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Qualitative Theory of Dynamical Systems最新文献

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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":"23 1","pages":""},"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":"19 1","pages":""},"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":"31 1","pages":""},"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":"46 1","pages":""},"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
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":"35 1","pages":""},"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
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":"23 1","pages":""},"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
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":"23 1","pages":""},"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":"25 1","pages":""},"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
Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation 针对广义非线性浅水波方程的孤子和相似性还原自动贝克隆变换
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-04 DOI: 10.1007/s12346-024-01034-8
Xin-Yi Gao
{"title":"Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation","authors":"Xin-Yi Gao","doi":"10.1007/s12346-024-01034-8","DOIUrl":"https://doi.org/10.1007/s12346-024-01034-8","url":null,"abstract":"<p>Studies on the shallow water waves belong to the cutting-edge issues in sciences and engineering. In this paper, introducing symbolic computation, for a generalized nonlinear shallow water wave equation, with respect to the displacement and velocity of the water, we establish an auto-Bäcklund transformation with some solitonic solutions, as well as a set of the similarity reductions, the latter of which ought to be focused towards a known ordinary differential equation. Our results are seen to tie to the gravitational force and wave height.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"55 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888912","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
Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity 具有克尔非线性定律的拉克什曼-波尔舍-丹尼尔方程的分岔分析和周期函数的单调性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-05-03 DOI: 10.1007/s12346-024-01042-8
Lin Lu, Xiaokai He, Aiyong Chen
{"title":"Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity","authors":"Lin Lu, Xiaokai He, Aiyong Chen","doi":"10.1007/s12346-024-01042-8","DOIUrl":"https://doi.org/10.1007/s12346-024-01042-8","url":null,"abstract":"<p>The bifurcations and monotonicity of the period function of the Lakshmanan–Porsezian–Daniel equation with Kerr law of nonlinearity are discussed. Firstly, by the traveling wave transformations, the Lakshmanan–Porsezian–Daniel equation is reduced to the planar Hamiltonian system whose Hamiltonian function includes a 6-<i>th</i> degree polynomial. Then we give the phase portraits of the Hamiltonian system, and some traveling waves including dark wave solutions, kink and anti-kink solutions and periodic solutions are constructed by using the bifurcation method of dynamical systems. Furthermore, we discuss the monotonicity of the period function of periodic wave solutions by using some Lemmas proposed by Yang and Zeng (Bull Sci Math 133(6):555-557, 2009). Finally, some numerical simulations are presented.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"44 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888911","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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