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1、J.FranklinInst.Vol.334B,No.5/6,pp.759792,1997~)Pergamonr@1997TheFranklinInstitutePII:S0016--0032(97)00032-XPublishedbyElsevierScienceLtdPrintedinGreatBritain0016~0032/97$17.00+0.00VisionsofSynergeticsbyHERMANNHAKENInstituteforTheoreticalPhysicsandSynergetics,Pfaffenwaldring57/4,D-70550,
2、Stuttgart,Germany(Receivedinfinalform1February1997,"accepted26February1997)ABSTRACT:SynergeticsisaninterdisciplinaryfieMofresearch.Itdealswit£opensystemsthatarecomposedofmanyindividualpartswhichinteractwitheachotherandcanformspatial,temporal,orfunctionalstructuresbvself-organization.The
3、researchgoalofsynergeticsisthree-fold:(1)aretheregeneralprinciplesofself-organization?(2)arethereanalogiesinthebehaviorofself-organizin9systems?(3)cannewdevicesbeconstructedbecauseoftheresults(l)and(2)?Fromamathematicalpointofview,synergeticsdealswithnonlinearpartialstochasticdifferenti
4、alequationsandstudiestheirsolutionsclosetothosepointswherethesolutionschangetheirbehaviorqualitatively.Aswillbeshowninthisarticle,synergeticsinitspresentformisbasedontheconceptsofstabilityandinstability,controlparameters,orderparametersandtheslavingprinciple.Theslavingprincipleallowsone
5、tocompresstheinformationthatisnecessarytodescribecomplexsystemsintoafeworderparameters.Thisispossibleifsystemsareclosetotheirinstabilitypoints,butitappearsthattheorderparameterconceptisalsoapplicabletosituationsawayfromsuchinstabilities.Attheleveloftheorderparameterequations,profoundana
6、logiesbetweenotherwisequitedifferentsystemsbecomevisible.Thisallowsonetorealizethesameprocess(forinstance,dealingwithinformation)onquitedifferentmaterialsubstrates.Theorderparameterconceptandtheslavingprincipleareexplainedandtheirextensiontodiscretenoisymapsandtodelayequationsaremention
7、ed.Theseresultscanbeappliedtopatternformationinfluids,lasers,semiconductors,plasmasandotherfields.Asectionisdevotedtotheanalysisofspatio-temporalpatternsintermsoforderparametersandtheslavingprinciple.Itisshownhowtheconceptsofsynergeticscanbeutilizedtodeviseanewtypeofcomputerfor
