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

1、蘭州大學碩士學位論文一類食餌捕食系統(tǒng)的Turing不穩(wěn)定性和模式生成姓名：王玉霞申請學位級別：碩士專業(yè)：數學、應用數學指導教師：李萬同20100501蘭州大學碩士學位論文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