Article(id=1242120523036037917, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242120519928058647, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1273075200000, receivedDateStr=2010-05-06, revisedDate=1282579200000, revisedDateStr=2010-08-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1284307200000, onlineDateStr=2010-09-13, pubDate=1284307200000, pubDateStr=2010-09-13, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1284307200000, onlineIssueDateStr=2010-09-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774074210170, creator=sys-migrate, updateTime=1774074210170, updator=sys-migrate, issue=Issue{id=1242120519928058647, tenantId=1146029695717560320, journalId=1146031591421210625, year='2010', volume='28', issue='17', pageStart='3', pageEnd='140', issueExtLink='null', onlineDate='null', pubDate='1284307200000', pubDateStr='2010-09-13', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774074209431, creator='sys-migrate', updateTime=1774074209431, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=42, endPage=45, ext={EN=ArticleExt(id=1242120527058375478, articleId=1242120523036037917, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=Multiple Complex Attractors and Basins of Attraction in a Duffing System with Delayed Position Feedbacks, columnId=1242116080374710456, journalTitle=Science & Technology Review, columnName=Articles, runingTitle=null, highlight=null, articleAbstract=The main purpose of this paper is to investigate the complex dynamics that the time delay induces in a kind of single degree-of-freedom self exciting vibration systems with linear delayed position feedbacks. The mathematical model under consideration is a delayed Duffing system, which is obtained by applying linear time delayed position feedbacks to a van der Pol-Duffing oscillator. The Hopf bifurcation of the delayed system derived by time delay is studied qualitatively. And it is found quantitatively that the time delay can make the multiple quasi-periodic and chaotic motions coexisting in the controlled system. Then the quasi-periodic attractors and chaotic attractors and their basins of attraction under different values of time delay in the delayed system are also classified by the 4th Runge-Kutta approach and Monte Carlo method. It is shown that each boundary of the basin of attraction in the delayed system is smooth and not fractal even if the attractor is chaotic. This paper shows some potential applications for the further study of the mechanism of chaotic motions., authors=null, authorsList=null, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=XehMPRQ7efH44ZJPJzaL/g==, pdfFileSize=742141, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242120526144013012, articleId=1242120523036037917, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=时滞位移反馈Duffing方程的复杂吸引子及其吸引域, columnId=1146540929516700224, journalTitle=科技导报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=对时滞线性位移反馈引起的一类单自由度非线性自激振动系统的复杂动力学行为进行研究。所考虑的数学模型为van der Pol-Duffing振子系统加入线性时滞位移反馈而得到的时滞Duffing方程。定性分析了时滞引起的系统Hopf分岔，并通过定量研究发现时滞可引起系统的混沌运动与多种概周期运动共存现象。通过4阶Runge-Kutta法和Monte Carlo方法，划分了不同时滞量下的时滞系统的概周期吸引子和混沌吸引子及其吸引域，发现系统各吸引子吸引域的边界均光滑而不分形，尽管系统出现了混沌运动。研究结果对进一步研究混沌运动机制存在着潜在的应用价值。, authors=尚慧琳, authorsList=尚慧琳, authorCompany=上海应用技术学院机械工程学院，上海 200235, correspAuthors=null, authorNote=null, correspAuthorsNote=尚慧琳, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=qYQ3Amww9RI9ayOAvY/hOA==, pdfFileSize=742141, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null)}, authors=null, keywords=[Keyword(id=1242120524323689248, tenantId=1146029695717560320, journalId=1146031591421210625, articleId=1242120523036037917, language=CN, orderNo=1, keyword=时滞反馈), Keyword(id=1242120524403381025, 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