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Qualitative Theory of Dynamical Systems最新文献

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Well-Posedness of Mild Solutions for Superdiffusion Equations with Spatial Nonlocal Operators 带空间非局部算子的超扩散方程温和解的良好拟合
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-07-02 DOI: 10.1007/s12346-024-01084-y
Xuan-Xuan Xi, Yong Zhou, Mimi Hou
{"title":"Well-Posedness of Mild Solutions for Superdiffusion Equations with Spatial Nonlocal Operators","authors":"Xuan-Xuan Xi, Yong Zhou, Mimi Hou","doi":"10.1007/s12346-024-01084-y","DOIUrl":"https://doi.org/10.1007/s12346-024-01084-y","url":null,"abstract":"<p>In this paper, we study the well-posedness for a class of semilinear superdiffusion equations with spatial nonlocal operators. We first establish the Gagliardo–Nirenberg inequality in <span>(psi )</span>-Bessel potential spaces. Based on this, the well-posedness results of local and global mild solution for corresponding linear problem are obtained via apriori estimates. We also obtain the well-posedness results for the nonlinear problem under different conditions. These conclusions are mainly based on the Mihlin–Hörmander’s multiplier estimates, embedding theorem and fixed point theory.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519367","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
Dynamics and Wong-Zakai Approximations of Stochastic Nonlocal PDEs with Long Time Memory 具有长时记忆的随机非局部 PDE 的动力学与 Wong-Zakai 近似值
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-07-02 DOI: 10.1007/s12346-024-01080-2
Jiaohui Xu, Tomás Caraballo, José Valero
{"title":"Dynamics and Wong-Zakai Approximations of Stochastic Nonlocal PDEs with Long Time Memory","authors":"Jiaohui Xu, Tomás Caraballo, José Valero","doi":"10.1007/s12346-024-01080-2","DOIUrl":"https://doi.org/10.1007/s12346-024-01080-2","url":null,"abstract":"<p>In this paper, a combination of Galerkin’s method and Dafermos’ transformation is first used to prove the existence and uniqueness of solutions for a class of stochastic nonlocal PDEs with long time memory driven by additive noise. Next, the existence of tempered random attractors for such equations is established in an appropriate space for the analysis of problems with delay and memory. Eventually, the convergence of solutions of Wong-Zakai approximations and upper semicontinuity of random attractors of the approximate random system, as the step sizes of approximations approach zero, are analyzed in a detailed way.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519479","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
Admissibility via Induced Delay Equations 通过诱导延迟方程进行受理
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-07-02 DOI: 10.1007/s12346-024-01086-w
Luís Barreira, Claudia Valls
{"title":"Admissibility via Induced Delay Equations","authors":"Luís Barreira, Claudia Valls","doi":"10.1007/s12346-024-01086-w","DOIUrl":"https://doi.org/10.1007/s12346-024-01086-w","url":null,"abstract":"<p>We give a new characterization of the existence of an exponential dichotomy for the class of <i>induced delay equations</i>, introduced recently in Barreira and Valls (JDE 391: 396–484, 2024), in terms of the admissibility of a new pair of Banach spaces. Moreover, as a consequence, we give a new application of the theory of induced delay equations to obtain results for nonautonomous delay equations via autonomous equations.\u0000</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519369","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
Existence and Linear Stability of Symmetric Periodic Orbits in the Generalized Planar Stark–Zeeman Problem 广义平面斯塔克-泽曼问题中对称周期轨道的存在性和线性稳定性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-28 DOI: 10.1007/s12346-024-01087-9
Angelo Alberti
{"title":"Existence and Linear Stability of Symmetric Periodic Orbits in the Generalized Planar Stark–Zeeman Problem","authors":"Angelo Alberti","doi":"10.1007/s12346-024-01087-9","DOIUrl":"https://doi.org/10.1007/s12346-024-01087-9","url":null,"abstract":"<p>The purpose of this paper is to demonstrate the existence of symmetric periodic solutions for a two-dimensional hydrogen atom subject to external electric and magnetic fields. We build upon the analysis of periodic orbits that was initially performed by De Bustos et al. (J Math Phys 53:082701, 2012). In this study, we utilize the symmetry of reflection and an appropriate set of variables to obtain results regarding the existence and stability of periodic solutions. Furthermore, we determine the presence of KAM 2-tori that enclose some of the linearly stable periodic solutions.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508856","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
Quartic Rigid Systems in the Plane and in the Poincaré Sphere 平面和泊恩卡球面上的四元刚性系统
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-28 DOI: 10.1007/s12346-024-01083-z
M. J. Álvarez, J. L. Bravo, L. A. Calderón
{"title":"Quartic Rigid Systems in the Plane and in the Poincaré Sphere","authors":"M. J. Álvarez, J. L. Bravo, L. A. Calderón","doi":"10.1007/s12346-024-01083-z","DOIUrl":"https://doi.org/10.1007/s12346-024-01083-z","url":null,"abstract":"<p>We consider the planar family of rigid systems of the form <span>(x'=-y+xP(x,y), y'=x+yP(x,y))</span>, where <i>P</i> is any polynomial with monomials of degree one and three. This is the simplest non-trivial family of rigid systems with no rotatory parameters. The family can be compactified to the Poincaré sphere such that the vector field along the equator is not identically null . We study the centers, singular points and limit cycles of that family on the plane and on the sphere.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529929","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
Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles 具有高阶极点的复杂夏尔马-塔索-奥尔弗方程的黎曼-希尔伯特方法
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-27 DOI: 10.1007/s12346-024-01053-5
Mengdie Liu, Biao Li
{"title":"Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles","authors":"Mengdie Liu, Biao Li","doi":"10.1007/s12346-024-01053-5","DOIUrl":"https://doi.org/10.1007/s12346-024-01053-5","url":null,"abstract":"<p>The inverse scattering transform is considered for the complex Sharma-Tasso-Olver equation with zero boundary condition by Riemann-Hilbert method. Under the reflection-less situation, we investigate the Riemann-Hilbert problem with one high-order pole and multiple high-order poles, respectively. By Laurent expansion of the Riemann-Hilbert problem and elimination of the integral factor involved in the solution, the explicit <i>N</i>-soliton solutions of the equation are derived. The interactions of several various solitons are displayed and their dynamics are analyzed.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532728","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
Reducibility of the Linear Quantum Harmonic Oscillators Under Quasi-periodic Reversible Perturbation 准周期可逆扰动下线性量子谐振子的可还原性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-26 DOI: 10.1007/s12346-024-01067-z
Zhaowei Lou, Yingnan Sun, Youchao Wu
{"title":"Reducibility of the Linear Quantum Harmonic Oscillators Under Quasi-periodic Reversible Perturbation","authors":"Zhaowei Lou, Yingnan Sun, Youchao Wu","doi":"10.1007/s12346-024-01067-z","DOIUrl":"https://doi.org/10.1007/s12346-024-01067-z","url":null,"abstract":"<p>In this paper, we establish the reducibility of a class of linear coupled quantum harmonic oscillator systems under time quasi-periodic, non-Hamiltonian, reversible perturbations. This essentially means that for most values of the frequency vector, these systems can be reduced to autonomous reversible systems with constant coefficients with respect to time. Our proof relies on an application of Kolmogorov–Arnold–Moser (KAM) theory for infinite dimensional reversible systems.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508857","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
Periodic Solutions of a Second Order Discontinuous Nonautonomous Differential Equation 二阶非自治非连续微分方程的周期解
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-25 DOI: 10.1007/s12346-024-01088-8
Fangfang Jiang, Yujuan Chen, Jitao Sun
{"title":"Periodic Solutions of a Second Order Discontinuous Nonautonomous Differential Equation","authors":"Fangfang Jiang, Yujuan Chen, Jitao Sun","doi":"10.1007/s12346-024-01088-8","DOIUrl":"https://doi.org/10.1007/s12346-024-01088-8","url":null,"abstract":"<p>In this paper, we are concerned with a problem of periodic solution for a second order nonautonomous differential equation with a discontinuity line. Under two types of assumptions, we analyze the geometric properties of solutions respectively. Then by using a fixed point theorem, we obtain several existence criteria of periodic solutions, where the periodic solutions are crossing harmonic and subharmonic solutions.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508858","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
Random Attractors of a Stochastic Hopfield Neural Network Model with Delays 带延迟的随机 Hopfield 神经网络模型的随机吸引子
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-21 DOI: 10.1007/s12346-024-01082-0
Wenjie Hu, Quanxin Zhu, Peter E. Kloeden, Yueliang Duan
{"title":"Random Attractors of a Stochastic Hopfield Neural Network Model with Delays","authors":"Wenjie Hu, Quanxin Zhu, Peter E. Kloeden, Yueliang Duan","doi":"10.1007/s12346-024-01082-0","DOIUrl":"https://doi.org/10.1007/s12346-024-01082-0","url":null,"abstract":"<p>The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is firstly proved that the trajectory field of the stochastic delayed HNNM admits an almost sure continuous version, which is compact for <span>(t&gt;tau )</span> (where <span>(tau )</span> is the delay) by a construction based on the random semiflow generated by the diffusion term due to Mohammed ( Stoch. Stoch. Rep. 29: 89–131, 1990). Then, this version is shown to generate a random dynamical system (RDS) by a Wong–Zakai approximation, after which the existence of a random absorbing set is obtained via uniform apriori estimate of the solutions. Subsequently, the pullback asymptotic compactness of the RDS generated by the stochastic delayed HNNM is established and hence the existence of random attractors is obtained. Sufficient conditions under which the attractors turn out to be an exponential attracting stationary solution are also given. Finally, some numerical simulations illustrate the results.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529930","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
Contractive Shadowing Property of Dynamical Systems 动态系统的收缩阴影特性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-06-19 DOI: 10.1007/s12346-024-01079-9
Noriaki Kawaguchi
{"title":"Contractive Shadowing Property of Dynamical Systems","authors":"Noriaki Kawaguchi","doi":"10.1007/s12346-024-01079-9","DOIUrl":"https://doi.org/10.1007/s12346-024-01079-9","url":null,"abstract":"<p>For topological dynamical systems defined by continuous self-maps of compact metric spaces, we consider the contractive shadowing property, i.e., the Lipschitz shadowing property such that the Lipschitz constant is less than 1. We prove some basic properties of contractive shadowing and show that non-degenerate homeomorphisms do not have the contractive shadowing property. Then, we consider the case of ultrametric spaces. We also discuss the spectral decomposition of the chain recurrent set under the assumption of contractive shadowing. Several examples are given to illustrate the results.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519368","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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