A class of linear differential dynamical systems with fuzzy matrices11111.pdf

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1、J.Math.Anal.Appl.368(2010)54–68ContentslistsavailableatScienceDirectJournalofMathematicalAnalysisandApplicationswww.elsevier.com/locate/jmaaAclassoflineardifferentialdynamicalsystemswithfuzzymatrices✩JiupingXua,∗,ZhigaoLiaoa,b,JuanJ.NietocaUncertaintyDecision-MakingLaboratory,SchoolofBusinessandAdmi

2、nistration,SichuanUniversity,Chengdu610064,PRChinabManagementDepartment,GuangxiTechnologyUniversity,Liuzhou545006,PRChinacDepartamentodeAnálisisMatemático,FacultaddeMatemáticas,UniversidaddeSantiagodeCompostela,15782,SpainarticleinfoabstractArticlehistory:Thispaperinvestigatesthefirstorderlinearfuzzy

3、differentialdynamicalsystemswithReceived25November2008fuzzymatrices.Weuseacomplexnumberrepresentationoftheα-levelsetsofthefuzzyAvailableonline4January2010system,andobtainthesolutionbyemployingsuchrepresentation.ItisapplicabletoSubmittedbyC.E.Waynepracticalcomputationsandhasalsosomeimplicationsforthe

4、theoryoffuzzydifferentialequations.Wethenpresentsomepropertiesofthe2-dimensionaldynamicalsystemsandKeywords:theirphaseportraits.SomeexamplesareconsideredtoshowtherichnessofthetheoryFuzzydifferentialequationFuzzydynamicalsystemsandwecanclearlyseethatnewbehaviorsappear.WefinallypresentsomeconclusionsFu

5、zzymatricesandnewdirectionsforfurtherresearchintheareaoffuzzydynamicalsystems.©2009ElsevierInc.Allrightsreserved.1.IntroductionSincetheconceptoffuzzysetandthecorrespondingfuzzyoperationswasintroducedbyZadeh[31],anenormousefforthasbeendedicatedtothedevelopmentofvariousaspectsofthetheoryandapplication

6、soffuzzysystems,inparticulartothetheoryofdifferentialequationswithuncertainty.Theusageoffuzzydifferentialequations(FDE)hasbeenanaturalwaytomodeldynamicalsystemsunderpossibilisticuncertainty[1,3,6,8,14,15,17,18,20,24,25,29,30].Thefuzzydynamicalsystemsbasedonfuzzydifferentialequationsarealsowidelyappl

7、iedtofuzzycontrolsystems[2],bifurcationsoffuzzynonlineardynamicalsystems[12]andmanyotherfields.FuzzydifferentialequationswerefirstformulatedbyKaleva[13]andSeikkala[26].KalevastudiedtheCauchyproblemoffuz