Quasi-periodic Response Solution to Scalar State-Dependent Delay Differential Equation with Degenerate Equilibrium

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-23 DOI:10.1007/s12346-024-01104-x

Xiaolong He, Feng Jin, Yongli Song

引用次数: 0

Abstract

We consider the state-dependent delay differential equation (SDDE) obtained by adding delayed perturbation to a one-dimensional ODE with a degenerate equilibrium. We prove the existence of the response solution of the equation, i.e., the quasi-periodic solution with the same frequency as the forcing. The novelty of our paper is to provide a concrete example to discuss the smoothness issues of SDDE, especially showing the analyticity of quasi-periodic solutions in some probability sense.

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具有退化平衡的标量状态相关延迟微分方程的准周期响应解

我们考虑了在具有退化平衡的一维 ODE 中加入延迟扰动而得到的状态依赖延迟微分方程（SDE）。我们证明了方程响应解的存在，即与强迫频率相同的准周期解。本文的新颖之处在于提供了一个具体的例子来讨论 SDDE 的平稳性问题，特别是展示了准周期解在某种概率意义上的可分析性。

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

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.