A general framework for validated continuation of periodic orbits in systems of polynomial ODEs

IF 1 Q3 Engineering Journal of Computational Dynamics Pub Date : 2021-01-01 DOI:10.3934/jcd.2021004

J. B. Berg, E. Queirolo

引用次数: 12

Abstract

In this paper a parametrized Newton-Kantorovich approach is applied to continuation of periodic orbits in arbitrary polynomial vector fields. This allows us to rigorously validate numerically computed branches of periodic solutions. We derive the estimates in full generality and present sample continuation proofs obtained using an implementation in Matlab. The presented approach is applicable to any polynomial vector field of any order and dimension. A variety of examples is presented to illustrate the efficacy of the method.

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多项式ode系统周期轨道验证延拓的一般框架

本文将参数化牛顿-坎托洛维奇方法应用于任意多项式向量场中周期轨道的延拓。这使我们能够严格地验证周期解的数值计算分支。我们得到了完全一般的估计，并给出了用Matlab实现得到的样本延拓证明。该方法适用于任何阶数和维数的多项式向量场。通过实例说明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.

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