Communications in Nonlinear Science and Numerical Simulation最新文献

Solvability, stability and its application in the P–M synchronization problem of discrete-time fractional order singular systems 离散时间分数阶奇异系统的P-M同步问题的可解性、稳定性及其应用

IF 3.8 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-29 DOI: 10.1016/j.cnsns.2025.109175

Duong Thi Hong , Do Duc Thuan

{"title":"Solvability, stability and its application in the P–M synchronization problem of discrete-time fractional order singular systems","authors":"Duong Thi Hong , Do Duc Thuan","doi":"10.1016/j.cnsns.2025.109175","DOIUrl":"10.1016/j.cnsns.2025.109175","url":null,"abstract":"<div><div>Fractional order singular systems are an important class of systems characterized by algebraic constraints combined with fractional-order dynamic behaviors. This paper focuses on discrete-time fractional order singular systems (DFOSSs), introducing the concept of the index to analyze their structural properties. Using the Drazin inverse, we establish a lemma that decomposes DFOSSs into simpler subsystems, forming the basis for deriving solvability and stability conditions. These results are achieved through techniques from fractional calculus and singular systems. Additionally, we provide an explicit solution formula for DFOSSs, enabling practical computation. A control strategy is then proposed to achieve <span><math><mrow><mi>P</mi><mtext>–</mtext><mi>M</mi></mrow></math></span> synchronization, a method that synchronizes different dimensions within the same master–slave system, surpassing traditional synchronization approaches. To demonstrate the utility of our findings, practical applications in electrical circuits are presented, showcasing the effectiveness of our methods. This study offers a comprehensive framework for analyzing and controlling DFOSSs, bridging theoretical insights with real-world applications.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109175"},"PeriodicalIF":3.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739271","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

The Riemann solutions of the Chaplygin Euler equations with discontinuity terms: The disappearance and generation of a delta shock wave 具有不连续项的Chaplygin Euler方程的Riemann解：delta激波的消失和产生

IF 3.8 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-28 DOI: 10.1016/j.cnsns.2025.109170

Zhijian Wei, Lihui Guo

引用次数: 0

Reduction of algebraic delay systems to state-dependent delay systems 代数时滞系统约简为状态相关时滞系统

IF 3.8 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-28 DOI: 10.1016/j.cnsns.2025.109174

Redouane Qesmi

{"title":"Reduction of algebraic delay systems to state-dependent delay systems","authors":"Redouane Qesmi","doi":"10.1016/j.cnsns.2025.109174","DOIUrl":"10.1016/j.cnsns.2025.109174","url":null,"abstract":"<div><div>In this paper, we show that a general class of algebraic-delay systems of differential equations <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mfenced><mrow><mi>τ</mi><mfenced><mrow><mi>t</mi></mrow></mfenced><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow></mfenced><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd><mi>h</mi><mfenced><mrow><mi>τ</mi><mfenced><mrow><mi>t</mi></mrow></mfenced><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where the delay <span><math><mrow><mi>τ</mi><mfenced><mrow><mi>t</mi></mrow></mfenced></mrow></math></span> is defined implicitly through the state history <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo></mrow></math></span> can be reduced to systems with state-dependent delay. The algebraic-delay framework covers a number of cases, including threshold-type delays and other implicitly defined mechanisms. This reduction enables the use of established theoretical tools from the study of state-dependent delay equations to analyze both the local and global dynamics of systems with algebraic delays. As an application, we present an SIRS epidemic model incorporating waning immunity and immune system boosting, and provide both quantitative and partial qualitative analysis of its dynamics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109174"},"PeriodicalIF":3.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722102","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

Spot solutions to a neural field equation on oblate spheroids 椭球面上神经场方程的点解

IF 3.8 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-28 DOI: 10.1016/j.cnsns.2025.109172

Hiroshi Ishii , Riku Watanabe

{"title":"Spot solutions to a neural field equation on oblate spheroids","authors":"Hiroshi Ishii , Riku Watanabe","doi":"10.1016/j.cnsns.2025.109172","DOIUrl":"10.1016/j.cnsns.2025.109172","url":null,"abstract":"<div><div>Understanding the dynamics of excitation patterns in neural fields is an important topic in neuroscience. Neural field equations are mathematical models that describe the excitation dynamics of interacting neurons to perform the theoretical analysis. Although many analyses of neural field equations focus on the effect of neuronal interactions on the flat surface, the geometric constraint of the dynamics is also an attractive topic when modeling organs such as the brain. This paper reports pattern dynamics in a neural field equation defined on spheroids as model curved surfaces. We treat spot solutions as localized patterns and discuss how the geometric properties of the curved surface change their properties. To analyze spot patterns on spheroids with small flattening, we first construct exact stationary spot solutions on the spherical surface and reveal their stability. We then extend the analysis to show the existence and stability of stationary spot solutions in the spheroidal case. One of our theoretical results is the derivation of a stability criterion for stationary spot solutions localized at poles on oblate spheroids. The criterion determines whether a spot solution remains at a pole or moves away. Finally, we conduct numerical simulations to discuss the dynamics of spot solutions with the insight of our theoretical predictions. Our results show that the dynamics of spot solutions depend on the curved surface and the coordination of neural interactions.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109172"},"PeriodicalIF":3.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723771","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

The modified characteristics FEMs for the incompressible vector potential MagnetoHydroDynamics system 不可压缩矢量位磁流体动力学系统的改进特性有限元分析

IF 3.8 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-27 DOI: 10.1016/j.cnsns.2025.109150

Zhiyong Si , Puxuan Xu , Yunxia Wang , Hongwei Wang

{"title":"The modified characteristics FEMs for the incompressible vector potential MagnetoHydroDynamics system","authors":"Zhiyong Si , Puxuan Xu , Yunxia Wang , Hongwei Wang","doi":"10.1016/j.cnsns.2025.109150","DOIUrl":"10.1016/j.cnsns.2025.109150","url":null,"abstract":"<div><div>In this paper, we investigate the modified characteristics finite element methods (FEMs) for the two- and three-dimensional incompressible magnetohydrodynamics (MHD) system, formulated using a magnetic vector potential approach. Specifically, we express the magnetic induction <span><math><mi>B</mi></math></span> as <span><math><mrow><mi>B</mi><mo>=</mo><mo>∇</mo><mo>×</mo><mi>A</mi></mrow></math></span>, where <span><math><mi>A</mi></math></span> is the magnetic vector potential. Through a rigorous analysis of the time-discrete system, we strictly establish that the error between the numerical solution and the time-discrete solution remains bounded, independent of the time step size <span><math><mi>τ</mi></math></span>. Theoretical results, including unconditional stability and 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, are presented. Additionally, numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method, validating the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109150"},"PeriodicalIF":3.8,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722104","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

The second type noncommutative KP and mKP equations with self-consistent sources and Miura transformation 具有自洽源和Miura变换的第二类非交换KP和mKP方程

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-26 DOI: 10.1016/j.cnsns.2025.109159

Muhammad Kashif, Chunxia Li

引用次数: 0

Dynamics of a nonlocal diffusive SIR epidemic model with nonlocal infection 具有非局部感染的非局部弥漫性SIR流行病模型动力学

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-26 DOI: 10.1016/j.cnsns.2025.109161

Subir Dey, Tapan Kumar Kar

{"title":"Dynamics of a nonlocal diffusive SIR epidemic model with nonlocal infection","authors":"Subir Dey, Tapan Kumar Kar","doi":"10.1016/j.cnsns.2025.109161","DOIUrl":"10.1016/j.cnsns.2025.109161","url":null,"abstract":"<div><div>Nonlocal diffusion offers a more realistic framework for modeling epidemic dynamics by capturing the movement of individuals across broader spatial regions. In this study, we develop a nonlocal diffusive SIR epidemic model incorporating nonlocal infection transmission, modeled via a convolution of a spatial kernel function with the infected population’s spatial distribution. Using semigroup theory, we establish the global well-posedness, compactness, and asymptotic smoothness of the semiflow generated by the system, ensuring the mathematical robustness of the model. A principal eigenvalue problem for a perturbed nonlocal diffusion operator is examined, and the existence of a positive eigenfunction corresponding to the principal eigenvalue is shown. This principal eigenvalue acts analogously to the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, serving as a threshold parameter. In particular, a globally stable disease-free equilibrium occurs when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span>, whereas a globally stable endemic equilibrium emerges when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. To analyze this, two scenarios are examined: (i) when susceptible individuals do not diffuse but infected individuals do, and (ii) when both diffuse. Numerical simulations show that wider spatial diffusion increases <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, thereby enhancing the potential for disease spread. Also, increasing the infection radius, based on the compact support of the spatial kernel, plays a key role in reducing infection spread, revealing key insights into spatial control strategies for epidemic containment.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109161"},"PeriodicalIF":3.4,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713536","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

Conservation laws of mean field games equations with time discounting 带时间折现的平均场运动方程的守恒定律

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-26 DOI: 10.1016/j.cnsns.2025.109157

Roman Kozlov

引用次数: 0

Heterogeneous consensus dynamics through reaction–diffusion models on graphs/networks 基于图/网络反应扩散模型的异质共识动力学

IF 3.8 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-25 DOI: 10.1016/j.cnsns.2025.109160

Manuel Miranda, Pablo Moreno-Spiegelberg, Ernesto Estrada

{"title":"Heterogeneous consensus dynamics through reaction–diffusion models on graphs/networks","authors":"Manuel Miranda, Pablo Moreno-Spiegelberg, Ernesto Estrada","doi":"10.1016/j.cnsns.2025.109160","DOIUrl":"10.1016/j.cnsns.2025.109160","url":null,"abstract":"<div><div>Consensus protocols (linear and nonlinear) are extensively used for multi-agent systems to perform a wide variety of tasks. Its connections with diffusive models make a natural bridge between engineering and social/natural complex systems. These protocols give rise to conservative processes on the graphs representing the systems, and reach homogeneous (consensus) steady states. Here we develop a model that extends the concept of global consensus (diffusion) to dynamical processes which are nonconservative on the graphs, and reach bounded steady states, which are not necessarily a global consensus. That is, they allow heterogeneous steady states in which different subsets of agents can reach a consensus among them, which may be different from the ones reached by other groups. We prove some mathematical results indicating how the structure of the graphs representing the system determines the final states of the dynamics. Finally, we illustrate the applications of the model by considering a heterogeneous rendezvous of a group of agents, as well as the connections of the model with the Bass model for diffusion of innovation and the Lotka–Volterra equations to model the evolution of groups of species that interact in different ways.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109160"},"PeriodicalIF":3.8,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723884","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

Two-to-one internal resonance response of a suspended cable with time-delayed positive velocity feedback control 时滞正速度反馈控制悬索的二对一内共振响应

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-24 DOI: 10.1016/j.cnsns.2025.109171

Yanan Li , Jian Peng , Xiangzhan Yang , Lianhua Wang

引用次数: 0