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1、FuzzySetsandSystems158(2007)2339–2358www.elsevier.com/locate/fssAclassoflineardifferentialdynamicalsystemswithfuzzyinitialconditionJiupingXua,∗,ZhigaoLiaoa,b,ZhinengHuaaUncertaintyDecision-MakingLaboratory,SchoolofBusinessandAdministration,SichuanUniversity,Chengdu610065,PRChinabManagemen
2、tDepartment,GuangxiTechnologyUniversity,Liuzhou545006,PRChinaReceived17January2007;receivedinrevisedform13April2007;accepted20April2007Availableonline22April2007AbstractThispaperinvestigateslinearfirst-orderfuzzydifferentialdynamicalsystemswheretheinitialconditionisdescribedbyafuzzynumber.W
3、euseacomplexnumberrepresentationofthe-levelsetsofthefuzzysystemandprovetheoremsthatprovidethesolutionsundersuchrepresentation,whichisapplicabletopracticalcomputationsandalsohassomeimplicationsfortheory.Thenthepapershowssomepropertiesofthetwo-dimensionaldynamicalsystems,andtheirphaseportra
4、itsaredescribedbymeansofexamples.Theremaybeasignificantdifferencebetweenthesolutionsaccordingtowhetherthematrixisnonnegativeornot;finally,thepaperpointsoutfutureresearchonthefuzzydynamicalsystems.©2007ElsevierB.V.Allrightsreserved.Keywords:Fuzzydifferentialequation;Fuzzydynamicalsystems;Init
5、ialvalueoffuzzynumber1.IntroductionSincetheconceptoffuzzysetandthecorrespondingfuzzyset-theoreticoperationswasintroducedbyZadeh[46],enormousresearchworkshavebeendedicatedondevelopmentofvariousaspectsofthetheoryandapplicationsoffuzzysets.Moreover,inviewofthedevelopmentofthecalculusforfuzzyf
6、unctions,theinvestigationoffuzzydifferentialequations(FDE)hasbeeninitiated[23,40]andhasnaturallyformedoneofthemostimportantareasinfuzzymathematics.Forfurtherinvestigation,thefuzzydynamicalsystemsbasedonFDEarealsowidelyappliedtofuzzycontrolsystems[9],bifurcationsoffuzzynonlineardynamicalsys
7、tems[20],artificialsystem[37]andmanyotherfields.However,linearfirst-orderFDEareoneofthesimplestFDEwithgreatapplicability.Althoughtheformofsuchanequationisverysimple,itraisesmanyproblemssinceunderdifferentFDEconcepts,thebehaviorofthesolutionsisdifferent[7,31].Amon
