究强调了长期健康生活方式和定制的抗淀粉样蛋白疗法在显著延缓肥胖引起的注意力缺失症进展方面的功效。这项研究揭示了肥胖与阿尔茨海默氏症之间的联系，强调了促炎性小胶质细胞对认知能力下降的负面影响，同时提出了控制策略。

{"title":"Existence of global attractor in reaction–diffusion model of obesity-induced Alzheimer’s disease and its control strategies","authors":"Ranjit Kumar Upadhyay , Debasish Pradhan , Rana D. Parshad , Parimita Roy","doi":"10.1016/j.cnsns.2024.108396","DOIUrl":"10.1016/j.cnsns.2024.108396","url":null,"abstract":"<div><div>Evidence suggests that obesity, diabetes, and aging notably increase susceptibility to dementia-related conditions such as Alzheimer’s disease (AD). This article explores the correlations between obesity, diabetes, and AD. It introduces a diffusion-driven model encompassing variables like glucose dynamics, insulin levels, beta cells, microglia, cytokines, amyloid-<span><math><mi>β</mi></math></span> plaques, neurofibrillary tangles (<span><math><mi>τ</mi></math></span> plaques), neurodegeneration, and cognitive decline. The study includes stability analysis (local and global), examining boundedness and long-time behavior via showing the existence of a global attractor for the diffusion-driven model. A global sensitivity analysis, utilizing the Partial Rank Correlation Coefficient (PRCC), identifies factors sensitively impacting <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>β</mi></mrow></msub></math></span> plaque growth, <span><math><mi>τ</mi></math></span> plaques, and neurodegeneration. The deterministic model solution illustrates spatiotemporal dynamics, revealing a link between obesity and Alzheimer’s, which is characterized by distinct patchy patterns. While Alzheimer’s has no cure, employing optimal control techniques can help alleviate its effects and enhance affected individuals’ quality of life. An optimal control problem for AD management is developed, optimizing multiple aspects of disease management. The study highlights the efficacy of long-term healthy lifestyle practices and customized anti-amyloid therapy in significantly delaying obesity-induced AD progression. This research sheds light on the connection between obesity and Alzheimer’s, underscoring the negative impact of pro-inflammatory microglia on cognitive decline while proposing control strategies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535991","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}

引用次数: 0

Fractional impulsive controller design of fractional-order fuzzy systems with average dwell-time strategy and its application to wind energy systems 采用平均停留时间策略的分数阶模糊系统的分数脉冲控制器设计及其在风能系统中的应用

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-16 DOI: 10.1016/j.cnsns.2024.108394

G. Narayanan , M. Syed Ali , Sangtae Ahn , Young Hoon Joo , Rajagopal Karthikeyan , Grienggrai Rajchakit

In this study, the issue of adaptive impulsive control of a permanent magnet synchronous generator (PMSG)-based wind energy system (WES) with an average dwell-time strategy is investigated using a Takagi–Sugeno (T–S) fuzzy model described by fractional-order differential equations. A T–S fuzzy model is employed to describe the nonlinear fractional-order PMSG (FOPMSG) model, an average dwell time, an average impulsive condition, a Lyapunov function, and a less conservative algebraic inequality criterion that guarantees stabilization for the considered nonlinear system. First, the mathematical model of the FOPMSG in the

n - m

reference frame is transformed into a dimensionless chaotic system through affine transformation and time scale transformation. Then, the stabilization problem of the nonlinear chaotic FOPMSG model is considered to validate the proposed sufficient conditions, leading to the derivation of a new stability criterion for the FOPMSG model, instead of addressing the general problem to validate the proposed result. Subsequently, the desired control gains can be obtained to ensure the stabilization of the addressed closed-loop system. By combining adaptive and impulsive control, the model under consideration can be stabilized for any target dynamics. Finally, we demonstrate the efficiency and feasibility of the suggested approach through numerical simulations and comparative results.

本研究利用分数阶微分方程描述的高木-菅野（Takagi-Sugeno，T-S）模糊模型，研究了采用平均停留时间策略对基于永磁同步发电机（PMSG）的风能系统（WES）进行自适应脉冲控制的问题。采用 T-S 模糊模型来描述非线性分数阶 PMSG（FOPMSG）模型、平均驻留时间、平均脉冲条件、Lyapunov 函数和较保守的代数不等式准则，以保证所考虑的非线性系统的稳定。首先，通过仿射变换和时标变换，将 n-m 参考框架下的 FOPMSG 数学模型转化为无量纲混沌系统。然后，考虑非线性混沌 FOPMSG 模型的稳定问题，以验证所提出的充分条件，从而推导出 FOPMSG 模型的新稳定准则，而不是解决一般问题来验证所提出的结果。随后，可以获得所需的控制增益，以确保所处理闭环系统的稳定。通过将自适应控制和脉冲控制相结合，所考虑的模型可以在任何目标动态下保持稳定。最后，我们通过数值模拟和比较结果证明了所建议方法的效率和可行性。

{"title":"Fractional impulsive controller design of fractional-order fuzzy systems with average dwell-time strategy and its application to wind energy systems","authors":"G. Narayanan , M. Syed Ali , Sangtae Ahn , Young Hoon Joo , Rajagopal Karthikeyan , Grienggrai Rajchakit","doi":"10.1016/j.cnsns.2024.108394","DOIUrl":"10.1016/j.cnsns.2024.108394","url":null,"abstract":"<div><div>In this study, the issue of adaptive impulsive control of a permanent magnet synchronous generator (PMSG)-based wind energy system (WES) with an average dwell-time strategy is investigated using a Takagi–Sugeno (T–S) fuzzy model described by fractional-order differential equations. A T–S fuzzy model is employed to describe the nonlinear fractional-order PMSG (FOPMSG) model, an average dwell time, an average impulsive condition, a Lyapunov function, and a less conservative algebraic inequality criterion that guarantees stabilization for the considered nonlinear system. First, the mathematical model of the FOPMSG in the <span><math><mrow><mi>n</mi><mo>−</mo><mi>m</mi></mrow></math></span> reference frame is transformed into a dimensionless chaotic system through affine transformation and time scale transformation. Then, the stabilization problem of the nonlinear chaotic FOPMSG model is considered to validate the proposed sufficient conditions, leading to the derivation of a new stability criterion for the FOPMSG model, instead of addressing the general problem to validate the proposed result. Subsequently, the desired control gains can be obtained to ensure the stabilization of the addressed closed-loop system. By combining adaptive and impulsive control, the model under consideration can be stabilized for any target dynamics. Finally, we demonstrate the efficiency and feasibility of the suggested approach through numerical simulations and comparative results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536031","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}

引用次数: 0

Structure-preserving weighted BDF2 methods for anisotropic Cahn–Hilliard model: Uniform/variable-time-steps 各向异性 Cahn-Hilliard 模型的结构保持加权 BDF2 方法：均匀/可变时间步长

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-16 DOI: 10.1016/j.cnsns.2024.108395

Meng Li, Jingjiang Bi, Nan Wang

In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn–Hilliard (CH) model, combining the scalar auxiliary variable approach with two types of stabilized techniques. Using the concept of

G

stability, the uniform-time-step WSBDF2 method is theoretically proved to be energy-stable. Due to the inapplicability of the relevant G-stability properties, another technique is adopted in this work to demonstrate the energy stability of the variable-time-step WSBDF2 method. In addition, the two numerical schemes are all mass-conservative. Finally, numerous numerical simulations are presented to demonstrate the stability and accuracy of these schemes.

本文结合标量辅助变量方法和两种稳定技术，创新性地开发了各向异性卡恩-希利亚德（Cahn-Hilliard，CH）模型的均匀/变时步长加权和移位 BDF2（WSBDF2）方法。利用 G 稳定性概念，从理论上证明了均匀时间步长 WSBDF2 方法是能量稳定的。由于相关的 G 稳定性不适用，本研究采用了另一种技术来证明变时步长 WSBDF2 方法的能量稳定性。此外，两种数值方案都是质量守恒的。最后，大量的数值模拟证明了这些方案的稳定性和准确性。

引用次数: 0

Results for double phase problem with fractional differential equations 分数微分方程双相问题的结果

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-16 DOI: 10.1016/j.cnsns.2024.108393

J. Vanterler da C. Sousa , Lamine Mbarki , H. Jafari

In this manuscript, our main focus is present on the existence and multiplicity results concerning a new set of fractional differential equations with double phase problem in the

ψ

-fractional space,

S_{H}^{α, β; ψ} (Ω)

. We also, we discuss a property for the double phase operator

K_{ψ}^{α, β} (\cdot)

and make some comments on the results obtained by the parameters

α, β

and the function

ψ (\cdot)

.

在本手稿中，我们主要关注在ψ-分数空间 SHα,β;ψ(Ω)中一组新的分数微分方程与双相问题的存在性和多重性结果。我们还讨论了双相算子 Kψα,β(⋅)的一个性质，并对参数 α,β 和函数 ψ(⋅) 得到的结果做了一些评论。

引用次数: 0

A stabilized finite volume method based on the rotational pressure correction projection for the time-dependent incompressible MHD equations 基于旋转压力校正投影的稳定有限体积法，用于时变不可压缩多流体力学方程

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-16 DOI: 10.1016/j.cnsns.2024.108389

Xiaoji Song , Xiaochen Chu , Tong Zhang , Pengliang Yang

This paper presents an efficient numerical scheme for solving the time-dependent incompressible Magnetohydrodynamics (MHD) equations based on the rotational pressure correction projection method within the finite volume framework. Utilizing the lowest equal-order mixed finite element pair (

P_{1} - P_{1} - P_{1}

) to approximate the velocity, magnetic and pressure fields, our numerical scheme satisfies the discrete inf–sup condition by the pressure projection stabilization. To tackle the coupling inherent in the time-dependent incompressible MHD equations,the rotational pressure correction projection method is introduced to split the original problem into several linear subproblems. The unconditional stability of numerical schemes are provided,optimal error estimates in both

L^{2}

and

H^{1}

-norms of numerical solutions are also presented. Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical schemes.

本文基于有限体积框架内的旋转压力修正投影法，提出了一种求解时变不可压缩磁流体动力学（MHD）方程的高效数值方案。利用最低等阶混合有限元对（P1-P1-P1）来逼近速度场、磁场和压力场，我们的数值方案通过压力投影稳定来满足离散 inf-sup 条件。为了解决时变不可压缩 MHD 方程中固有的耦合问题，我们引入了旋转压力校正投影法，将原问题分割成多个线性子问题。此外，还给出了数值方案的无条件稳定性，以及数值解的 L2 和 H1 值的最优误差估计。最后，给出了一些数值结果，以验证已建立的理论结论，并显示所考虑的数值方案的性能。

{"title":"A stabilized finite volume method based on the rotational pressure correction projection for the time-dependent incompressible MHD equations","authors":"Xiaoji Song , Xiaochen Chu , Tong Zhang , Pengliang Yang","doi":"10.1016/j.cnsns.2024.108389","DOIUrl":"10.1016/j.cnsns.2024.108389","url":null,"abstract":"<div><div>This paper presents an efficient numerical scheme for solving the time-dependent incompressible Magnetohydrodynamics (MHD) equations based on the rotational pressure correction projection method within the finite volume framework. Utilizing the lowest equal-order mixed finite element pair (<span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span>) to approximate the velocity, magnetic and pressure fields, our numerical scheme satisfies the discrete inf–sup condition by the pressure projection stabilization. To tackle the coupling inherent in the time-dependent incompressible MHD equations,the rotational pressure correction projection method is introduced to split the original problem into several linear subproblems. The unconditional stability of numerical schemes are provided,optimal error estimates in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norms of numerical solutions are also presented. Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical schemes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535988","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}

引用次数: 0

A modified neural network method for computing the Lyapunov exponent spectrum in the nonlinear analysis of dynamical systems 计算动力系统非线性分析中的李雅普诺夫指数谱的改进型神经网络方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-15 DOI: 10.1016/j.cnsns.2024.108397

T.V. Yakovleva , A.V. Krysko , V.V. Dobriyan , V.A. Krysko

This study presents a modified neural network method for computing the Lyapunov exponent spectrum in non-linear dynamical systems. Its mathematical description is an introduction. The proposed modified neural network method allows the addition of bias and constant neurons to the neural network topology and the use of different numbers of activation functions to suit different cases. Various algorithms for computing Lyapunov exponents, such as the Benettin method, the Wolf method, the Rosenstein method, the Kantz method, the Synchronisation method, the Sano-Sawada algorithm and the proposed modification of the neural network method, are used for classical problems in nonlinear dynamics. These problems include the generalised Hénon map, the chaotic attractor of the Baier-Klein map, and the vibrations of mechanical systems such as the flexible Bernoulli-Euler beam and the flexible functionally graded porous closed cylindrical shell under alternating load. The comparative analyses presented in this study are aimed at validating the accuracy and effectiveness of the methods, and at identifying the most relevant approaches for different types of systems and classes of problems. The proposed method is demonstrated to be superior to existing methods based on time-series evaluation in terms of sample size and accuracy. Furthermore, it does not require the initial system equations.

本研究提出了一种计算非线性动力系统中 Lyapunov 指数谱的改进型神经网络方法。其数学描述是一种介绍。所提出的改进型神经网络方法允许在神经网络拓扑结构中添加偏置神经元和常数神经元，并允许使用不同数量的激活函数以适应不同情况。计算李亚普诺夫指数的各种算法，如贝内廷法、沃尔夫法、罗森斯坦法、康茨法、同步法、佐野-泽田算法和拟议的改进神经网络法，都用于非线性动力学的经典问题。这些问题包括广义赫农图、拜尔-克莱因图的混沌吸引子，以及机械系统的振动，如交变载荷下的柔性伯努利-欧拉梁和柔性功能分级多孔封闭圆柱壳。本研究中的对比分析旨在验证这些方法的准确性和有效性，并确定与不同类型系统和问题类别最相关的方法。事实证明，所提出的方法在样本量和准确性方面都优于基于时间序列评估的现有方法。此外，该方法不需要初始系统方程。

{"title":"A modified neural network method for computing the Lyapunov exponent spectrum in the nonlinear analysis of dynamical systems","authors":"T.V. Yakovleva , A.V. Krysko , V.V. Dobriyan , V.A. Krysko","doi":"10.1016/j.cnsns.2024.108397","DOIUrl":"10.1016/j.cnsns.2024.108397","url":null,"abstract":"<div><div>This study presents a modified neural network method for computing the Lyapunov exponent spectrum in non-linear dynamical systems. Its mathematical description is an introduction. The proposed modified neural network method allows the addition of bias and constant neurons to the neural network topology and the use of different numbers of activation functions to suit different cases. Various algorithms for computing Lyapunov exponents, such as the Benettin method, the Wolf method, the Rosenstein method, the Kantz method, the Synchronisation method, the Sano-Sawada algorithm and the proposed modification of the neural network method, are used for classical problems in nonlinear dynamics. These problems include the generalised Hénon map, the chaotic attractor of the Baier-Klein map, and the vibrations of mechanical systems such as the flexible Bernoulli-Euler beam and the flexible functionally graded porous closed cylindrical shell under alternating load. The comparative analyses presented in this study are aimed at validating the accuracy and effectiveness of the methods, and at identifying the most relevant approaches for different types of systems and classes of problems. The proposed method is demonstrated to be superior to existing methods based on time-series evaluation in terms of sample size and accuracy. Furthermore, it does not require the initial system equations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535992","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}

引用次数: 0

Fixed-time consensus of nonlinear multi-agent systems via both event-triggered intermittent communication and sampled-data control 通过事件触发间歇通信和采样数据控制实现非线性多代理系统的固定时间共识

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-15 DOI: 10.1016/j.cnsns.2024.108391

Haijuan Liu , Zhiyong Yu , Haijun Jiang

This paper investigates the fixed-time (FXT) consensus issue for nonlinear multi-agent systems (MASs) via both event-triggered intermittent communication and sampled-data control. Firstly, combining the event-triggered mechanism and the centralized sampled-data control method, a new type of the event-triggered intermittent control protocol is devised, in which the auxiliary function is introduced to determine the control intervals of the protocol. Secondly, the centralized strategy, which requires obtaining the global information, may be difficult to apply in large-scale networks. Therefore, we design an intermittent communication protocol with the distributed sampled-data control strategy, in which the event-triggering condition is given only by using local neighbors’ states. Furthermore, based on the Lyapunov stability theory, some sufficient conditions are obtained for achieving FXT consensus of MASs with the centralized and distributed sampled-data control strategies, and the Zeno phenomena are avoided. Finally, two examples are provided to verify the validity of the theoretical results.

本文通过事件触发间歇通信和采样数据控制两种方法，研究了非线性多代理系统（MAS）的固定时间（FXT）共识问题。首先，结合事件触发机制和集中采样数据控制方法，设计了一种新型的事件触发间歇控制协议，其中引入了辅助函数来确定协议的控制间隔。其次，集中式策略需要获取全局信息，在大规模网络中可能难以应用。因此，我们设计了一种采用分布式采样数据控制策略的间歇通信协议，其中事件触发条件仅通过本地邻居的状态给出。此外，基于李亚普诺夫稳定性理论，我们得到了一些充分条件，以实现采用集中式和分布式采样数据控制策略的 MAS 的 FXT 共识，并避免了 Zeno 现象。最后，通过两个实例验证了理论结果的正确性。

{"title":"Fixed-time consensus of nonlinear multi-agent systems via both event-triggered intermittent communication and sampled-data control","authors":"Haijuan Liu , Zhiyong Yu , Haijun Jiang","doi":"10.1016/j.cnsns.2024.108391","DOIUrl":"10.1016/j.cnsns.2024.108391","url":null,"abstract":"<div><div>This paper investigates the fixed-time (FXT) consensus issue for nonlinear multi-agent systems (MASs) via both event-triggered intermittent communication and sampled-data control. Firstly, combining the event-triggered mechanism and the centralized sampled-data control method, a new type of the event-triggered intermittent control protocol is devised, in which the auxiliary function is introduced to determine the control intervals of the protocol. Secondly, the centralized strategy, which requires obtaining the global information, may be difficult to apply in large-scale networks. Therefore, we design an intermittent communication protocol with the distributed sampled-data control strategy, in which the event-triggering condition is given only by using local neighbors’ states. Furthermore, based on the Lyapunov stability theory, some sufficient conditions are obtained for achieving FXT consensus of MASs with the centralized and distributed sampled-data control strategies, and the Zeno phenomena are avoided. Finally, two examples are provided to verify the validity of the theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535990","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}

引用次数: 0

Scaled Brownian motion with random anomalous diffusion exponent 具有随机反常扩散指数的缩放布朗运动

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-11 DOI: 10.1016/j.cnsns.2024.108388

Hubert Woszczek , Aleksei Chechkin , Agnieszka Wyłomańska

The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, characterized by anomalous diffusion through the diffusion exponent. It is a Gaussian, self-similar process with independent increments and has found applications across various fields, from turbulence and stochastic hydrology to biophysics. In our paper, inspired by recent single particle tracking biological experiments, we introduce a process called scaled Brownian motion with random exponent (SBMRE), which retains the key features of SBM at the level of individual trajectories, but with anomalous diffusion exponents that vary randomly across trajectories.

We discuss the main probabilistic properties of SBMRE, including its probability density function (pdf) and the qth absolute moment. Additionally, we present the expected value of the time-averaged mean squared displacement (TAMSD) and the ergodicity breaking parameter. Furthermore, we analyze the pdf of the first hitting time in a semi-infinite domain, the martingale property of SBMRE, and its stochastic exponential. As special cases, we consider two distributions for the anomalous diffusion exponent, namely the mixture of two point distributions and beta distribution, and explore the asymptotics of the corresponding characteristics. Theoretical results for SBMRE are validated through numerical simulations and compared with the analogous characteristics of SBM.

缩放布朗运动（SBM）被认为是典型的随机过程之一，其特点是通过扩散指数进行反常扩散。它是一个具有独立增量的高斯自相似过程，已在从湍流、随机水文学到生物物理学等多个领域得到应用。在我们的论文中，受最近的单粒子跟踪生物实验的启发，我们引入了一种称为具有随机指数的缩放布朗运动（SBMRE）的过程，它在单个轨迹的水平上保留了 SBM 的主要特征，但在不同轨迹上具有随机变化的异常扩散指数。此外，我们还提出了时间平均均方位移（TAMSD）的期望值和遍历性破坏参数。此外，我们还分析了半无限域中首次命中时间的 pdf、SBMRE 的马氏特性及其随机指数。作为特例，我们考虑了异常扩散指数的两种分布，即两点混合分布和贝塔分布，并探讨了相应特征的渐近性。通过数值模拟验证了 SBMRE 的理论结果，并与 SBM 的类似特征进行了比较。

{"title":"Scaled Brownian motion with random anomalous diffusion exponent","authors":"Hubert Woszczek , Aleksei Chechkin , Agnieszka Wyłomańska","doi":"10.1016/j.cnsns.2024.108388","DOIUrl":"10.1016/j.cnsns.2024.108388","url":null,"abstract":"<div><div>The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, characterized by anomalous diffusion through the diffusion exponent. It is a Gaussian, self-similar process with independent increments and has found applications across various fields, from turbulence and stochastic hydrology to biophysics. In our paper, inspired by recent single particle tracking biological experiments, we introduce a process called scaled Brownian motion with random exponent (SBMRE), which retains the key features of SBM at the level of individual trajectories, but with anomalous diffusion exponents that vary randomly across trajectories.</div><div>We discuss the main probabilistic properties of SBMRE, including its probability density function (pdf) and the qth absolute moment. Additionally, we present the expected value of the time-averaged mean squared displacement (TAMSD) and the ergodicity breaking parameter. Furthermore, we analyze the pdf of the first hitting time in a semi-infinite domain, the martingale property of SBMRE, and its stochastic exponential. As special cases, we consider two distributions for the anomalous diffusion exponent, namely the mixture of two point distributions and beta distribution, and explore the asymptotics of the corresponding characteristics. Theoretical results for SBMRE are validated through numerical simulations and compared with the analogous characteristics of SBM.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535995","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}

引用次数: 0

Unconditional superconvergence analysis of a new energy stable nonconforming BDF2 mixed finite element method for BBM–Burgers equation 针对 BBM-Burgers 方程的新型能量稳定不符 BDF2 混合有限元法的无条件超收敛性分析

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-10 DOI: 10.1016/j.cnsns.2024.108387

Xuemiao Xu , Dongyang Shi

The focus of this paper is to establish a new energy stable 2-step backward differentiation formula (BDF2) fully-discrete mixed finite element method (MFEM) for the Benjamin–Bona–Mahony–Burgers (BBM–Burgers) equation with the nonconforming rectangular

E Q_{1}^{r o t}

element and zero-order Raviart–Thomas (R–T) element (

E Q_{1}^{r o t} / Q_{10} \times Q_{01}

). Based on the energy stable property, the existence and uniqueness of the numerical solution are proved by the Brouwer fixed point theorem. Subsequently, with the assistance of some typical properties of this element pair and the interpolation post-processing approach, the unconditional superclose and superconvergence results with

O (h^{2} + τ^{2})

are obtained directly without any constraints between the spatial partition parameter

h

and the time step

τ

. It is worthy to mention that the method and analysis presented herein are very different from the time–space splitting approach utilized in the previous studies and simplify the implement. Finally, two numerical experiments are executed to validate the theoretical analysis.

本文的重点是针对本杰明-博纳-马霍尼-伯格斯（BBM-Burgers）方程建立一种新的能量稳定的两步反向微分公式（BDF2）全离散混合有限元法（MFEM），该方法采用非顺应矩形 EQ1rot 元件和零阶 Raviart-Thomas (R-T) 元件 (EQ1rot/Q10×Q01)。基于能量稳定特性，利用布劳威尔定点定理证明了数值解的存在性和唯一性。随后，借助该元素对的一些典型特性和插值后处理方法，在空间分区参数 h 和时间步长 τ 之间没有任何约束的情况下，直接得到了 O(h2+τ2)的无条件超闭合和超收敛结果。最后，我们进行了两次数值实验来验证理论分析。

{"title":"Unconditional superconvergence analysis of a new energy stable nonconforming BDF2 mixed finite element method for BBM–Burgers equation","authors":"Xuemiao Xu , Dongyang Shi","doi":"10.1016/j.cnsns.2024.108387","DOIUrl":"10.1016/j.cnsns.2024.108387","url":null,"abstract":"<div><div>The focus of this paper is to establish a new energy stable 2-step backward differentiation formula (BDF2) fully-discrete mixed finite element method (MFEM) for the Benjamin–Bona–Mahony–Burgers (BBM–Burgers) equation with the nonconforming rectangular <span><math><mrow><mi>E</mi><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>r</mi><mi>o</mi><mi>t</mi></mrow></msubsup></mrow></math></span> element and zero-order Raviart–Thomas (R–T) element (<span><math><mrow><mi>E</mi><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>r</mi><mi>o</mi><mi>t</mi></mrow></msubsup><mo>/</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>01</mn></mrow></msub></mrow></math></span>). Based on the energy stable property, the existence and uniqueness of the numerical solution are proved by the Brouwer fixed point theorem. Subsequently, with the assistance of some typical properties of this element pair and the interpolation post-processing approach, the unconditional superclose and superconvergence results with <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> are obtained directly without any constraints between the spatial partition parameter <span><math><mi>h</mi></math></span> and the time step <span><math><mi>τ</mi></math></span>. It is worthy to mention that the method and analysis presented herein are very different from the time–space splitting approach utilized in the previous studies and simplify the implement. Finally, two numerical experiments are executed to validate the theoretical analysis.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536029","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}

引用次数: 0

Randomness suppress backward bifurcation in an epidemic model with limited medical resources 在医疗资源有限的流行病模型中，随机性抑制了向后分叉

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2024-10-10 DOI: 10.1016/j.cnsns.2024.108380

A. Lahrouz , T. Caraballo , I. Bouzalmat , A. Settati

This paper delves into the dynamic features of a stochastic SIR epidemic model featuring a perturbed transmission rate influenced by white noise. Our primary aim is to unravel the intricate interplay between restricted medical resources, their supply efficiency, and environmental stochasticity, shedding light on their collective impact on the transmission dynamics of infectious diseases. Our findings bring to light a notable distinction from the deterministic counterpart of the model. Specifically, under varying scenarios of medical resource availability and supply efficiency, the stochastic model exhibits a departure from bifurcation phenomena. This stands in contrast to the deterministic model, which is characterized by the presence of both backward bifurcation and Hopf bifurcation phenomena. To complement and validate our theoretical findings, numerical simulations are employed, providing concrete illustrations of the dynamical phenomena discussed in the paper. This research contributes to a nuanced understanding of the intricate interplay between stochastic environmental factors, medical resource constraints, and disease transmission dynamics, offering valuable insights for public health management and epidemic control strategies.

本文深入探讨了一个随机 SIR 流行病模型的动态特征，该模型具有受白噪声影响的扰动传播率。我们的主要目的是揭示受限医疗资源、其供应效率和环境随机性之间错综复杂的相互作用，阐明它们对传染病传播动态的共同影响。我们的研究结果揭示了该模型与确定性模型的显著区别。具体来说，在医疗资源可用性和供应效率不同的情况下，随机模型表现出偏离分叉现象。这与确定性模型形成鲜明对比，后者的特点是同时存在后向分岔和霍普夫分岔现象。为了补充和验证我们的理论发现，我们采用了数值模拟，对论文中讨论的动力学现象进行了具体说明。这项研究有助于深入理解随机环境因素、医疗资源限制和疾病传播动态之间错综复杂的相互作用，为公共卫生管理和流行病控制策略提供了宝贵的见解。

{"title":"Randomness suppress backward bifurcation in an epidemic model with limited medical resources","authors":"A. Lahrouz , T. Caraballo , I. Bouzalmat , A. Settati","doi":"10.1016/j.cnsns.2024.108380","DOIUrl":"10.1016/j.cnsns.2024.108380","url":null,"abstract":"<div><div>This paper delves into the dynamic features of a stochastic SIR epidemic model featuring a perturbed transmission rate influenced by white noise. Our primary aim is to unravel the intricate interplay between restricted medical resources, their supply efficiency, and environmental stochasticity, shedding light on their collective impact on the transmission dynamics of infectious diseases. Our findings bring to light a notable distinction from the deterministic counterpart of the model. Specifically, under varying scenarios of medical resource availability and supply efficiency, the stochastic model exhibits a departure from bifurcation phenomena. This stands in contrast to the deterministic model, which is characterized by the presence of both backward bifurcation and Hopf bifurcation phenomena. To complement and validate our theoretical findings, numerical simulations are employed, providing concrete illustrations of the dynamical phenomena discussed in the paper. This research contributes to a nuanced understanding of the intricate interplay between stochastic environmental factors, medical resource constraints, and disease transmission dynamics, offering valuable insights for public health management and epidemic control strategies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445729","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}

引用次数: 0