Deterministic and Stochastic Surrogate Models for a Slowly Driven Fast Oscillator

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-29 DOI:10.1137/23m1602176

Marcel Oliver, Marc A. Tiofack Kenfack

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引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1090-1107, June 2024.
Abstract.It has long been known that the excitation of fast motion in certain two-scale dynamical systems is linked to the singularity structure in complex time of the slow variables. We demonstrate that, in the context of a fast harmonic oscillator forced by one component of the Lorenz 1963 model, this principle can be used to construct time-discrete surrogate models by numerically extracting approximate locations and residues of complex poles via adaptive Antoulas–Anderson (AAA) rational interpolation and feeding this information into the known “connection formula” to compute the resulting fast amplitude. Despite small but nonnegligible local errors, the surrogate model maintains excellent accuracy over very long times. In addition, we observe that the long-time behavior of fast energy offers a continuous-time analogue of Gottwald and Melbourne’s 2004 “0–1 test for chaos”; that is, the asymptotic growth rate of the energy in the oscillator can discern whether or not the forcing function is chaotic.

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慢速驱动快速振荡器的确定性和随机替代模型

SIAM 应用动力系统期刊》第 23 卷第 2 期第 1090-1107 页，2024 年 6 月。摘要.众所周知，某些双尺度动力系统中快速运动的激发与慢变量在复时间内的奇异结构有关。我们证明，在由洛伦兹 1963 模型的一个分量强迫的快速谐振子中，可以利用这一原理构建时间离散的代用模型，方法是通过自适应安图拉斯-安德森（AAA）有理插值法数值提取复极点的近似位置和残差，并将这些信息输入已知的 "连接公式 "以计算所得到的快速振幅。尽管存在微小但不可忽略的局部误差，代用模型仍能在很长时间内保持极高的精度。此外，我们还观察到，快速能量的长期行为提供了 Gottwald 和 Melbourne 2004 年 "0-1 混沌测试 "的连续时间类比；也就是说，振荡器中能量的渐近增长率可以判别强迫函数是否是混沌的。

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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.