含兩種競(jìng)爭(zhēng)食餌和兩種捕食者的捕食者-食餌模型的定性分析.pdf

1、西北師范大學(xué)碩士學(xué)位論文含兩種競(jìng)爭(zhēng)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(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)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