Qualitative Theory of Dynamical Systems最新文献_第3页

Metric Mean Dimension and Mean Hausdorff Dimension Varying the Metric 公因子平均维度和豪斯多夫平均维度的变化

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-19 DOI: 10.1007/s12346-024-01100-1

J. Muentes, A. J. Becker, A. T. Baraviera, É. Scopel

{"title":"Metric Mean Dimension and Mean Hausdorff Dimension Varying the Metric","authors":"J. Muentes, A. J. Becker, A. T. Baraviera, É. Scopel","doi":"10.1007/s12346-024-01100-1","DOIUrl":"https://doi.org/10.1007/s12346-024-01100-1","url":null,"abstract":"Let (f:mathbb {M}rightarrow mathbb {M}) be a continuous map on a compact metric space (mathbb {M}) equipped with a fixed metric d, and let (tau ) be the topology on (mathbb {M}) induced by d. We denote by (mathbb {M}(tau )) the set consisting of all metrics on (mathbb {M}) that are equivalent to d. Let ( text {mdim}_{text {M}}(mathbb {M},d, f)) and ( text {mdim}_{text {H}} (mathbb {M},d, f)) be, respectively, the metric mean dimension and mean Hausdorff dimension of f. First, we will establish some fundamental properties of the mean Hausdorff dimension. Furthermore, it is important to note that ( text {mdim}_{text {M}}(mathbb {M},d, f)) and ( text {mdim}_{text {H}} (mathbb {M},d, f)) depend on the metric d chosen for (mathbb {M}). In this work, we will prove that, for a fixed dynamical system (f:mathbb {M}rightarrow mathbb {M}), the functions (text {mdim}_{text {M}} (mathbb {M}, f):mathbb {M}(tau )rightarrow mathbb {R}cup {infty }) and ( text {mdim}_{text {H}}(mathbb {M}, f): mathbb {M}(tau )rightarrow mathbb {R}cup {infty }) are not continuous, where ( text {mdim}_{text {M}}(mathbb {M}, f) (rho )= text {mdim}_{text {M}} (mathbb {M},rho , f)) and ( text {mdim}_{text {H}}(mathbb {M}, f) (rho )= text {mdim}_{text {H}} (mathbb {M},rho , f)) for any (rho in mathbb {M}(tau )). Furthermore, we will present examples of certain classes of metrics for which the metric mean dimension is a continuous function.","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227492","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

Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph 耦合希尔费分微分系统的若干存在性结果与圆图上的微分包容

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-19 DOI: 10.1007/s12346-024-01117-6

Lihong Zhang, Xuehui Liu

引用次数: 0

Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds 正则化片断线性可见-不可见二折线的滑动循环

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-16 DOI: 10.1007/s12346-024-01111-y

Renato Huzak, Kristian Uldall Kristiansen

引用次数: 0

Simultaneous Hopf and Bogdanov–Takens Bifurcations on a Leslie–Gower Type Model with Generalist Predator and Group Defence 具有通才捕食者和群体防御的莱斯利-高尔型模型上的霍普夫分岔和波格丹诺夫-塔肯斯分岔同时发生

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-14 DOI: 10.1007/s12346-024-01118-5

Liliana Puchuri, Orestes Bueno, Eduardo González-Olivares, Alejandro Rojas-Palma

引用次数: 0

Observer Design and State-Feedback Stabilization for Nonlinear Systems via Equilibrium Manifold Expansion Linearization 通过平衡漫域展开线性化实现非线性系统的观测器设计和状态反馈稳定

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-12 DOI: 10.1007/s12346-024-01115-8

Tianjian Hou, Jun Zhou

引用次数: 0

Traveling Wave Solutions for a Continuous and Discrete Diffusive Modified Leslie–Gower Predator–Prey Model 连续和离散扩散修正莱斯利-高尔捕食者-猎物模型的行波解法

IF 1.9 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-10 DOI: 10.1007/s12346-024-01116-7

Zixuan Tian, Liang Zhang

引用次数: 0

Averaging Principle for McKean-Vlasov SDEs Driven by FBMs 由 FBM 驱动的 McKean-Vlasov SDEs 的平均原理

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-06 DOI: 10.1007/s12346-024-01099-5

Tongqi Zhang, Yong Xu, Lifang Feng, Bin Pei

引用次数: 0

Streams and Graphs of Dynamical Systems 动态系统的流与图

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-06 DOI: 10.1007/s12346-024-01112-x

Roberto De Leo, James A. Yorke

{"title":"Streams and Graphs of Dynamical Systems","authors":"Roberto De Leo, James A. Yorke","doi":"10.1007/s12346-024-01112-x","DOIUrl":"https://doi.org/10.1007/s12346-024-01112-x","url":null,"abstract":"While studying gradient dynamical systems, Morse introduced the idea of encoding the qualitative behavior of a dynamical system into a graph. Smale later refined Morse’s idea and extended it to Axiom-A diffeomorphisms on manifolds. In Smale’s vision, nodes are indecomposable closed invariant subsets of the non-wandering set with a dense orbit and there is an edge from node M to node N (we say that N is downstream from M) if the unstable manifold of M intersects the stable manifold of N. Since then, the decomposition of the non-wandering set was studied in many other settings, while the edges component of Smale’s construction has been often overlooked. In the same years, more sophisticated generalizations of the non-wandering set, introduced by Birkhoff in 1920s, were elaborated first by Auslander in early 1960s, by Conley in early 1970s and later by Easton and other authors. In our language, each of these generalizations involves the introduction of a closed and transitive extension of the prolongational relation, that is closed but not transitive. In the present article, we develop a theory that generalizes at the same time both these lines of research. We study the general properties of closed transitive relations (which we call streams) containing the space of orbits of a discrete-time or continuous-time semi-flow and we argue that these relations play a central role in the qualitative study of dynamical systems. All most studied concepts of recurrence currently in literature can be defined in terms of our streams. Finally, we show how to associate to each stream a graph encoding its qualitative properties. Our main general result is that each stream of a semi-flow with “compact dynamics” has a connected graph. The range of semi-flows covered by our theorem goes from 1-dimensional discrete-time systems like the logistic map up to infinite-dimensional continuous-time systems like the semi-flow of quasilinear parabolic reaction–diffusion partial differential equations.","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948000","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

Some Generalizations of Dynamic Hardy-Knopp-Type Inequalities on Time Scales 时间尺度上动态哈代-克诺普类不等式的一些泛化

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-02 DOI: 10.1007/s12346-024-01102-z

Ahmed A. El-Deeb

引用次数: 0

Qualitative Properties and Optimal Control Strategy on a Novel Fractional Three-Species Food Chain Model 新型分数三物种食物链模型的定性特性和优化控制策略

IF 1.4 3区数学

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-02 DOI: 10.1007/s12346-024-01110-z

R. N. Premakumari, Chandrali Baishya, Shahram Rezapour, Manisha Krishna Naik, Zaher Mundher Yaseem, Sina Etemad

{"title":"Qualitative Properties and Optimal Control Strategy on a Novel Fractional Three-Species Food Chain Model","authors":"R. N. Premakumari, Chandrali Baishya, Shahram Rezapour, Manisha Krishna Naik, Zaher Mundher Yaseem, Sina Etemad","doi":"10.1007/s12346-024-01110-z","DOIUrl":"https://doi.org/10.1007/s12346-024-01110-z","url":null,"abstract":"In this study, the dynamics of a novel three-species food chain model featuring the Sokol–Howell functional response are explored. The fear of predators is incorporated into prey reproduction, and refuge is integrated into the middle predators within the framework of the Caputo fractional derivative. Theoretical aspects such as the existence and uniqueness of equilibria, their boundedness, and stability analysis are encompassed in the investigation. To examine the existence of chaos, Lyapunov exponents are computed. The optimal control measure concerning the growth of the prey population was considered, and the conditions that must be met for the optimal response to exist in the optimal control issue were determined using Pontryagin’s Maximum Principle. The theoretical outcomes were validated by using numerical simulation powered by the Adams–Bashforth–Moulton type predictor-corrector technique. Numerical justifications are provided for the influences of fear and refuge factors. When fear is absent, a numerical analysis is conducted on the global stability of the system for fractional order derivative.","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881825","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