几类功能性反应捕食系统的最优收获问题-研究

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1、=²ÏŒÆa¬ÆØ©AbstractCurrently,theresearchfieldsaremorewidelyaboutdevelopmentmanagementissuesonpopulationresource.Inthecourseofthestudy,wemainlyarebasedonecologicalandeconomicbenefits,inorderthatresourcesofbiologicalpopulationscanbeeffectivelydevelopedanduti-lized.Weconsideredtheactualpro

2、blemandcreatedbiologicalmathematicalmodelsinordertomakequalitativeanalysisandselectthebestcapturestrategywhichmakesbiologicalresourcesbeunderthepremiseofmaintainingthebalanceofecosystemsandmeetthevariousneedsofhumanbeings.Therefore,establishingtheoptimalharvestingsystemofbiologicalpop

3、ulationshasbecomearesearchtrend.Establishingtheoptimalharvestmodelofbiologicalpopulationscanhelpthegovernmenteffectivelycontrolthefishermencaptureactivities,andthenmaintainecologicalbalanceandstability.Thispaperismainlybasedontheresearchstatusofthebiologicalspeciesmodelsathomeandabroad

4、inrecentyears,theresearchresultofdevelopmentandmanagementofbiologicalpopulationsisregardedasastartingpoint,whichhasastrongbackgroundandpracticalapplica-tionvalue,andthefollowingissuesaremainlyraisedthroughextensiveresearch.Thefirstprob-lemisthatweconsideredseveralpredatorsystemswiththe

5、effectofpreyrefugeandfunctionalresponseandconcludedtheexistenceandstabilityoftheequilibriumpointbyusingqualitativeandstabilityanalysismethodsofdifferentialequationsaftertheestablishmentofeconomicandrevenuecapturemodel.Thesecondproblemisthatweimposedtaxestocontroldevelopmentfortheunitc

6、apturepopulations(preyandpredator)byusingPontryaginmaximumprincipleandobtainedtheoptimaltaxation.Theseresultsprovideatheoreticalbasisfortheeffectivemanagementofrenewableresourcesforthecertainpopulations.Weanalyzedtheimpactofhar-vestingeffectsandrefugeeffectsonasylumlocalstabilityandgl

7、obalstabilityofthesystembyusingeigenvaluemethodandboundedtheoryofthesystem.Weobtainedaresultthatacer-tainpercentageoftheshelterundercertainconditionshasstabilizationonthesystemthroughobservationandanalysis.Itisprovedthatallpositivesolutionsareuniformlyboundedbyusingthetheoryofdif-fere

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