多项式ode系统周期轨道验证延拓的一般框架

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.3934/jcd.2021004

J. B. Berg, E. Queirolo

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引用次数: 12

摘要

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

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.