资源描述：
《Springer.Ausloos.M.Dirickx.M.(eds.).The.logistic.map.and.the.route.to.chaos.from.the.beginnings.to.modern.applications.(UCS.Springer.2006)(ISBN.3540283668)(400s)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、ChaoticGrowthwiththeLogisticModelofP.-F.VerhulstHugoPastijnDepartmentofMathematics,RoyalMilitaryAcademyB-1000Brussels,BelgiumHugo.Pastijn@rma.ac.beSummary.Pierre-Fran¸coisVerhulstwasborn200yearsago.Afterashortbiogra-phyofP.-F.VerhulstinwhichthelinkwiththeRoyalMilitaryAcademyinBrusselsisemphasized,t
2、heearlyhistoryoftheso-called“LogisticModel”isdescribed.Therelationshipwitholdergrowthmodelsisdiscussed,andthemotivationofVerhulsttointroducedifferentkindsoflimitedgrowthmodelsispresented.The(re-)discoveryofthechaoticbehaviourofthediscreteversionofthislogisticmodelinthelatepre-viouscenturyisreminded.
3、Weconcludebyreferringtosomegeneralizationsofthelogisticmodel,whichwereusedtodescribegrowthanddiffusionprocessesinthecontextoftechnologicalinnovation,andforwhichtheauthorstudiedthechaoticbehaviourbymeansofaseriesofcomputerexperiments,performedintheeightiesoflastcenturybymeansofthethenemerging“micro-c
4、omputer”technology.1P.-F.VerhulstandtheRoyalMilitaryAcademyinBrusselsIntheyear1844,attheageof40,whenPierre-Fran¸coisVerhulstonNovember30presentedhiscontributiontothe“M´emoiresdel’Acad´emie”oftheyoungBelgiannation,apaperwhichwaspublishedthenextyearin“tomeXVIII”withthetitle:“Recherchesmath´ematiquess
5、urlaloid’accroissementdelapopulation”(mathematicalinvestigationsofthelawofpopulationgrowth),hedidcertainlynotknowthathisworkwouldbethestartingpointforfur-therresearchbyRaymondPearlandLowellJ.Reed[10,11],bythefamousA.-J.Lotka[8]andindependentlybyVolterra[16]andlaterbyV.A.Kos-titzin[5],inthefieldsofma
6、thematicalbiology,biometry,anddemography.ItwasintheseM´emoiresthatheintroducedagrowthmodelforaclosedpopulation(noimmigration,noemigration)facingalivingenvironmentwithlimitedresourcesforthesubsistenceofitsmembers.ThepurposewastopredictthedemographicevolutionoftheyoungBelgiansociety,andtoan-swerthequ
7、estionaboutthemaximumpopulationsizesustainablewiththeselimitedresources.Hecertainlydidnotexpectthatmorethanonecenturylater,thestudyofadiscreteversionofthismodelwouldgiverisetoanewfieldinscience:chaostheory.B
