混沌和超混沌系统的模型生成及应用研究

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1、AbstractAbstractTherealworldisnonlinear．Ifhumanbeingswanttoinvestigatethenature11101"@clearly,itisnecessarytostudythecomplexnonlinearsystem．Chaos，whichisadeterministicsystemwithrandombehaviors，existsintheworldandisoneoftheimportantresearchfieldsofnonlinearsystems．Withthecont

2、inualendeavorforthepastfortyyears，chaostheoryhasobtainedlotsofsubstantialresultsandalreadybeenappliedinsomefieldssuchascommunicationandinformationprocess．Atpresent,itisnotdifficulttoconstructageneralchaoticsystemwiththeaidofcomputer．Therearenomaturetheoreticmethodstogenerate

3、specialchaoticsystems，forexampleonesystemwithacomplexattractorbuthavingaverysimplealgebraicform．ItisalsodifficulttoconstnletIleWhyperchaos．ThemainmethodistocalculatetheLyapunovexponentsbynumericalsimulationsanddecidewhetheritishyperchaoticornot．Thepaperintroducesthedevelopme

4、ntofchaosatfirst,andthensummarizesthebasicknowledgeofdynamicalsystemsanddescribesseinemethodsfornumericalanalysisofchaosindetails．Basedonthecurrentresearches，generatingspecialchaoticandhyperchaoticsystemsarestudiedinthispaper．Atlast,weapplythechaoticsysteminthemissile’Smaneu

5、vering,andthanverifythevalidityofthismethodbysimulating．Themainworksa∞asfollows：1．Anewsmooththree-dimensionalquadraticautonomoussystemisreported．Thenewsystemisabletogenerateasinglethreewings01"fourwingsattractor．Funhcmnore，therearetwodifferentattractorsexistinginthesystemwit

6、hdifferentinitialvalues．AndthetwoaRraetorsCanbothbechaotic，onechaotictheotherperiodic，andbothbeperiodic．2．Twonewhyperchaoticsystemsareproposed．Onesystemhasonlyoneequilibriumandtheotherhasthreeones．Thetwosystemsarebothfour-dimensionalquadraticmodifiedfromtheLorenzsystem．Theya

7、rebothhyperchaoficwhenparametervariesinalargerange，andtheyhavetwobigpositiveLyapunovexponents．Thenovelhyperchaoticsystemcanbeappliedinengineeringwithgoodprospectintheory．II3．Applythechaotictimeseriesintothemissile’Smaneuvering．Theexpected媳jectoryofmissileisunpredictable．Cons

8、ideringthepropertiesofchaos，wemixedthechaotictimeseriesintothereferencesign