漸近周期的Logistic方程.pdf

1、東北師范大學(xué)碩士學(xué)位論文漸近周期的Logistic方程姓名：魏鳳英申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王克2003.5.1AbstractItwasknowntoallthatPFVerhulstandALJQueteletwhoproposedtheclassicalLogisticmodelin1838，andthenTGHallamandCEClarkmendedtheclassicalLogisticmodelin1993

2、Andafterthat，manyexpertsandscholarshadstudiedtheintrinsicgrowthrateandcarryingcapability，whichweretwoimportantindexesaboutLogisticequationNevertheless，theLogisticequationWasnotfarfromprecise，butafterahunderdyears，itwasst

3、illanimportantandwidelyappliedmodelinecologyEspeciallyinrecentscoreyears，inautonomousandnonautonolnoussystems，theneutral，finitedelay，infinitedelaydiffusive，discrete，discretedelaygeneralized，differenceandotherstylemodelsw

4、erediscussedonoptimalharvesting，osiUation，stability，globalstability，andotherasmptoticbehaviorsofLogisticequationReferenceweresearchedin[t6】，【10181，1203q，【341TheperiodicandalmostperiodicfunctionLogisticequation，whicharewi

5、delystudiedrecentlytheresultsabouttheabovearefoundOnmanykindsofmagazinesThearticle【l】1hasauniqueperiodicsolution，whichisgloballyasmptoticstableperiodicsolutionwithperiodTTheexpressionisobtainedin[1]Andwegetglobalattracti

6、vityinthearticle【2】，f3】Withintheauthor’Sknowledge，recentlytheresultsarefewabouttheasmptoticLogisticequationThearticles，[32—33】discusstheLogisticequation，inwhichthetwoimportantindexesr(t)andK(t)arenotonlydependentont，buta

7、lsoasmptoticallytendtoperiodicfunctionInarticlef14]，aboutthethreespeciescompetitionsystem，undermoderateconditions，alla3mptoticperiodicsolutionstendtoauniqueperiodicsolutiononagivensystemTherefore，weneednmreconcretefuncti

8、ontobetterdiscribethevariationofsomebiologicalDopulationsinourrealworldThetwoimportantindexesr(t)andK(t)ofLo‘gisticequationareasmptoticperiodicfunction，anddiscussedbyauthorTheasmptoticsolutionoftheasmptoticperiodicLogist

9、icfunctionisobtainedSomegoodproperties，suchas，existence，uniqueness，globalattractivityarediscussedThepropertiesofasmptoticperiodicfunctionandtheasmptoticperiodicfunctionspacearestudied，accordingly，wehave，theasmptoticperio