Journal of Computational Dynamics最新文献_第3页

Contraction analysis of Volterra integral equations via realization theory and frequency-domain methods 利用实现理论和频域方法对Volterra积分方程进行收缩分析

IF 1

Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022020

E. Kudryashova, V. Reitmann

引用次数: 0

Continuation methods for principal foliations of embedded surfaces 嵌入面主叶理的延拓方法

IF 1

Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022007

J. Guckenheimer

{"title":"Continuation methods for principal foliations of embedded surfaces","authors":"J. Guckenheimer","doi":"10.3934/jcd.2022007","DOIUrl":"https://doi.org/10.3934/jcd.2022007","url":null,"abstract":"Continuation methods are a well established tool for following equilibria and periodic orbits in dynamical systems as a parameter is varied. Properly formulated, they locate and classify bifurcations of these key components of phase portraits. Principal foliations of surfaces embedded in begin{document}$ mathbb{R}^3 $end{document} resemble phase portraits of two dimensional vector fields, but they are not orientable. In the spirit of dynamical systems theory, Gutierrez and Sotomayor investigated qualitative geometric features that characterize structurally stable principal foliations and their bifurcations in one parameter families. This paper computes return maps and applies continuation methods to obtain new insight into bifurcations of principal foliations.Umbilics are the singularities of principal foliations and lines of curvature connecting umbilics are analogous to homoclinic and heteroclinic bifurcations of vector fields. Here, a continuation method tracks a periodic line of curvature in a family of surfaces that deforms an ellipsoid. One of the bifurcations of these periodic lines of curvature are connections between lemon umbilics. Differences between these bifurcations and analogous saddle connections in two dimensional vector fields are emphasized. A second case study tracks umbilics in a one parameter family of surfaces with continuation methods and locates their bifurcations using Taylor expansions in \"Monge coordinates.\" Return maps that are generalized interval exchange maps of a circle are constructed for generic surfaces with no monstar umbilics.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"28 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81636158","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

Sensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint method 用伴随法分析周期轨道和准周期不变环面灵敏度

IF 1

Journal of Computational Dynamics Pub Date : 2021-11-03 DOI: 10.3934/jcd.2022006

H. Dankowicz, J. Sieber

{"title":"Sensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint method","authors":"H. Dankowicz, J. Sieber","doi":"10.3934/jcd.2022006","DOIUrl":"https://doi.org/10.3934/jcd.2022006","url":null,"abstract":"This paper presents a rigorous framework for the continuation of solutions to nonlinear constraints and the simultaneous analysis of the sensitivities of test functions to constraint violations at each solution point using an adjoint-based approach. By the linearity of a problem Lagrangian in the associated Lagrange multipliers, the formalism is shown to be directly amenable to analysis using the COCO software package, specifically its paradigm for staged problem construction. The general theory is illustrated in the context of algebraic equations and boundary-value problems, with emphasis on periodic orbits in smooth and hybrid dynamical systems, and quasiperiodic invariant tori of flows. In the latter case, normal hyperbolicity is used to prove the existence of continuous solutions to the adjoint conditions associated with the sensitivities of the orbital periods to parameter perturbations and constraint violations, even though the linearization of the governing boundary-value problem lacks a bounded inverse, as required by the general theory. An assumption of transversal stability then implies that these solutions predict the asymptotic phases of trajectories based at initial conditions perturbed away from the torus. Example COCO code is used to illustrate the minimal additional investment in setup costs required to append sensitivity analysis to regular parameter continuation. 200 words.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85373020","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 converse sum of squares lyapunov function for outer approximation of minimal attractor sets of nonlinear systems 非线性系统最小吸引子集外逼近的逆平方和lyapunov函数

IF 1

Journal of Computational Dynamics Pub Date : 2021-10-06 DOI: 10.3934/jcd.2022019

Morgan Jones, M. Peet

引用次数: 3

Classification with Runge-Kutta networks and feature space augmentation 龙格-库塔网络和特征空间增强分类

IF 1

Journal of Computational Dynamics Pub Date : 2021-04-06 DOI: 10.3934/jcd.2021018

E. Giesecke, Axel Kroner

引用次数: 0

An algebraic approach to the spontaneous formation of spherical jets 球形射流自发形成的代数方法

IF 1

Journal of Computational Dynamics Pub Date : 2021-04-01 DOI: 10.3934/jcd.2021028

M. Viviani

{"title":"An algebraic approach to the spontaneous formation of spherical jets","authors":"M. Viviani","doi":"10.3934/jcd.2021028","DOIUrl":"https://doi.org/10.3934/jcd.2021028","url":null,"abstract":"The global structure of the atmosphere and the oceans is a continuous source of intriguing challenges in geophysical fluid dynamics (GFD). Among these, jets are determinant in the air and water circulation around the Earth. In the last fifty years, thanks to the development of more and more precise and extensive observations, it has been possible to study in detail the atmospheric formations of the giant-gas planets in the solar system. For those planets, jets are the dominant large scale structure. Starting from the 70s, various theories combining observations and mathematical models have been proposed in order to describe their formation and stability. In this paper, we propose a purely algebraic approach to describe the spontaneous formation of jets on a spherical domain. Analysing the algebraic properties of the 2D Euler equations, we give a characterization of the different jets' structures. The calculations are performed starting from the discrete Zeitlin model of the Euler equations. For this model, the classification of the jets' structures can be precisely described in terms of reductive Lie algebras decomposition. The discrete framework provides a simple tool for analysing both from a theoretical and and a numerical perspective the jets' formation. Furthermore, it allows to extend the results to the original Euler equations.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"129 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85358098","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

Computer-assisted estimates for birkhoff normal forms birkhoff范式的计算机辅助估计

IF 1

Journal of Computational Dynamics Pub Date : 2021-02-11 DOI: 10.3934/jcd.2020017

Chiara Caracciolo, U. Locatelli

{"title":"Computer-assisted estimates for birkhoff normal forms","authors":"Chiara Caracciolo, U. Locatelli","doi":"10.3934/jcd.2020017","DOIUrl":"https://doi.org/10.3934/jcd.2020017","url":null,"abstract":"Birkhoff normal forms are commonly used in order to ensure the so called \"effective stability\" in the neighborhood of elliptic equilibrium points for Hamiltonian systems. From a theoretical point of view, this means that the eventual diffusion can be bounded for time intervals that are exponentially large with respect to the inverse of the distance of the initial conditions from such equilibrium points. Here, we focus on an approach that is suitable for practical applications: we extend a rather classical scheme of estimates for both the Birkhoff normal forms to any finite order and their remainders. This is made for providing explicit lower bounds of the stability time (that are valid for initial conditions in a fixed open ball), by using a fully rigorous computer-assisted procedure. We apply our approach in two simple contexts that are widely studied in Celestial Mechanics: the Henon-Heiles model and the Circular Planar Restricted Three-Body Problem. In the latter case, we adapt our scheme of estimates for covering also the case of resonant Birkhoff normal forms and, in some concrete models about the motion of the Trojan asteroids, we show that it can be more advantageous with respect to the usual non-resonant ones.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89127094","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: 10

Hamiltonian control of magnetic field lines: Computer assisted results proving the existence of KAM barriers 磁力线的哈密顿控制:计算机辅助结果证明了KAM障碍的存在

IF 1

Journal of Computational Dynamics Pub Date : 2021-01-19 DOI: 10.3934/jcd.2022002

L. Valvo, U. Locatelli

引用次数: 8

Numerical preservation issues in stochastic dynamical systems by $ vartheta $-methods 随机动力系统数值保存问题的$ vartheta $-方法

IF 1

Journal of Computational Dynamics Pub Date : 2021-01-01 DOI: 10.3934/jcd.2021023

R. D'Ambrosio, S. Di Giovacchino

引用次数: 3

Analysis of the fractional descriptor discrete-time linear systems by the use of the shuffle algorithm 用shuffle算法分析分数阶广义离散线性系统