27882.一類(lèi)食餌捕食系統(tǒng)的turing不穩(wěn)定性和模式生成

1、蘭州大學(xué)碩士學(xué)位論文一類(lèi)食餌捕食系統(tǒng)的Turing不穩(wěn)定性和模式生成姓名：王玉霞申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：數(shù)學(xué)、應(yīng)用數(shù)學(xué)指導(dǎo)教師：李萬(wàn)同20100501蘭州大學(xué)碩士學(xué)位論文AbstractAsoneoftheimportanttoolstodescribetheinteractionbetweenthespeciesofecologicalsystem，thepreypredatormodelcangeneraterichdynamics

2、anditsdynamicsbehaviordependsmainlyonthepropertiesofitssteadystatesInthisthesis，wearemainlyconcernedabouttheTuringinstabilityandtheexistenceandnonexistenceofnonconstantpositivesteadystates，thatispatterns，ofaclassofratiod

3、ependentHollingTannerpreypredatorsystemwithdiffusionandcrossdiffusionInChapter2，wechangethepreypredatorsystemwithdiffusionandcrossdiffusionintotheotherequivalentsystembythemethodoftransformationvariableanddiscussthestabi

4、litiesofthetwoequilibriabytheLinearizationmethod；thecorrespondingordinarysystemisalsoconsidered；finally，weanalyzetheeffectsofthecrossdiffusionandselfdiffusiontothestabilitiesoftheequilibriaInChapter3，aprioriestimatesfort

5、hepositivesolutionsofthecorrespondingellipticproblemarefirstlyobtainedbythemaximumprim’ipleandHarnackinequality；thenwegivesomesufficientconditionsforthenonexistenceofnonconstantpositivesteadystatesbyenergyintegral；finall

6、yweobtaintheexistenceofnonconstantpositivesteadystatesbyLeraySchaudertheoryOurresultshowsthatthecrossdiffusionandselfdiffusionofthepreyarebeneficialtotheconstantspreadsofthespecies；whenthebirthrateofthepreyisverylarge，th

7、ecrossdiffusionandselfdiffusionofthepredatorarealsobeneficialtotheconstantspreadsofthespecies；however，whenthebirthrateofthepreyisincertainranges，thecrossdiffusionandselfdiffusionofthepredatormayleadtoTuringinstabilityMor

8、eover，ourresultshowsthateventhoughtheuniqueconstantpositivesteadystateisgloballyasymptoticallystableforthesystemwithoutcrossdiffusion，nonconstantpositivesteadystatecanstillexistduetotheemergenceofthecrossdiffusionforthes