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1、MoredocumentsanddatumdownloadwebsiteLuZhenbo'sBlog:blog.sina.com.cn/luzhenbo2Communication&Cooperation:luzhenbo@yahoo.com.cnApracticalmethodforcalculatinglargestLyapunovexponentsfromsmalldatasetsMichaelT.Rosenstein,JamesJ.Collins,andCarloJ.DeLucaNeuroMuscularResearchCenterandDepa
2、rtmentofBiomedicalEngineering,BostonUniversity,44CummingtonStreet,Boston,MA02215,USANovember20,1992RunningTitle:LyapunovexponentsfromsmalldatasetsKeyWords:chaos,Lyapunovexponents,timeseriesanalysisPACScodes:05.45.+b,02.50.+s,02.60.+yCorrespondingAuthor:MichaelT.RosensteinNeuroMus
3、cularResearchCenterBostonUniversity44CummingtonStreetBoston,MA02215USATelephone:(617)353-9757Fax:(617)353-5737Internet:ROSENSTEIN@BUNMRG.BU.EDUMoredocumentsanddatumdownloadwebsiteLuZhenbo'sBlog:blog.sina.com.cn/luzhenbo2Communication&Cooperation:luzhenbo@yahoo.com.cnAbstractDetec
4、tingthepresenceofchaosinadynamicalsystemisanimportantproblemthatissolvedbymeasuringthelargestLyapunovexponent.Lyapunovexponentsquantifytheexponentialdivergenceofinitiallyclosestate-spacetrajectoriesandestimatetheamountofchaosinasystem.WepresentanewmethodforcalculatingthelargestLy
5、apunovexponentfromanexperimentaltimeseries.ThemethodfollowsdirectlyfromthedefinitionofthelargestLyapunovexponentandisaccuratebecauseittakesadvantageofalltheavailabledata.Weshowthatthealgorithmisfast,easytoimplement,androbusttochangesinthefollowingquantities:embeddingdimension,siz
6、eofdataset,reconstructiondelay,andnoiselevel.Furthermore,onemayusethealgorithmtocalculatesimultaneouslythecorrelationdimension.Thus,onesequenceofcomputationswillyieldanestimateofboththelevelofchaosandthesystemcomplexity.MoredocumentsanddatumdownloadwebsiteLuZhenbo'sBlog:blog.sina
7、.com.cn/luzhenbo2Communication&Cooperation:luzhenbo@yahoo.com.cn1.IntroductionOverthepastdecade,distinguishingdeterministicchaosfromnoisehasbecomeanimportantprobleminmanydiversefields,e.g.,physiology[18],economics[11].Thisisdue,inpart,totheavailabilityofnumericalalgorithmsforquan
8、tifyingchaosusingexperimentaltimeseries.
