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1、Eur.Phys.J.B62,247–255(2008)THEEUROPEANDOI:10.1140/epjb/e2008-00139-4PHYSICALJOURNALBTheeffectoftheforget-remembermechanismonspreadingJ.Gu1,W.Li1,2,3,a,andX.Cai11ComplexityScienceCenter,andInstituteofParticlePhysics,Hua-ZhongNormalUniversity,Wuhan430079,China2Ma
2、x-Planck-InstituteforMathematicsintheSciences,Inselstr.22,04103Leipzig,Germany3SantaFeInstitute,1399HydeParkRd,NM87501,USAReceived18October2007/Receivedinfinalform13March2008Publishedonline4April2008–cEDPSciences,Societ`aItalianadiFisica,Springer-Verlag2008Abst
3、ract.Weintroduceanewmechanism—theforget-remembermechanismintothespreadingprocess.Equippedwithsuchamechanismanindividualispronetoforgetthe“message”receivedandremembertheoneforgotten,namelyswitchinghisstatebetweenactive(withmessage)andinactive(withoutmessage).The
4、probabilityofstateswitchisgovernedbylinearorexponentialforget-rememberfunctionsofhistorytimewhichismeasuredbythetimeelapsedsincethemostrecentstatechange.Ourextensivesimulationsrevealthattheforget-remembermechanismhassignificanteffectsonthesaturationofmessagesprea
5、ding,andmayevenleadtoaterminationofspreadingundercertainconditions.Thisfindingmayshedsomelightonhowtocontrolthespreadingofepidemics.Itisfoundthatpercolation-likephasetransitionscanoccur.Byinvestigatingthepropertiesofclusters,formedbyconnected,activeindividuals,w
6、emaybeabletojustifytheexistenceofsuchphasetransitions.PACS.89.75.FbStructuresandorganizationincomplexsystems–89.70.+cInformationtheoryandcommunicationtheory–89.75.HcNetworksandgenealogicaltrees1Introductionstates,havingamessageornot.Ifhehasamessage,anindividual
7、isoptedtotransmititornot;otherwise,hecanThespreadingprocess,throughwhichnews,rumorsandacceptordeclineamessagefromothers.Altogethertherediseases,etc.,canbetransmitted,isubiquitousinnaturecanbefourpossiblestatesforeachindividual,whichare[1–3].Recentresearchalongt
8、histopichasbeenlargelyfo-nottotallyincludedbymostmodels.Forexample,theSIScusedonthemodellingofepidemics[4–10]anditsinter-modelforepidemicsassumesthateachindividualiseitherpl
