28318.兩類具有年齡結(jié)構(gòu)的n種群競(jìng)爭(zhēng)系統(tǒng)的最優(yōu)輸入率控制

1、天津師范大學(xué)碩士學(xué)位論文兩類具有年齡結(jié)構(gòu)的n種群競(jìng)爭(zhēng)系統(tǒng)的最優(yōu)輸入率控制姓名：王巍申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：趙春20100301Theoptimalinputtingratecontrolfortwoclassesofage卜dependeIltcompetingsystemofnspeciesAbstractThevalueofbiolo舀calresourceshasIongbeenrecogIlized，aIldm

2、oreaIldmorepeople’sattentionfoc峭0nitAsarenewabkresouroe，biolo百calresouroesno乞0nlyha、ree)(tremelyhigheconoIIlicv砒ue，butaLlsohaVeiIIlme瓣lrableV可uefbrecolo百caleIlv主ronmentThepr豁entsituationisthatbiol孵c以re80urc鶴arereducillgr

3、apidly姐dtheecolo舀calen訪ronmentalsoh嬲beendet砸oratedsharplyTheref撕e，toachievetheSustainabkdevel叩mentofbiolo百c砒r嗍1rces，itmustberationallyusedTheoptim8lcontrolproblemofpopulationdynamicssyst鋤studiespopulation’sdeVelopmentand

4、controlbymath哪a土icalmethods，aIlditisanacti、，efieldincontroltheoryAthomeandabroadmanyac孤拈micia璐trytheirbesttesearchtheoptimalcontrolproblemofpopulationdynamicssystemandobtaillalotofachievementsTakingintoauccountthereaLlit

5、ythattheree】(istmultiplepopulationsinthes鋤eenVironment，inthepapertheoptimalinputtingratecontrolproblemf6ra剛印enden七咖petingsystemofnspeciesisresearchedAccordingtothecontents，thispaperisdiVidediIltothreechapters：Inthefirstc

6、hapter，itintroduceStheba出gronndandsigni＆aIlce，themodelofpopulationdyn鋤icssystem，thepresentstudyofpopulationdyn鋤icssystema七h(yuǎn)omeandabroadandthepr印arativetheor灑1nthesecondch印ter，the0ptimalinputtingratecontr01problemf|0racla

7、ssofageIdependentcompetingsystemof扎speciesisdiscus鼬dBymeansofEl【eland’sVariationalprinciple，GronwaULemma，BellmanL啪ma，F(xiàn)砒ouLemma，theBanac魅艤edpointtheorem，conjugatedsystemandsoon，thee)cistenceanduniquenessoftheoptimalcontro

8、larepraven，furthermorethenecess∞7conditionoftheoptimalcon七rolproblemisobtainedbytheconceptionofnormalconeInthethirdchapter，itisabouttheoptimalinputtingra上econtrolprobl鋤fbraclassofagedependentcompetingsys乞emofnspecieSwith

9、di目沁sionThemodelofthecolljugatedsystemis百venandanalyzed，moreov盯thenecessaryconditionof叩timalcontrolproblemisdbtainedbytheconceptionofnormaLlconeKeywordsoptimalcontrol；competingsystem；叩timalinputtingrate；normalconetheorem