随机常微分方程的均方lyapunov盆地构造

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/jcd.2022024

Florian Rupp

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引用次数: 0

摘要

我们提出了一个简单的盆地搜索算法来确定一个合适的大的均方李雅普诺夫函数水平集，该水平集对应于随机常微分方程(RODE)的路径均衡解的线性化。噪声强度对RODEs解的行为与相应的确定性系统的相似程度起着至关重要的作用。在这方面，盆地搜索算法还允许在数值上估计噪声强度线性化均方渐近稳定性。

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Construction of mean-square Lyapunov-basins for random ordinary differential equations

We propose a straightforward basin search algorithm to determine a suitably large level set of the mean-square Lyapunov-function that corresponds to the linearization about an path-wise equilibrium solution of a random ordinary differential equation (RODE). Noise intensity plays a crucial role for how similar the behavior of solutions of RODEs is compared to the corresponding deterministic system. In this regards, the basin search algorithm also allows to numerically estimate up to which noise intensities linearized mean-square asymptotic stability remains.

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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.