48282.關于一類污染治理的單種群模型的數(shù)學研究

1、遼寧師范大學碩士學位論文關于一類污染治理的單種群模型的數(shù)學研究姓名：欒施申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：劉兵201204關于一類污染治理的單種群模型的數(shù)學研究MathematicalStudyonaSingleSpeciesModelwithPollutionTreatmentAbstract蚴坊eglobalizationofeconomyandtrade，environmentalpollutionincreasingly

2、becomesoneofthemostseriOUSproblemsfacedbya11thecountriesintheworldEnvironmentalpollutionisamajorcontributortospeciesextinctionornearextinctionandthefurtherreductionofbiodiversityBasedonthebiologicalbackgroundmentionedabo

3、ve，toprotectendangeredspecies，inthispaperweestablishandstudyasinglespeciesmodelwithperiodicimpulsivepollutiontreatmentatfixedtimeInChapter1，weintroduce0111“researchbackgroundandgivesomepreliminariesInChapter2，basedonimpu

4、lsivedifferentialequation，weinvestigatethedynamicsofasinglespeciesmodelwithimpulsivepollutiontreatmentatfixedtimeinapollutedenvironmentSufficientconditionsforpermanenceandextinctionofthepopulationareobtainedWeshowthatthe

5、reexistsauniquepositiveperiodicsolutionwhichiSglobalasymptoticallystableunderpermanentconditionBesides，accordingtopracticalproblems，wewillconsiderconstructingahybridimpulsivesinglespeciesmodelcombiningperiodicpollutiontr

6、eatmentatfixedtimewithstatedependentpollutiontreatmentappliedwhenthepollutionconcentrationreachesthe百venEnvironmentThreshold(ET)andgivespecificbiologicalexplanationsbasedonnumericalsimulationsandourconclusionwillprovidet

7、hetheoreticaldecisionmakingbasisforpracticalproblemsInChapter3，weestablishasinglespeciesstage—structuredmodelwithimpulsivepollutiontreatmentandtimedelayinapollutedenvironmentWeshowthatthespeciesispermanentwhentheimpulsiv

8、eperiodislessthansomecriticalvalueotherwisethespeciesiseXtinctMoreoverattheendofeachchapterbyusingmathematicalsotharesuchasMatlabandMaple，wegivesomenumericalsimulationsresultswhichconfirmthetheoreticalconclusionsKeywords