几类捕获模型稳定性分析

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&"%#!"#$'%%'$%()()#'#&*#$+,&()$%'%*)'(1$+'(-()*%''./%#&*#$+,%0)++,',%#*&,+%'*,,1%23"'-(%23+)-1)-2-%.*/23/)#..3-'%&1/#$%23"00-(%/)+*4105%&1*+%00/1123+,$#)%6/+)

3、+)+'2,-. '00$+%''12223/,-.%.-3*$4*,7'#'*#$30500*#$8%/23-*41,2341,05'3,.2300467*%'%#305//2341,05':305;00;';-.;*41;41,;.23AbstractThedevelopmentofmodernscienceandtechnologylargelydependsontheachievementsandprogressesinphys

4、ics,chemistryandbiology,whoseprecisede-scriptionisusuallybasedonappropriatemathematicalmodels.Therefore,itbecomesoneoftheimportantdirectionstostudymathematicalmodelsarisingfromapplicationsbyusingthesetheoriesandmethods.Inthisthesis,thesta-bilitytheoryofordinarydifferentialequationsisu

5、sedtostudyseveralimportantbiologicalmathematicalmodels.Themainworkisasfollows:1.Abiologicalresourceharvestingmodelwithpricechangesisdiscussed.First,weestablishthestabilityofequilibriumpointsbythestabilitytheoryofordinarydifferentialequations.Then,thePoincaremap,impulsivedifferentialine

6、qualityandthemethodsofqualitativeanalysisareusedtodiscusssystemwithimpulse,weprovetheexistenceandthestabilityoforder-1ororder-2periodicsolutionforthismodel.Moreover,weshowthatthereisnoperiodicsolutionwithorderlargerthanorequaltothree.Finally,byanalyzingcharacteristicequation,westudyt

7、heinfluenceoftimedelayandobtainsomesufficientconditionswhichensuretheglobalstabilityoftheequilibriumpointsofthesystem.Italsoshowsthatthetimedelaycancauseastableequilibriumtobecomeunstable.2.Weinvestigateabioeconomicsmodelwithage-structure,impulseandtimedelay.Itdividesthissingle-populati

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