arXiv - MATH - Dynamical Systems最新文献_第9页

Dynamical Properties of Random Boolean Hypernetworks 随机布尔超网络的动态特性

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-30 DOI: arxiv-2408.17388

Kevin M. Stoltz, Cliff A. Joslyn

引用次数: 0

No Infinite Spin for Partial Collisions converging to isolated CC on the plane 平面上收敛到孤立 CC 的部分碰撞没有无限旋转

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-29 DOI: arxiv-2408.16409

Anna Gierzkiewicz, Rodrigo Gonçalves Schaefer, Piotr Zgliczyński

{"title":"No Infinite Spin for Partial Collisions converging to isolated CC on the plane","authors":"Anna Gierzkiewicz, Rodrigo Gonçalves Schaefer, Piotr Zgliczyński","doi":"arxiv-2408.16409","DOIUrl":"https://doi.org/arxiv-2408.16409","url":null,"abstract":"The infinite spin problem is a problem concerning the rotational behavior of\u0000total collision orbits in the $n$-body problem. The question makes also sense\u0000for partial collision. When a~cluster of bodies tends to a (partial) collision,\u0000then its normalized shape curve tends to the set of normalized central\u0000configurations, which in the planar case has $SO(2)$ symmetry. This leaves a\u0000possibility that the normalized shape curve tends to the circle obtained by\u0000rotation of some central configuration instead of a particular point on it.\u0000This is the emph{infinite spin problem}. We show that it is not possible if\u0000the limiting circle is isolated from other connected components of set of\u0000normalized central configuration. Our approach extends the method from recent\u0000work for total collision by Moeckel and Montgomery, which was based on\u0000combination of the center manifold theorem with {L}ojasiewicz inequality. To\u0000that we add a shadowing result for pseudo-orbits near normally hyperbolic\u0000manifold and careful estimates on the influence of other bodies on the cluster\u0000of colliding bodies.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195952","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

Deformations of acid-mediated invasive tumors in a model with Allee effect 阿利效应模型中酸介导的侵袭性肿瘤的变形

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-28 DOI: arxiv-2408.16172

Paul Carter, Arjen Doelman, Peter van Heijster, Daniel Levy, Philip Maini, Erin Okey, Paige Yeung

引用次数: 0

The Eisenhart Lift and Hamiltonian Systems 艾森哈特升降机和哈密顿系统

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-28 DOI: arxiv-2408.16139

Amir Babak Aazami

{"title":"The Eisenhart Lift and Hamiltonian Systems","authors":"Amir Babak Aazami","doi":"arxiv-2408.16139","DOIUrl":"https://doi.org/arxiv-2408.16139","url":null,"abstract":"It is well known in general relativity that trajectories of Hamiltonian\u0000systems lift to geodesics of pp-wave spacetimes, an example of a more general\u0000phenomenon known as the \"Eisenhart lift.\" We review and expand upon the\u0000benefits of this correspondence for dynamical systems theory. One benefit is\u0000the use of curvature and conjugate points to study the stability of Hamiltonian\u0000systems. Another benefit is that this lift unfolds a Hamiltonian system into a\u0000family of ODEs akin to a moduli space. One such family arises from the\u0000conformal invariance of lightlike geodesics, by which any Hamiltonian system\u0000unfolds into a \"conformal class\" of non-diffeomorphic ODEs with solutions in\u0000common. By utilizing higher-index versions of pp-waves, a similar lift and\u0000conformal class are shown to exist for certain second-order complex ODEs.\u0000Another such family occurs by lifting to a Riemannian metric that is dual to a\u0000pp-wave, a process that in certain cases yields a \"square root\" for the\u0000Hamiltonian. We prove a two-point boundary result for the family of ODEs\u0000arising from this lift, as well as the existence of a constant of the motion\u0000generalizing conservation of energy.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195957","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 piecewise contractive map on triangles 三角形上的片断收缩映射

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-26 DOI: arxiv-2408.16019

Samuel Everett

引用次数: 0

Analysis of anaerobic digestion model with two serial interconnected chemostats 带两个串行互联恒温器的厌氧消化模型分析

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-09 DOI: arxiv-2408.04984

Thamer Hmidhi, Radhouane Fekih-Salem, Jérôme Harmand

{"title":"Analysis of anaerobic digestion model with two serial interconnected chemostats","authors":"Thamer Hmidhi, Radhouane Fekih-Salem, Jérôme Harmand","doi":"arxiv-2408.04984","DOIUrl":"https://doi.org/arxiv-2408.04984","url":null,"abstract":"In this paper, we study a well known two-step anaerobic digestion model in a\u0000configuration of two chemostats in series. This model is an eight-dimensional\u0000system of ordinary differential equations. Since the reaction system has a\u0000cascade structure, we show that the eight-order model can be reduced to a\u0000four-dimensional one. Using general growth rates, we provide an in-depth\u0000mathematical analysis of the asymptotic behavior of the system. First, we\u0000determine all the steady states of the model where there can be more than\u0000fifteen equilibria with a non-monotonic growth rate. Then, the necessary and\u0000sufficient conditions of existence and local stability of all steady states are\u0000established according to the operating parameters: the dilution rate, the input\u0000concentrations of the two nutrients, and the distribution of the total process\u0000volume considered. The operating diagrams are then analyzed theoretically to\u0000describe the asymptotic behavior of the process according to the four control\u0000parameters. There can be seventy regions with rich behavior where the system\u0000may exhibit bistability or tristability with the coexistence of both microbial\u0000species in the two bioreactors.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937128","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

On the amenability of semigroups of entire maps and formal power series 论全映射半群和形式幂级数的可亲和性

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-09 DOI: arxiv-2408.05180

C. Cabrera, P. Dominguez, P. Makienko

引用次数: 0

Holomorphic vector fields with real integral manifolds 具有实积分流形的全纯向量场

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-09 DOI: arxiv-2408.05186

Martin Kolář, Ilya Kossovskiy, Bernhard Lamel

引用次数: 0

The two-dimensional border-collision normal form with a zero determinant 行列式为零的二维边界碰撞正则表达式

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-08 DOI: arxiv-2408.04790

David J. W. Simpson

{"title":"The two-dimensional border-collision normal form with a zero determinant","authors":"David J. W. Simpson","doi":"arxiv-2408.04790","DOIUrl":"https://doi.org/arxiv-2408.04790","url":null,"abstract":"The border-collision normal form is a piecewise-linear family of continuous\u0000maps that describe the dynamics near border-collision bifurcations. Most prior\u0000studies assume each piece of the normal form is invertible, as is generic from\u0000an abstract viewpoint, but in applied problems one piece of the map often has\u0000degenerate range, corresponding to a zero determinant. This provides\u0000simplification, yet even in two dimensions the dynamics can be incredibly rich.\u0000The purpose of this paper is to determine broadly how the dynamics of the\u0000two-dimensional border-collision normal form with a zero determinant differs\u0000for different values of its parameters. We identify parameter regions of\u0000period-adding, period-incrementing, mode-locking, and component doubling of\u0000chaotic attractors, and characterise the dominant bifurcation boundaries. The\u0000intention is for the results to enable border-collision bifurcations in\u0000mathematical models to be analysed more easily and effectively, and we\u0000illustrate this with a flu epidemic model and two stick-slip friction\u0000oscillator models. We also describe three novel bifurcation structures that\u0000remain to be explored.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937127","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

Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures 定向性对米定向高阶结构图灵模式出现的影响

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-08 DOI: arxiv-2408.04721

Marie Dorchain, Wilfried Segnou, Riccardo Muolo, Timoteo Carletti

引用次数: 0