{"title":"Periodic and Quasi-periodic Responses of Van der Pol–Mathieu System Subject to Various Excitations","authors":"Q. Fan, A. Leung, Y. Lee","doi":"10.1515/ijnsns-2015-0012","DOIUrl":null,"url":null,"abstract":"Abstract This paper addresses the steady-state periodic and quasi-periodic responses of van der Pol–Mathieu system subject to three excitations (i.e., self, parametric and external excitations). Method of multiple scales and double perturbation technique are employed to study the original system. The cases of van der Pol–Mathieu oscillator with and without external excitation are considered, and periodic and quasi-periodic solutions are obtained and discussed. In the parametric study, the effects of various parameters and self, parametric and external excitations on the system behaviors are studied. Results from method of multiple scales well agree with those from numerical method.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijnsns-2015-0012","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1515/ijnsns-2015-0012","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 12
Abstract
Abstract This paper addresses the steady-state periodic and quasi-periodic responses of van der Pol–Mathieu system subject to three excitations (i.e., self, parametric and external excitations). Method of multiple scales and double perturbation technique are employed to study the original system. The cases of van der Pol–Mathieu oscillator with and without external excitation are considered, and periodic and quasi-periodic solutions are obtained and discussed. In the parametric study, the effects of various parameters and self, parametric and external excitations on the system behaviors are studied. Results from method of multiple scales well agree with those from numerical method.
本文研究了van der Pol-Mathieu系统在三种激励(即自激励、参数激励和外部激励)下的稳态周期和准周期响应。采用多尺度法和双摄动技术对原系统进行了研究。考虑了有和没有外部激励的范德波尔-马修振子的情况，得到并讨论了周期解和拟周期解。在参数化研究中，研究了各种参数以及自激励、参数激励和外部激励对系统行为的影响。多尺度法计算结果与数值法计算结果吻合较好。
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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