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Dynamical Analysis Of Fractional Order Generalized Logistic Map 分数阶广义逻辑图的动态分析
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-11 DOI: arxiv-2409.07174
Sachin Bhalekar, Janardhan Chevala, Prashant M. Gade
{"title":"Dynamical Analysis Of Fractional Order Generalized Logistic Map","authors":"Sachin Bhalekar, Janardhan Chevala, Prashant M. Gade","doi":"arxiv-2409.07174","DOIUrl":"https://doi.org/arxiv-2409.07174","url":null,"abstract":"In this work, we propose a generalization to the classical logistic map. The\u0000generalized map preserves most properties of the classical map and has richer\u0000dynamics as it contains the fractional order and one more parameter. We propose\u0000the stability bounds for each equilibrium point. The detailed bifurcation\u0000analysis with respect to both parameters is presented using the bifurcation\u0000diagrams in one and two dimensions. The chaos in this system is controlled\u0000using delayed feedback. We provide some non-linear feedback controllers to\u0000synchronize the system. The multistability in the proposed system is also\u0000discussed.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear port-Hamiltonian systems and their connection to passivity 非线性端口-哈密顿系统及其与被动性的联系
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-10 DOI: arxiv-2409.06256
Attila Karsai, Tobias Breiten, Justus Ramme, Philipp Schulze
{"title":"Nonlinear port-Hamiltonian systems and their connection to passivity","authors":"Attila Karsai, Tobias Breiten, Justus Ramme, Philipp Schulze","doi":"arxiv-2409.06256","DOIUrl":"https://doi.org/arxiv-2409.06256","url":null,"abstract":"Port-Hamiltonian (pH) systems provide a powerful tool for modeling physical\u0000systems. Their energy-based perspective allows for the coupling of various\u0000subsystems through energy exchange. Another important class of systems, passive\u0000systems, are characterized by their inability to generate energy internally. In\u0000this paper, we explore first steps towards understanding the equivalence\u0000between passivity and the feasibility of port-Hamiltonian realizations in\u0000nonlinear systems. Based on our findings, we present a method to construct\u0000port-Hamiltonian representations of a passive system if the dynamics and the\u0000Hamiltonian are known.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"403 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A surprising regularizing effect of the nonlinear semigroup associated to the semilinear heat equation and applications to reaction diffusion systems 与半线性热方程相关的非线性半群的惊人正则效应及其在反应扩散系统中的应用
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-10 DOI: arxiv-2409.06606
Said Kouachi
{"title":"A surprising regularizing effect of the nonlinear semigroup associated to the semilinear heat equation and applications to reaction diffusion systems","authors":"Said Kouachi","doi":"arxiv-2409.06606","DOIUrl":"https://doi.org/arxiv-2409.06606","url":null,"abstract":"In this paper we prove that positive weak solutions for quasilinear parabolic\u0000equations on bounded domains subject to homogenous Neumann boundary conditions\u0000becme classical and global under the unique condition that the reaction doesn't\u0000change sign after certain positive time. We apply this result to reaction\u0000diffusion systems and prove global existence of theirs positive weak solutions\u0000under the same condition on theirs reactions. The nonlinearities growth isn't\u0000taken in consideration. The proof is based on the maximum principle.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics 深度学习用于理想化大气动力学中的库普曼算子估计
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-10 DOI: arxiv-2409.06522
David Millard, Arielle Carr, Stéphane Gaudreault
{"title":"Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics","authors":"David Millard, Arielle Carr, Stéphane Gaudreault","doi":"arxiv-2409.06522","DOIUrl":"https://doi.org/arxiv-2409.06522","url":null,"abstract":"Deep learning is revolutionizing weather forecasting, with new data-driven\u0000models achieving accuracy on par with operational physical models for\u0000medium-term predictions. However, these models often lack interpretability,\u0000making their underlying dynamics difficult to understand and explain. This\u0000paper proposes methodologies to estimate the Koopman operator, providing a\u0000linear representation of complex nonlinear dynamics to enhance the transparency\u0000of data-driven models. Despite its potential, applying the Koopman operator to\u0000large-scale problems, such as atmospheric modeling, remains challenging. This\u0000study aims to identify the limitations of existing methods, refine these models\u0000to overcome various bottlenecks, and introduce novel convolutional neural\u0000network architectures that capture simplified dynamics.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost automorphic subshifts with finiteness conditions for the boundary of the separating cover 带分离盖边界有限性条件的近自形子移动
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-09 DOI: arxiv-2409.06005
Daniel Sell, Franziska Sieron
{"title":"Almost automorphic subshifts with finiteness conditions for the boundary of the separating cover","authors":"Daniel Sell, Franziska Sieron","doi":"arxiv-2409.06005","DOIUrl":"https://doi.org/arxiv-2409.06005","url":null,"abstract":"In this article we study orbits of proximal pairs in almost automorphic\u0000subshifts. The corresponding orbits in the maximal equicontinuous factor are\u0000precisely those orbits that intersect the boundary of the subshift's separating\u0000cover. We impose certain finiteness conditions on this boundary and investigate\u0000the resulting consequences for the subshift, for instance in terms of\u0000complexity or the relations between proximal and asymptotic pairs. The last\u0000part of our article deals with Toeplitz subshifts without a finite boundary.\u0000There we treat the question of necessary conditions and sufficient conditions\u0000for the existence of a factor subshift with a finite boundary. Throughout the\u0000whole article, we provide numerous Toeplitz subshifts as examples and\u0000counterexamples to illustrate our findings and the necessity of our\u0000assumptions.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periodic points of endperiodic maps 端周期图的周期点
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-09 DOI: arxiv-2409.05963
Ellis Buckminster
{"title":"Periodic points of endperiodic maps","authors":"Ellis Buckminster","doi":"arxiv-2409.05963","DOIUrl":"https://doi.org/arxiv-2409.05963","url":null,"abstract":"Let $gcolon Lrightarrow L$ be an atoroidal, endperiodic map on an infinite\u0000type surface $L$ with no boundary and finitely many ends, each of which is\u0000accumulated by genus. By work of Landry, Minsky, and Taylor, $g$ is isotopic to\u0000a spun pseudo-Anosov map $f$. We show that spun pseudo-Anosov maps minimize the\u0000number of periodic points of period $n$ for sufficiently high $n$ over all maps\u0000in their homotopy class, strengthening a theorem of Landry, Minsky, and Taylor.\u0000We also show that the same theorem holds for atoroidal Handel--Miller maps when\u0000you only consider periodic points that lie in the intersection of the stable\u0000and unstable laminations.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"188 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite Periodic Data Rigidity For Two-Dimensional Area-Preserving Anosov Diffeomorphisms 二维保面积阿诺索夫衍射的有限周期数据刚性
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-09 DOI: arxiv-2409.05857
Thomas Aloysius O'Hare
{"title":"Finite Periodic Data Rigidity For Two-Dimensional Area-Preserving Anosov Diffeomorphisms","authors":"Thomas Aloysius O'Hare","doi":"arxiv-2409.05857","DOIUrl":"https://doi.org/arxiv-2409.05857","url":null,"abstract":"Let $f,g$ be $C^2$ area-preserving Anosov diffeomorphisms on $mathbb{T}^2$\u0000which are topologically conjugate by a homeomorphism $h$ ($hf=gh$). We assume\u0000that the Jacobian periodic data of $f$ and $g$ are matched by $h$ for all\u0000points of some large period $Ninmathbb{N}$. We show that $f$ and $g$ are\u0000``approximately smoothly conjugate.\" That is, there exists a $C^{1+alpha}$\u0000diffeomorphism $overline{h}_N$ such that $h$ and $overline{h}_N$ are $C^0$\u0000exponentially close in $N$, and $f$ and\u0000$f_N:=overline{h}_N^{-1}goverline{h}_N$ are $C^1$ exponentially close in $N$.\u0000Moreover, the rates of convergence are uniform among different $f,g$ in a $C^2$\u0000bounded set of Anosov diffeomorphisms. The main idea in constructing\u0000$overline{h}_N$ is to do a ``weighted holonomy\" construction, and the main\u0000technical tool in obtaining our estimates is a uniform effective version of\u0000Bowen's equidistribution theorem of weighted discrete orbits to the SRB\u0000measure.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 spatial perturbed elliptic restricted 3-body problem with double-averaging 带双平均的空间扰动椭圆受限三体问题的稳定性分析
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-09 DOI: arxiv-2409.05299
Yan Luo, Kaicheng Sheng
{"title":"Stability analysis of spatial perturbed elliptic restricted 3-body problem with double-averaging","authors":"Yan Luo, Kaicheng Sheng","doi":"arxiv-2409.05299","DOIUrl":"https://doi.org/arxiv-2409.05299","url":null,"abstract":"This paper investigates the secular motion of a massless asteroid within the\u0000framework of the double-averaged elliptic restricted three-body problem. By\u0000employing Poincar'e variables, we analyze the stability properties of asteroid\u0000orbits in the presence of planetary perturbations. Our study reveals that\u0000periodic orbits identified in the planar configuration maintain stability in\u0000the spatial perturbed problem across a wide range of parameter values. These\u0000findings, supported by numerical simulations, contribute to a deeper\u0000understanding of asteroid dynamics and have implications for studying\u0000exoplanetary systems with highly eccentric host stars.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"188 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of ACIM for Piecewise Expanding $C^{1+varepsilon}$ maps 片断展开 $C^{1+varepsilon}$ 地图的 ACIM 存在性
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-09 DOI: arxiv-2409.06076
Aparna Rajput, Paweł Góra
{"title":"Existence of ACIM for Piecewise Expanding $C^{1+varepsilon}$ maps","authors":"Aparna Rajput, Paweł Góra","doi":"arxiv-2409.06076","DOIUrl":"https://doi.org/arxiv-2409.06076","url":null,"abstract":"In this paper, we establish Lasota-Yorke inequality for the Frobenius-Perron\u0000Operator of a piecewise expanding $C^{1+varepsilon}$ map of an interval. By\u0000adapting this inequality to satisfy the assumptions of the Ionescu-Tulcea and\u0000Marinescu ergodic theorem cite{ionescu1950}, we demonstrate the existence of\u0000an absolutely continuous invariant measure (ACIM) for the map. Furthermore, we\u0000prove the quasi-compactness of the Frobenius-Perron operator induced by the\u0000map. Additionally, we explore significant properties of the system, including\u0000weak mixing and exponential decay of correlations.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strange Attractors in Fractional Differential Equations: A Topological Approach to Chaos and Stability 分数微分方程中的奇异吸引子：混沌与稳定性的拓扑方法
arXiv - MATH - Dynamical Systems Pub Date : 2024-09-08 DOI: arxiv-2409.05053
Ronald Katende
{"title":"Strange Attractors in Fractional Differential Equations: A Topological Approach to Chaos and Stability","authors":"Ronald Katende","doi":"arxiv-2409.05053","DOIUrl":"https://doi.org/arxiv-2409.05053","url":null,"abstract":"In this work, we explore the dynamics of fractional differential equations\u0000(FDEs) through a rigorous topological analysis of strange attractors. By\u0000investigating systems with Caputo derivatives of order ( alpha in (0, 1) ),\u0000we identify conditions under which chaotic behavior emerges, characterized by\u0000positive topological entropy and the presence of homoclinic and heteroclinic\u0000structures. We introduce novel methods for computing the fractional Conley\u0000index and Lyapunov exponents, which allow us to distinguish between chaotic and\u0000non-chaotic attractors. Our results also provide new insights into the fractal\u0000and spectral properties of strange attractors in fractional systems,\u0000establishing a comprehensive framework for understanding chaos and stability in\u0000this context.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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