捕食问题英语论文.docx

捕食问题英语论文.docx

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捕食问题英语论文

Predator-PreyProblems

Abstract

Wehaveestablishedapredator-preyunderinterferencesystemdynamicmodel,theevolutionequationsofthesystemandthecurveevolutionandtheevolutionofthephasediagram,respectivelydiscussedwithoutinterferenceandinterferenceeffectofevolutionofspecies,isillustratedbyconsideringadisturbancemodelismorereasonable,butalsomoreconducivetotheevolutionofspeciesandnewspecies.

Modelone:

theestablishmentofamathematicalmodelofdifferentialequationmodeltodescribethepreyonrabbitsandfoxespreyecosystem,reachedasteadystatetheirfinal.

Modeltwo:

the5forestrelatedparametersforrabbitsandfoxes,correlationanalysisbySPSSsoftwaretoachieveastateofequilibrium,thusfurtheronourmodelvalidation.

Modelthree:

predatorpredatorintroductiontootherforeignaidnotonlytoeatfood,butthepredatorpreyorjusteattheprey.

Introduction

Wewillconsideranenvironmentcontainingtworelatedpopulations—apreypopulation,suchasrabbits,andapredatorpopulation,suchasfoxes.Clearly,itisreasonabletoexpectthatthetwopopulationsreactinsuchawayastoinfluenceeachother'ssize.

ProblemStatement

Buildamathematicalmodeltodescribethepredator-preyecologicalsystemandanalyzeitsstablestate.

Pleaseconsulttherelatedliteratureanddatatocompletethesimulationcalculationofyourmathematicalmodel.

Studyyourpredator-preyecologicalmodelwithalternatefoodforthepredatorandapartialcoverfortheprey.

Assumptions

1,thepopulationoftheactivitieswithinthescopeofnoothermajornaturaldisasters

2,therabbitsinthemodelofnaturalenemiesisthefox;

3,assumingtherabbitsandfoxesarerelativelyadequatefood

4,ifthesamespeciesdonotcompetewithmassdeath;

Model1:

Predatorpreysystemmodel

Simplicity,thesystemonlyrabbitsandfoxeswerediscussed.Supposeinthegrasslandsonlygrass,rabbitsandfoxes,rabbitsattimetandthefoxdensityrespectively

and

。

Iftheprairiegrassisrichinresources,therabbitfeedongrasstosurviveindependently,andaccordingtothemodeofgrowth

Growth,which

Rabbit'sgrowthrate,maximumrabbitrepresentstheenvironmentcanaccommodatethedensity.Thenconsiderthepresenceofthefox,therabbitgrowthtodrop,efficiencydecreaseddensityhypothesisdependsonrabbitsandfoxesandpredatorfoundandattackingprey,sothegrowthequationofrabbit（i.e.preyequation）for[6]:

（1）Intheformula,reflectstheabilityoffoxespreyonrabbits,canbecalledthepressureconstant[7].

Similarly,thepredator,foxlefttherabbitcannotsurvive,letthefoxexistindependentlyofmortality,

ToreducetheindexformpredatororKa-VoLlterramodel.Ontheotherhand,therabbitprovidedfoodforthefox,thefoxisequivalenttothemortality,reducedtheextentalsodependsonthefoxandharedensity,sotheevolutionequationsinto:

（2）type,reflectstheabilitytosupporttherabbittothefox,isameasureofpredationefficiencyconstant[7].

Whenthesystemtendstobestable,thepredatorandthepreydensitydidnotchange,

and

By

（1）and

（2）thesteadystateequationofsystemcanbeobtained:

（3）

（4）

Becauseif,

、

for0,thepredatorpreysystemdoesnotexist,sotheabovetwoequationscanbewrittenas:

（5）

（6）

answer:

_（7）

（8）

（7）,（8）typeisthesystemstability,rabbitandfoxdensity.Wheretheconstant

、

、

、

_and

Bythespecificcircumstances.Becauseymustbegreaterthan0,otherwisethesystemdoesnotexist.Thenby（8）known

tomeet

。

Inordertodiscusstherelationshipbetweenwolvesanddeerqualitativegrowth,wetake[7],

thentheequation

（1）and

（2）canbewrittenas:

（9）

（10）

Consideringx,ycannotbe0,by（7）and（8）typecangettwoequationisnot0solution（orequilibrium）,namely

systemstability,thedensityis25,thedensityis7.5.

Accordingtoequation（9）and（10）thetimeevolutionofthefoxandrabbitresultsfromFigure1tofigure2shows.

Inordertodiscusstherelationshipbetweenwolvesanddeerqualitativegrowth,wetake

Thentheequation

（1）and

（2）canbewrittenas:

（11）

（12）

Consideringx,ycannotbe0,by（7）and（8）typecangettwoequationisnot0solution（orequilibrium）for

Thesystemisstable,thedensityis25,thedensityis7.5.Accordingtoequation（9）and（10）thetimeevolutionofthefoxandrabbitresultsfromFigure1tofigure2shows.

Figure1depictstheevolutionprocessofthefoxandrabbitwithtime

Volterra-Lotokfittingcurvefiguretwodepictsthefoxandhare

Wecanknowfromthegraph,beganwhen=0.1,=0.02,wolvesanddeerdensityfluctuationislarge,thenthesystemisinthestateof"turmoil".Overtime,moreandmoresmallfluctuationsindensity,ataboutt=250unitsoftime,thewolfanddeerdensitydoesnotchange,thenthesystemcanreachastaticbalance.Canalsobeseen,wolvesanddeerdensityofstablevalueswere7.5and25,consistentwiththeabovediscussion.AsyoucanseefromFigure2,thephasediagramisasmoothspiralline,fromoutsidetoinside,graduallyreduced,finallytogetherinonepoint,coordinatethepointscorrespondingto（25,7.5）.Alsotheimagegivestheevolutionprocessofwolvesanddeersaidvectorthesamephasediagram,gatheringcenterin（25,7.5）,namely,tothispoint,thesystemwillnotchange.

Conclusion

Whenthesystemisstable,rabbitsandfoxesintheconstantdensity,

、

、

、

and

andthespecificcircumstancesofthetimeisrelativelystable.Sothepredator-preyrelationshipatsteadystate.

Model2:

Theproblem,findthepopulationdensityof5forestrabbitsandfoxesintheinternet.Thefollowingtable:

大兴安岭

小兴安岭

美国红木国家森林

日本

Aonomori

森林

模型得到的

兔子密度

19

22

11

18

20

狐狸密度

7

5

2

8

6

表一

PartialcorrelationanalysiswasconductedbySPSS,withtheresultsfromthemodelvariables"GreaterKhinganRange,XiaoXinganLing,AmericanRedwoodNationalForest,aonomoriforest"controlasshownintable2:

Table2

Table3

Conclusion

Throughtheanalysisonthetablegivestheforestrabbitsandfoxesandmodelapopulationdensity,wherecircumstancespermit,themeanvalueandthestandarddifferenceisobtainedintherangeoferrorconditionsarepermitted.

Model3:

Predatorininterferenceconditionswereabovethedynamicmodelofpredatorsystemmodelisanidealsituation,withoutinterference,tostudytheexternalinterferenceandinternalfluctuationsontheimpactofsystemevolution,namelythedeerandwolfevolutionbothfromoutsideinterference,evolutionequationafterconsideringtheinterferenceonitchangeasfollowsLangevin（Langevin）equation[8,9]

（11）

（12）

Intwo,

_and

isnotassociatedwiththevariablesdescribingtheinterferenceeffectoftheexternalenvironment,representativeorinternalfluctuationsonthegrowthofdeerandwolf.Whencutinhalf

=0.05,

=0.02

Figure3:

Increaseonetimes

=0.04.Figure4:

Reducebyhalf

=0.05,increaseonetimes

=0.04.inFigure5

=0.08，

=0.03.Figure6

Thefigure3tofigure6

and

theparameterschange,describethewolvesanddeerindifferentconditionsandthetimeevolution.Inthebeginning,curveswithandwithoutnoiseisconsistent（seeFigure1）.Therefore,theinterferenceofunreasonableshouldreduceorreducethedisturbanceintensity.Butontheotherhand,whenthebalanceisbroken,itmayleadtotheemergenceofnewspecies,soastoconstituteanewpredatorpreysystem,toachieveanewdynamicequilibrium.

Conclusion

Thepredatorpreysystemmodel,thesystemevolutioncurveintheidealconditionandinterferenceconditionsandevolutionofphasediagramsarediscussed.Theresultsshowthat,ideally,theevolutionofthissystemwillreachastaticequilibrium,whichisnotconducivetotheevolutionofspeciesandnewspecies.

Whileintheinterferencecondition,theevolutionofthesystemwillreachadynamicbalance,andevendestroythebalance,thisprovidesthenecessaryconditionsfortheevolutionofspecies,andtheemergenceofnewspeciesso,consideringtheinterference（noise）afterthemodelismorereasonable.Andtoprovidethescientificbasisforthefuturegovernmentrecoveryandprotectionpoliciesofecologicalsystem.

StrengthsandWeaknesses

Model1

Strengths；Comprehensiveconsiderationofvariousfactorsisintheecosystemofpredatorandprey.Suchas:

growthrate,predation,mortalityandsteady.Allowsthemodelinthepremiseconditionsallow,canwellpredictthestabledevelopmentofthesystemortheneedtoprotectouranimalgoodtrackingandinvestigation.

Weaknesses：

Doesnotexistinnaturesothatindividualfoodchain,notsumupthewholeecologicalsystem.

Model2

Strengths:

Moreclearlyshowsthedifferencesbetweenthenatureoftherabbit,foxdensityandthedensityandcorrelationmodel.

Weaknesses：

lesssamplecollection,alsocannotverywellmakethecontrast.

Model3

Strengths:

Whenparameterschange,usematlabmapping,veryconcise.Canclearlyreaction.

Weaknesses：

Nolimitanalysis,whenthepredatorfoodentirelybyexternalsupplyinsteadofpredatorprey,therelationshipbetweenthemis:

predatorpreyintoacompetitiverelationship,theycompeteforspaceandresources.Becausetimeislimited,sothecompetitionmodelofsubsequentanalysiswasnotperformed.

References

[1]XuR,HaoF,ChenL.Astage-structuredpredator-preymodelwithtimedelaysActaMathematicaScientia,2006,26A（3）:

387.

[2]_DuYK,XuR,Du