1、西北師范大學碩士學位論文含兩種競爭食餌和兩種捕食者的捕食者食餌模型的定性分析姓名：王永斌申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：伏升茂200906AbstractInthispaperglobalbehaviofsolutionsfthefollowingpredatpreymodelwithtwopredatstwocompetitivepreysisinvestigated?????????????????????????????

2、??????????????u1t=?(d1u1a11u21)u1(1?u1?αu2?ε1u3?ε2u4)x∈?t0u2t=?(d2u2a22u22)u2(1?βu1?u2?γ1u3?γ2u4)x∈?t0u3t=?(d3u3a31u1u3a32u2u3a33u23)u3(?1nε1u1nγ1u2)x∈?t0u4t=?(d4u4a41u1u4a42u2u4a44u24)u4(?1nε2u1nγ2u2)x∈?t0?ηu1=?ηu2=?ηu3

3、=?ηu4=0x∈??t0ui(x0)=ui0(i=1234)x∈?(1)where?isaboundedregioninRNwithsmoothboundary??ηdenotestheoutwardunitnmalvectontheboundary??.Thepaperisdividedintothreesections.InSection1thestabilityofnonnegativeequilibriumpointsfthe

4、model(1)ofODEtypeisdiscussed.InSection2theunifmboundednessofglobalsolutionsthestabilityofthenonnegativeequilibriumpointsfthemodeloftheweaklycoupledreactiondiffusiontypeareconsidered.InSection3usingmethodofenergyestimates

5、GagliardoNirenbergtypeinequalitiestheexistenceunifmboundednessofnonnegativeglobalsolutionsfthemodel(1)ofcrossdiffusiontypeareprovedwhenthespacedimensionisone.Keywds:Diffusionselfdiffusioncrossdiffusionpositiveequilibrium