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1、1¦Z-"'"'^*:f^NONLINEARDYNAMICSANDCHAOSWithApplicationstoPhysics,Biology,Chemistry,andEngineeringSTEVENH.STROGATZAdvancedBookProgramPERSEUSBOOKSReading,MassachusettsManyofthedesignationsusedbymanufacturersandsellerstodistinguishtheirproductsareclaimedastrademarks.Wherethosedesignationsappeari
2、nthisbookandPerseusBookswasawareofatrademarkclaim,thedesignationshavebeenprintedininitialcapitalletters.LibraryofCongressCataloging-in-PublicationDataStrogatz,StevenH.(StevenHenry)NonUneardynamicsandchaos:withapplicationstophysics,biology,chemistry,andengineering/StevenH.Strogatz.p.cm.Include
3、sbibliographicalreferencesandindex.ISBN0-201-54344-31.Chaoticbehaviorinsystems.2.Dynamics.3.Nonlineartheories.I.Title.Q172.5.C45S767199450r.r85—dc2093-6166CIPCopyright©1994byPerseusBooksPublishing,L.L.C.PerseusBooksisamemberofthePerseusBooksGroup.Allrightsreserved.Nopartofthispublicationmaybe
4、reproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.PublishedsimultaneouslyinCanada.CoverdesignbyLynneReedTextdesignbyJoyceC.WestonSeti
5、n10-pointTimesbyCompset,Inc.Coverartisacomputer-generatedpictureofascrollring,fromStrogatzA985)withpermission.Scrollringsareself-sustainingsourcesofwavesindiverseexcitablemedia,includingheartmuscle,neuraltissue,andexcitablechemicalreactions(WinfreeandStrogatz1984,Winfree1987b).101112131415—MA
6、—0302010099PerseusBooksareavailableforspecialdiscountsforbulkpurchasesintheU.S.bycorporations,institutions,andotherorganizations.Formoreinformation,pleasecontacttheSpecialMarketsDepartmentatHarperCollinsPublishers,10East53rdStreet,NewYork,NY10022,orcall1-212-207-7528.CONTENTSPrefaceix1.Overvi
7、ew11.0Chaos,Fractals,andDynamics11.1CapsuleHistoryofDynamics21.2TheImportanceofBeingNonlinear41.3ADynamicalViewoftheWorld9PartI.One-DimensionalFlovs^s2.FlowsontheLine152.0Introduction152.1AGeometricWayofThinking162.2FixedPointsandStability182
