{"title":"随机常微分方程的均方lyapunov盆地构造","authors":"Florian Rupp","doi":"10.3934/jcd.2022024","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Construction of mean-square Lyapunov-basins for random ordinary differential equations\",\"authors\":\"Florian Rupp\",\"doi\":\"10.3934/jcd.2022024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/jcd.2022024\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jcd.2022024","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.
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