2078.兩類生物種群反應(yīng)擴(kuò)散模型的動力學(xué)研究

1、學(xué)校代碼：10270分類號:0175.2學(xué)號：142200607碩士學(xué)位論文論文題目兩類生物種群反應(yīng)擴(kuò)散模型的動力學(xué)研究學(xué)院數(shù)理學(xué)院專業(yè)基礎(chǔ)數(shù)學(xué)研究方向偏微分方程研究生姓名王高雅指導(dǎo)教師徐本龍教授完成日期2017年3月28日AbstractDiffusionandspatialenvironmenthaveasignificantinfluenceonthetotalspeciesevenrelatedtothesurvivalofth

2、especies.ThefirstmodelintroducedinthispaperisabouttheclassicalLotkaVolterracompetitiondiffusionsystem.Wemainlystudythecombinedeffectsofdiffusionspatialenvironmentandcompetitionabilityonthemodel.Infactthecompetitionabilit

3、yofspecieswillalsochangeunderdifferentenvironments.Sospatialrelativityismergedintocompetitionability.Weaimatgeneralizingtheconstantcompetitionabilitytononconstantabilityinpreviousmodels.Ourresultsconfirmthatunderthecondi

4、tionofweakcompetitionassumethatatleastoneofthespatialenvironmentishomogeneousthespeciescanalwaysovercometheotherspecieswhentheinfimumofthecompetitionabilityreachedacriticalvalueWhenspatialheterogeneitywithtwospeciesisinc

5、ludedinthemodelifthespeciescancompletelyprevailoveritscompetitortheinfimumofthecompetitionabilityreachedacriticalvalueisneededandalsoneedsitscompetitorislesscompetitivethanacriticalvalue.Theflowofpeoplehaveagreatimpacton

6、thedisappearanceandspreadofinfectiousdiseases.Inadditiontimelytreatmentcontributestopreventingthespreadofdiseasesbutthetreatmentofaninfectiousdiseaseislimitedineachregion.Thereforediffusionandthesaturatedtreatmentareintr

7、oducedintothismodel.Basedonthisthesecondmodelintroducedinthispaperisthereactiondiffusionequationwithsaturatedtreatmentundertheheterogeneousspace.Throughanalysiswefinallygettheexistinguniquenessofthediseasefreeequilibrium

8、.Andwealsogetthethresholdoftheepidemicsthroughtheprincipaleigenvaluewhichisdefinedasbasicreproductionnumberusedfordiscussingthestabilityofequilibriumsolution.ItshowsthatifRo1thediseasefreeequilibriumisunstableandthereisa