捕食被捕食反應(yīng)擴(kuò)散模型的斑圖與行波解.pdf

1、中北大學(xué)碩士學(xué)位論文捕食被捕食反應(yīng)擴(kuò)散模型的斑圖與行波解姓名：申紅霞申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：靳禎20080531中北大學(xué)學(xué)位論文ABSTRACTRecentlyspatialdynamicbehaviorsareconcernedvastlyinpredatorpreysystemsInthispaper，wemajIllyinvestigatetheturingpatternstructuresandtravelin

2、gwavesolutionsofspatialextendedpredatorpreysystemsInchapter2，thepatternformationofthereactiondiffusionsystembasedonclassicalBazykinmodelinspatialtwodimensionaldomainisresearchedwederivetheconditionsforturinginstabilityin

3、detailandobtaintheturingspaceinwhichthespatialsystemcanemergeturingpatternFurthermore，wesimulatethepatternstructureusingtheperiodicalboundaryconditionOurresult甚showthattheBazykinsystemstabilizestoastriplikepatternstructu

4、rewhendiffusionispresentInchapter3，thepatternstructuresofthespatiallyextendedHoUingTannermodelareinvestigatedBylinearstabilityandbifurcationanalysis，wepresentthedispersionrelationdiagramsandthefourdifferentTaringspacesCh

5、oosingappropriateparametervaluesinthesespaces，weobtainrichpatternstructuresindifferentTuringregions，whicharespot，stripeandspotcoexistpatternstructuresand80OilFurthermore，westudytheTuringHopfbifurcationandalsopresentlabyr

6、inthinepatternsintherelatedregionFinallywediscussthechoiceproblemoftheparameter口andfindthatthesepatternscanemergeonlyifthehalfsaturationismuchsmallerthanthecarryingcapacity’Inchapter4，theexistenceoftravelingwavesolutions

7、fortworeactiondiffusionsystems，whicharebasedonthediffusiveHollingTannermodelforpredatorandpreyinteractions，isestablishedFromdynamic，thetravelingwavesolutionisequivalentto8heteroclinicorbitin3dimensionalphasespaceTheproof

8、ofexistenceUSesWazewski’STheorem，theStableManifoldTheorem，andLaSalle’sInvariancePrincipleWealsodiscusssomepossiblebiologicalimplicationsoftheexistenceofthesewavesKeywords：Reactiondiffusion，HollingTannermodel，Dispersionre