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Qualitative Theory of Dynamical Systems最新文献

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Dynamical Behavior and Numerical Simulation of an Influenza A Epidemic Model with Log-Normal Ornstein–Uhlenbeck Process 具有对数正态 Ornstein-Uhlenbeck 过程的甲型流感流行模型的动态行为和数值模拟
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-10 DOI: 10.1007/s12346-024-01051-7
Xiaoshan Zhang, Xinhong Zhang
{"title":"Dynamical Behavior and Numerical Simulation of an Influenza A Epidemic Model with Log-Normal Ornstein–Uhlenbeck Process","authors":"Xiaoshan Zhang, Xinhong Zhang","doi":"10.1007/s12346-024-01051-7","DOIUrl":"https://doi.org/10.1007/s12346-024-01051-7","url":null,"abstract":"<p>Influenza remains one of the most widespread epidemics, characterized by serious pathogenicity and high lethality, posing a significant threat to public health. This paper focuses on an influenza A infection model that includes vaccination and asymptomatic patients. The deterministic model examines the existence and local asymptotic stability of equilibria. In light of the influence of environmental disruption on the spread of disease, we develop a stochastic model in which the transmission rate follows a log-normal Ornstein–Uhlenbeck process. To demonstrate the dynamic behavior of the stochastic model, we verify the existence and uniqueness of the global positive solution. The establishment of suitable Lyapunov functions allows for the determination of sufficient conditions for the stationary distribution and extinction of the disease. Furthermore, the expression of the local density function around the quasi-endemic equilibrium is represented. Eventually, numerical simulations are conducted to support theoretical results and explore the effect of environmental noise. Our findings indicate that high noise intensity can expedite the extinction of the disease, while low noise intensity can facilitate the disease reaching a stationary distribution. This information may be valuable in developing strategies for disease prevention and control.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear Effect 具有恐惧效应的异莱尔浮游植物模型的动力学分析
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-10 DOI: 10.1007/s12346-024-01047-3
Shangming Chen, Fengde Chen, Vaibhava Srivastava, Rana D. Parshad
{"title":"Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear Effect","authors":"Shangming Chen, Fengde Chen, Vaibhava Srivastava, Rana D. Parshad","doi":"10.1007/s12346-024-01047-3","DOIUrl":"https://doi.org/10.1007/s12346-024-01047-3","url":null,"abstract":"<p>This paper is the first to propose an allelopathic phytoplankton competition ODE model influenced by the fear effect based on natural biological phenomena. It is shown that the interplay of this fear effect and the allelopathic term cause rich dynamics in the proposed competition model, such as global stability, transcritical bifurcation, pitchfork bifurcation, and saddle-node bifurcation. We also consider the spatially explicit version of the model and prove analogous results. Numerical simulations verify the feasibility of the theoretical analysis. The results demonstrate that the primary cause of the extinction of non-toxic species is the fear of toxic species compared to toxins. Allelopathy only affects the density of non-toxic species. The discussion guides the conservation of species and the maintenance of biodiversity.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Orbit Growth of Sofic Shifts and Periodic-Finite-Type Shifts 索菲克位移和周期-菲尼克斯型位移的轨道增长
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-09 DOI: 10.1007/s12346-024-01055-3
Azmeer Nordin, Mohd Salmi Md Noorani, Mohd Hafiz Mohd
{"title":"Orbit Growth of Sofic Shifts and Periodic-Finite-Type Shifts","authors":"Azmeer Nordin, Mohd Salmi Md Noorani, Mohd Hafiz Mohd","doi":"10.1007/s12346-024-01055-3","DOIUrl":"https://doi.org/10.1007/s12346-024-01055-3","url":null,"abstract":"<p>A sofic shift is a shift space consisting of bi-infinite labels of paths from a labelled graph. Being a dynamical system, the distribution of its closed orbits may indicate the complexity of the shift. For this purpose, prime orbit and Mertens’ orbit counting functions are introduced as a way to describe the growth of the closed orbits. The asymptotic behaviours of these counting functions can be implied from the analyticity of the Artin–Mazur zeta function of the shift. Its zeta function is expressed implicitly in terms of several signed subset matrices. In this paper, we will prove the asymptotic behaviours of the counting functions for sofic shifts via their zeta function. This involves investigating the properties of the said matrices. Suprisingly, the proof simply uses some well-known facts about sofic shifts, especially on the minimal right-resolving presentations. Furthermore, we will demonstrate this result by revisiting the case for periodic-finite-type shifts, which are a particular type of sofic shifts. At the end, we will briefly discuss the application of our finding towards the finite group and homogeneous extensions of a sofic shift.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Estimates for the Number of Limit Cycles in Discontinuous Generalized Liénard Equations 非连续广义李纳方程中极限循环次数的估计值
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-07 DOI: 10.1007/s12346-024-01048-2
Tiago M. P. de Abreu, Ricardo M. Martins
{"title":"Estimates for the Number of Limit Cycles in Discontinuous Generalized Liénard Equations","authors":"Tiago M. P. de Abreu, Ricardo M. Martins","doi":"10.1007/s12346-024-01048-2","DOIUrl":"https://doi.org/10.1007/s12346-024-01048-2","url":null,"abstract":"<p>In this paper, we study the maximum number of limit cycles for the piecewise smooth system of differential equations <span>(dot{x}=y, dot{y}=-x-varepsilon cdot (f(x)cdot y +textrm{sgn}(y)cdot g(x)))</span>. Using the averaging method, we were able to generalize a previous result for Liénard systems. In our generalization, we consider <i>g</i> as a polynomial of degree <i>m</i>. We conclude that for sufficiently small values of <span>(|{varepsilon }|)</span>, the number <span>(h_{m,n}=left[ frac{n}{2}right] +left[ frac{m}{2}right] +1)</span> serves as a lower bound for the maximum number of limit cycles in this system, which bifurcates from the periodic orbits of the linear center <span>(dot{x}=y)</span>, <span>(dot{y}=-x)</span>. Furthermore, we demonstrate that it is indeed possible to obtain a system with <span>(h_{m,n})</span> limit cycles.\u0000</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Logarithmic Stability Estimates of Non-autonomous Systems: Applications to Control Systems 论非自治系统的对数稳定性估计：控制系统的应用
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-07 DOI: 10.1007/s12346-024-01040-w
Chaker Jammazi, Ghada Bouamaied, Mohamed Boutayeb
{"title":"On the Logarithmic Stability Estimates of Non-autonomous Systems: Applications to Control Systems","authors":"Chaker Jammazi, Ghada Bouamaied, Mohamed Boutayeb","doi":"10.1007/s12346-024-01040-w","DOIUrl":"https://doi.org/10.1007/s12346-024-01040-w","url":null,"abstract":"<p>This paper concerns the polynomial-logarithmic stability and stabilization of time-varying control systems. We present sufficient Lyapunov-like conditions guaranteeing this polynomial-logarithmic stability with applications to several linear and nonlinear control systems.\u0000</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Limit Cycles for a Class of Non-autonomous Piecewise Differential Equations 一类非自治片断微分方程的极限循环
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-07 DOI: 10.1007/s12346-024-01050-8
Renhao Tian, Yulin Zhao
{"title":"The Limit Cycles for a Class of Non-autonomous Piecewise Differential Equations","authors":"Renhao Tian, Yulin Zhao","doi":"10.1007/s12346-024-01050-8","DOIUrl":"https://doi.org/10.1007/s12346-024-01050-8","url":null,"abstract":"<p>In this paper, we study a class of non-autonomous piecewise differential equations defined as follows: <span>(dx/dt=a_{0}(t)+sum _{i=1}^{n}a_{i}(t)|x|^{i})</span>, where <span>(nin mathbb {N}^{+})</span> and each <span>(a_{i}(t))</span> is real, 1-periodic, and smooth function. We deal with two basic problems related to their limit cycles <span>(big (text {isolated solutions satisfying} x(0) = x(1)big ))</span>. First, we prove that, for any given <span>(nin mathbb {N}^{+})</span>, there is no upper bound on the number of limit cycles of such equations. Second, we demonstrate that if <span>(a_{1}(t),ldots , a_{n}(t))</span> do not change sign and have the same sign in the interval [0, 1], then the equation has at most two limit cycles. We provide a comprehensive analysis of all possible configurations of these limit cycles. In addition, we extend the result of at most two limit cycles to a broader class of general non-autonomous piecewise polynomial differential equations and offer a criterion for determining the uniqueness of the limit cycle within this class of equations.\u0000</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
In the Shallow Water: Auto-Bäcklund, Hetero-Bäcklund and Scaling Transformations via a (2+1)-Dimensional Generalized Broer-Kaup System 浅水区：通过 (2+1)-Dimensional Generalized Broer-Kaup System（2+1）维广义 Broer-Kaup 系统实现自贝克兰德、异贝克兰德和缩放变换
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-06 DOI: 10.1007/s12346-024-01025-9
Xin-Yi Gao
{"title":"In the Shallow Water: Auto-Bäcklund, Hetero-Bäcklund and Scaling Transformations via a (2+1)-Dimensional Generalized Broer-Kaup System","authors":"Xin-Yi Gao","doi":"10.1007/s12346-024-01025-9","DOIUrl":"https://doi.org/10.1007/s12346-024-01025-9","url":null,"abstract":"<p>These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal velocity, this paper avails of symbolic computation to obtain (A) an auto-Bäcklund transformation with some solitons; (B) a group of the scaling transformations and (C) a group of the hetero-Bäcklund transformations, to a known linear partial differential equation, from that system. Results rely on the coefficients in that system</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Hadamard Fractional Differential Equations on an Unbounded Domain with Integro-initial Conditions 带整数初始条件的无界域上的哈达玛分式微分方程
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-06 DOI: 10.1007/s12346-024-01044-6
Nemat Nyamoradi, Bashir Ahmad
{"title":"Hadamard Fractional Differential Equations on an Unbounded Domain with Integro-initial Conditions","authors":"Nemat Nyamoradi, Bashir Ahmad","doi":"10.1007/s12346-024-01044-6","DOIUrl":"https://doi.org/10.1007/s12346-024-01044-6","url":null,"abstract":"<p>In this paper, we introduce and investigate a Hadamard-type fractional differential equation on the interval <span>((1, infty ))</span> equipped with a new class of logarithmic type integro-initial conditions. We apply the Leggett–Williams fixed point theorem and the concept of iterative positive solutions to establish the existence of solutions for the problem at hand. Our results are new and enrich the literature on Hadamard-type fractional differential equations on the infinite domain. Examples illustrating the main results are presented.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Modeling and Qualitative Dynamics of the Effects of Internal and External Storage device in a Discrete Fractional Computer Virus 离散分形计算机病毒中内部和外部存储设备效应的建模和定性动态分析
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-05 DOI: 10.1007/s12346-024-01041-9
R. Dhineshbabu, J. Alzabut, A. G. M. Selvam, S. Etemad, S. Rezapour
{"title":"Modeling and Qualitative Dynamics of the Effects of Internal and External Storage device in a Discrete Fractional Computer Virus","authors":"R. Dhineshbabu, J. Alzabut, A. G. M. Selvam, S. Etemad, S. Rezapour","doi":"10.1007/s12346-024-01041-9","DOIUrl":"https://doi.org/10.1007/s12346-024-01041-9","url":null,"abstract":"<p>In this work, we focus on the application of epidemic approaches to computer viruses and investigate the dynamic transmission of multiple viruses, aiming to reduce computer destruction. Our goal is to create and examine computer viruses using the Atangana-Baleanu sense, which is employed in the fractional difference model for the spread of computer viruses. It included removable storage devices and external computer peripherals that were infected with computer viruses. The applications of fixed-point theory and iterative techniques are employed to analyze the existence and uniqueness results concerning the suggested model. Moreover, we extend several kinds of Ulam’s stability results for this discrete model. To demonstrate the implications of changing the fractional order in this instance of numerical simulation, we employed the Atanagana–Baleanu technique. The graphical outcomes validate our theoretical findings, which we used to evaluate the impact of infected external computers and removable storage devices on computer viruses.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Relative Controllability and Hyers–Ulam Stability of Riemann–Liouville Fractional Delay Differential System 黎曼-刘维尔分数延迟微分系统的相对可控性和海尔-乌兰稳定性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-04 DOI: 10.1007/s12346-024-01046-4
Wangmin An, Danfeng Luo, Jizhao Huang
{"title":"Relative Controllability and Hyers–Ulam Stability of Riemann–Liouville Fractional Delay Differential System","authors":"Wangmin An, Danfeng Luo, Jizhao Huang","doi":"10.1007/s12346-024-01046-4","DOIUrl":"https://doi.org/10.1007/s12346-024-01046-4","url":null,"abstract":"<p>In this work, we focus on the relative controllability and Hyers–Ulam stability of Riemann–Liouville fractional delay differential system of order <span>(alpha in (1,2))</span>. Firstly, for the linear system based on Mittag-Laffler matrix function, we define a controllability Grammian matrix to judge whether the system is relatively controllable. Additionally, with the aid of Krasnoselskii’s fixed point theorem, sufficient conditions for the relative controllability of the corresponding semilinear system is also studied. Furthermore, we used Grönwall’s inequality to investigate Hyers–Ulam stability for Riemann–Liouville fractional semilinear delay differential equations. Lastly, three instances are provided to verify that our theoretical results are accurate.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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