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Dynamical Systems on Graph Limits and Their Symmetries 图极限上的动力系统及其对称性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-23 DOI: 10.1007/s10884-023-10334-7
{"title":"Dynamical Systems on Graph Limits and Their Symmetries","authors":"","doi":"10.1007/s10884-023-10334-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10334-7","url":null,"abstract":"<h3>Abstract</h3> <p>The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and the dynamics thereon. We elucidate the symmetry properties of dynamical systems on graph limits—including graphons and graphops—and analyze how the symmetry shapes the dynamics, for example through invariant subspaces. In addition to traditional symmetries, dynamics on graph limits can support generalized noninvertible symmetries. Moreover, as asymmetric networks can have symmetric limits, we note that one can expect to see ghosts of symmetries in the dynamics of large but finite asymmetric networks.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"101 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stability Analysis of Random Attractors for Stochastic Modified Swift–Hohenberg Equations with Delays 带延迟的随机修正斯威夫特-霍恩伯格方程的随机吸引子稳定性分析
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-23 DOI: 10.1007/s10884-024-10348-9
Qiangheng Zhang, Tomás Caraballo, Shuang Yang
{"title":"Stability Analysis of Random Attractors for Stochastic Modified Swift–Hohenberg Equations with Delays","authors":"Qiangheng Zhang, Tomás Caraballo, Shuang Yang","doi":"10.1007/s10884-024-10348-9","DOIUrl":"https://doi.org/10.1007/s10884-024-10348-9","url":null,"abstract":"<p>A new type of random attractors is introduced to study dynamics of a stochastic modified Swift–Hohenberg equation with a general delay. A compact, pullback attracting and dividedly invariant set is called a <i>backward attractor</i>, while the criteria for its existence are established in terms of increasing dissipation and backward asymptotic compactness of a cocycle. If the delay term in the equation is Lipschitz continuous such that the Lipschitz bound and the external force are backward limitable, then we prove the existence of a backward attractor, which further leads to the longtime stability as well as the existence of a pullback attractor, where the pullback attractor and the backward attractor are shown to be random and dividedly random, respectively. Two examples of the delay term are provided to illustrate variable and distributed delays without restricting the upper bound of Lipschitz bounds.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"138 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Synchronization and Random Attractors in Reaction Jump Processes 反应跳跃过程中的同步和随机吸引子
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-23 DOI: 10.1007/s10884-023-10345-4
Maximilian Engel, Guillermo Olicón-Méndez, Nathalie Wehlitz, Stefanie Winkelmann
{"title":"Synchronization and Random Attractors in Reaction Jump Processes","authors":"Maximilian Engel, Guillermo Olicón-Méndez, Nathalie Wehlitz, Stefanie Winkelmann","doi":"10.1007/s10884-023-10345-4","DOIUrl":"https://doi.org/10.1007/s10884-023-10345-4","url":null,"abstract":"<p>This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. Based on Gillespie’s stochastic simulation algorithm, a corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including random jump times. We uncover a time-shifted synchronization in the sense that—after some initial waiting time—one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behavior occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"138 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Long Term Behavior of 2D and 3D Non-autonomous Random Convective Brinkman–Forchheimer Equations Driven by Colored Noise 彩色噪声驱动的二维和三维非自主随机对流布林克曼-福克海默方程的长期行为
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-23 DOI: 10.1007/s10884-024-10347-w
Kush Kinra, Manil T. Mohan
{"title":"Long Term Behavior of 2D and 3D Non-autonomous Random Convective Brinkman–Forchheimer Equations Driven by Colored Noise","authors":"Kush Kinra, Manil T. Mohan","doi":"10.1007/s10884-024-10347-w","DOIUrl":"https://doi.org/10.1007/s10884-024-10347-w","url":null,"abstract":"<p>The long time behavior of Wong–Zakai approximations of 2D as well as 3D non-autonomous stochastic convective Brinkman–Forchheimer (CBF) equations with non-linear diffusion terms on some bounded and unbounded domains is discussed in this work. To establish the existence of pullback random attractors, the concept of asymptotic compactness (AC) is used. In bounded domains, AC is proved via compact Sobolev embeddings. In unbounded domains, due to the lack of compact embeddings, the ideas of energy equations and uniform tail-estimates are exploited to prove AC. In the literature, CBF equations are also known as <i>Navier–Stokes equations (NSE) with damping</i>, and it is interesting to see that the modification in NSE by linear and nonlinear damping provides better results than that available for NSE in 2D and 3D. The presence of linear damping term helps to establish the results in the whole space <span>(mathbb {R}^d)</span>. The nonlinear damping term supports to obtain the results in 3D and to cover a large class of nonlinear diffusion terms also. In addition, we prove the existence of a unique pullback random attractor for stochastic CBF equations driven by additive white noise. Finally, for additive as well as multiplicative white noise cases, we establish the convergence of solutions and upper semicontinuity of pullback random attractors for Wong–Zakai approximations of stochastic CBF equations towards the pullback random attractors for stochastic CBF equations when the correlation time of colored noise converges to zero.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"11 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms 同构公制平均维度水平集的密度
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-10 DOI: 10.1007/s10884-023-10344-5
{"title":"Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms","authors":"","doi":"10.1007/s10884-023-10344-5","DOIUrl":"https://doi.org/10.1007/s10884-023-10344-5","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>N</em> be an <em>n</em>-dimensional compact riemannian manifold, with <span> <span>(nge 2)</span> </span>. In this paper, we prove that for any <span> <span>(alpha in [0,n])</span> </span>, the set consisting of homeomorphisms on <em>N</em> with lower and upper metric mean dimensions equal to <span> <span>(alpha )</span> </span> is dense in <span> <span>(text {Hom}(N))</span> </span>. More generally, given <span> <span>(alpha ,beta in [0,n])</span> </span>, with <span> <span>(alpha le beta )</span> </span>, we show the set consisting of homeomorphisms on <em>N</em> with lower metric mean dimension equal to <span> <span>(alpha )</span> </span> and upper metric mean dimension equal to <span> <span>(beta )</span> </span> is dense in <span> <span>(text {Hom}(N))</span> </span>. Furthermore, we also give a proof that the set of homeomorphisms with upper metric mean dimension equal to <em>n</em> is residual in <span> <span>(text {Hom}(N))</span> </span>. </p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"34 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stability and Instability of Equilibria in Age-Structured Diffusive Populations 年龄结构扩散种群平衡的稳定性和不稳定性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-05 DOI: 10.1007/s10884-023-10340-9
Christoph Walker
{"title":"Stability and Instability of Equilibria in Age-Structured Diffusive Populations","authors":"Christoph Walker","doi":"10.1007/s10884-023-10340-9","DOIUrl":"https://doi.org/10.1007/s10884-023-10340-9","url":null,"abstract":"<p>The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the corresponding linearization at an equilibrium determine the latter’s stability or instability. The key ingredient of the proof is the eventual compactness of the semigroup associated with the linearized problem, which is derived by a perturbation argument. The results are illustrated with examples.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"53 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Global Well-Posedness to the n-Dimensional Compressible Oldroyd-B Model Without Damping Mechanism 无阻尼机制的 n 维可压缩奥尔德罗伊德-B 模型的全局拟合优度
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-05 DOI: 10.1007/s10884-023-10346-3
Xiaoping Zhai, Zhi-Min Chen
{"title":"Global Well-Posedness to the n-Dimensional Compressible Oldroyd-B Model Without Damping Mechanism","authors":"Xiaoping Zhai, Zhi-Min Chen","doi":"10.1007/s10884-023-10346-3","DOIUrl":"https://doi.org/10.1007/s10884-023-10346-3","url":null,"abstract":"<p>We are concerned with the global well-posedness to the compressible Oldroyd-B model without a damping term in the stress tensor equation. By exploiting the intrinsic structure of the equations and introducing several new quantities for the density, the velocity and the divergence of the stress tensor, we overcome the difficulty of the lack of dissipation for the density and the stress tensor, and construct unique global solutions to this system with initial data in critical Besov spaces. As a byproduct, we obtain the optimal time decay rates of the solutions by using the pure energy argument. A similar result can be also proved for the compressible viscoelastic system without “div–curl\" structure.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"285 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Shadowing for Local Homeomorphisms, with Applications to Edge Shift Spaces of Infinite Graphs 局部同构的阴影，及其在无限图边缘移动空间中的应用
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-28 DOI: 10.1007/s10884-023-10342-7
Daniel Gonçalves, Bruno B. Uggioni
{"title":"Shadowing for Local Homeomorphisms, with Applications to Edge Shift Spaces of Infinite Graphs","authors":"Daniel Gonçalves, Bruno B. Uggioni","doi":"10.1007/s10884-023-10342-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10342-7","url":null,"abstract":"<p>In this paper, we develop the basic theory of the shadowing property for local homeomorphisms of metric locally compact spaces, with a focus on applications to edge shift spaces connected with C*-algebra theory. For the local homeomorphism (the Deaconu–Renault system) associated with a directed graph, we completely characterize the shadowing property in terms of conditions on sets of paths. Using these results, we single out classes of graphs for which the associated system presents the shadowing property, fully characterize the shadowing property for systems associated with certain graphs, and show that the system associated with the rose of infinite petals presents the shadowing property and that the Renewal shift system does not present the shadowing property.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"8 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Continuity of the Unbounded Attractors for a Fractional Perturbation of a Scalar Reaction-Diffusion Equation 标量反应-扩散方程的分数扰动的无界吸引子的连续性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-23 DOI: 10.1007/s10884-023-10341-8
Maykel Belluzi, Matheus C. Bortolan, Ubirajara Castro, Juliana Fernandes
{"title":"Continuity of the Unbounded Attractors for a Fractional Perturbation of a Scalar Reaction-Diffusion Equation","authors":"Maykel Belluzi, Matheus C. Bortolan, Ubirajara Castro, Juliana Fernandes","doi":"10.1007/s10884-023-10341-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10341-8","url":null,"abstract":"<p>In this work we study the continuity (both upper and lower semicontinuity), defined using the Hausdorff semidistance, of the unbounded attractors for a family of fractional perturbations of a scalar reaction-diffusion equation with a non-dissipative nonlinear term.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"14 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems 纤维部分双曲系统的双曲性和刚性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-23 DOI: 10.1007/s10884-023-10343-6
Sankhadip Chakraborty, Marcelo Viana
{"title":"Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems","authors":"Sankhadip Chakraborty, Marcelo Viana","doi":"10.1007/s10884-023-10343-6","DOIUrl":"https://doi.org/10.1007/s10884-023-10343-6","url":null,"abstract":"<p>Every volume-preserving accessible centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (a) has two distinct centre Lyapunov exponents, or (b) exhibits an invariant continuous line field (or pair of line fields) tangent to the centre leaves, or (c) admits a continuous conformal structure on the centre leaves invariant under both the dynamics and the stable and unstable holonomies. The last two alternatives carry strong restrictions on the topology of the centre leaves: (b) can only occur on tori, and for (c) the centre leaves must be either tori or spheres. Moreover, under some additional conditions, such maps are rigid, in the sense that they are topologically conjugate to specific algebraic models. When the system is symplectic (a) implies that the centre Lyapunov exponents are non-zero, and thus the system is (non-uniformly) hyperbolic.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"39 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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