系统动力学全英文版期末考试汇总doc.docx
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系统动力学全英文版期末考试汇总doc.docx
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系统动力学全英文版期末考试汇总doc
SystemDynamic
郑春燕
Chapter1:
IntroductiontoSystemDynamics
1.Thefivedisciplines
1)Systemsthinking2)Personalmastery3)Mentalmodels
4)Buildingsharedvision5)Teamlearning
2.ThedefinitionofMentalModels
Mentalmodelsaretheimages(att让udesandassumptions)wecarryinourmindsaboutourselves,otherpeople,inst让utions,andeveryaspectoftheworldwhichguideourinterpretationsandbehavior
3.ButterflyEffect
Thebutterflyeffectisthesensitivedependenceoninitialcond让ionsinwhichasmallchangeatoneplaceinadeterministicnonlinearsystemcanresultinlargedifferencesinalaterstate.
Chapter2\SystemsandSystemThinking
l.Modelingconcepts
Amodelisanabstractionofarealobjectorsystem.
2・Systemdefinition
Asystemisasetoftwoormoreelementsthatsatisfiesthefollowingthreeconditions:
◊Itfulfillsacertainfunction
◊Thebehaviorofeachelementhasaneffectonthebehaviorofthewhole
◊Thebehavioroftheelementsandtheireffectsonthewholeareinterdependent
Thebehaviorofasystemdependsnotonlyonthebehaviorofthecomponentsofasystembutalsoonhowthesecomponentsinteract.
3.Systemcomponents
1)Objects2)States3)Events4)Time5)Space6)Structure
4・"Complexsystems"aresystemsinwhichtherearemultipleinteractionsbetweenmanydifferentcomponents(oragentsj.Acomplexsystemischaracterizedbymultipleagentswhoseinteractionsgiverisetostructuraleffectsthataren'tapparentintheagentsthemselves.
Chapter4:
StructureandBehaviorofDynamicSystems
4.1Fundamentalmodesofdynamicbehavior
Fundamentalmodesofdynamicbehavior
Themostfundamentalmodesofbehaviorareexponentialgrowth,goalseeking,andoscillation.Eachoftheseisgeneratedbyasimplefeedbackstructure:
•Exponentialgrowtharisesfrompositivefeedback
■Goalseekingarisesfromnegativefeedback
-Qscillationarisesfromnegativefeedbackwithtimedelaysintheloop.
OthercommonmodesofbehaviorincludingS-shapedgrowth,S-shapedgrowthwithovershootandoscillation,andovershootandcollapse,arisefromnonlinearinteractionsofthefundamentalfeedbackstructures.
4.1.1ExponentialGrowth
Exponentialgrowtharisesfrompositive(self-reinforcing)feedback・Thelargerthequantity,thegreater让snetincrease,furtheraugmentingthequantityandleadingtoever-fastergrowth.
Pureexponentialgrowthhastheremarkablepropertythatthedoublingtimeisconstant:
thestateofthesystemdoublesinafixedperiodoftime,nomatterhowlarge.
MienaRateIsNotaRate
Indynamicmodeling,theterm"rate"generallyreferstotheabsoluterateofchangeinaquantity.Theterm'birthrate"herereferstothenumberofpeoplebornpertimeperiod.Often,however;theterm"rate”isusedasshorthandforthefractionalrateofchangeofavariable.Forexample,thebirthrateisofteninterpretedasthenumberofbirthsperyearperthousandpeople.Similarly,wecommonlyspeakoftheunemploymentrate.Theword"Tate”inthesecasesactuallymeans"ratio":
theunemploymentrateistheratioofthenumberofunemployedworkerstothelaborforce
◊Theunitsofmeasureforratesofflowareunits/timeperiod.
◊Theunitsofmeasureforfractionalratesofflowareunitsperunitpertimeperiod
=1/timeperiods・
4.1.2GoalSeeking
Negativeloopsseekbalance,equilibrium,andstasis.Negativefeedbackloopsacttobringthestateofthesysteminlinew让hagoalordesiredstate.
Whentherelationshipbetweenthesizeofthegapandthecorrectiveactionislinear;therateofadjustmentisexactlyproportionaltothesizeofthegapandtheresulting
goal-seekingbehaviorisexponentialdecay.Asthegapfalls,sotoodoestheadjustmentrate.
Goal(DesiredStateofSystem)Discrepancy^CorrectiveJAction+
Everynegativeloopincludesaprocesstocomparethedesiredandactualconditionsandtakecorrectiveaction.
4.1.3Oscillation
Oscillationisthethirdfundamentalmodeofbehaviorobservedindynamicsystems.Likegoal-seekingbehavior;oscillationsarecausedbynegativefeedbackloops.
Inanoscillatorysystem,thestateofthesystemconstantlyovershoots让sgoalorequilibriumstate,reverses,thenundershoots,andsoon.
Theovershootingarisesfromthepresenceofsignificanttimedelaysinthenegativeloop.Thetimedelayscausecorrectiveactionstocontinueevenafterthestateofthesystemreaches让sgoal,forcingthesystemtoadjusttoomuch,andtriggeringanewcorrectionintheoppositedirection
Goal(DesiredStateofSystem)
Administrativeand、DecisionMaking
Delays
Oscillationsareamongthemostcommonmodesofbehaviorindynamicsystems.
DampedoscillationsLimitcyclesChaos
Oscillationscanariseifthereisasignificantdelayinanypartofthenegativeloop.PerceivingthestateofthesystemcausedbythemeasurementandreportingsystemInitiatingcorrectiveactionsafterthediscrepancyisperceivedduetothetimerequiredtoreachadecision.
Delaysbetweentheinitiationofacorrectiveactionanditseffectonthestateofthesystem
eg.Ittakestimeforacompanytomeasureandreportinventorylevels,timeformanagementtomeetanddecidehowmuchtoproduce,andmoretimewhilerawmaterialsprocurement,thelaborforce,andotherneededresourcesrespondtothenewproductionschedule.
4.2Interactionsofthefundamentalmodes
4.2.1S・shapedGrowth
AcommonlyobservedmodeofbehaviorindynamicsystemsisS-shapedgrowth
Growthisexponentialatfirst,butthengraduallyslowsuntilthestateofthesystemreachesanequilibriumlevel.Theshapeofthecurveresemblesastretched-outuS cairyingcapacity Thecarryingcapacityofanyhabitatisthenumberoforganismsofaparticulartypeitcansupportandisdeterminedbytheresourcesavailableintheenvironmentandtheresourcerequirementsofthepopulation. eg.Asapopulationapproaches让scarryingcapacity,resourcespercapitadiminishtherebyreducingthefractionalnetincreaserateuntiltherearejustenoughresourcespercap让atobalancebirthsanddeaths. AsystemgeneratesS-shapedgrowthonlyiftwocriticalconditionsaremet: First,thenegativeloopsmustnotincludeanysignificanttimedelays-Second,thecarryingcapacitymustbefixed. 4.2.2S・ShapedGrowthwithOvershoot S・shapedgrowthrequiresthenegativefeedbacksthatconstraingrowthtoactswiftlyasthecarryingcapacityisapproached. Often,however;therearesignificanttimedelaysinthesenegativeloops. Timedelaysinthenegativeloopsleadtothepossibilitythatthestateofthesystemwillovershootandoscillatearoundthecarryingcapacity. Chapter5: CasualLoopDiagram 1.Definitionofadirected(ordi^raDh) Itisagraph,orsetofnodesconnectedbyedges,wheretheedgeshaveadirectionassociatedw让hthem. AdirectedgraphGinthesystemconsistsofanon-emptyfinitesetV(t)=V(G(t))andsetX(t)=X(G(t))whichisconnectedbyvi(t),vj(t)V(t).ThedirectedgraphisdenotedasG= (V(t),X(t))・V(t)isthevertexofG(t),andX(t)isthearcofG(t).Thearcsvi(t)vj(t)arerelatedtothevertexvi(t)andvj(t).vi(t)istherootofthearcandvj(t)istheendofthearc.Therootandtheendarebothcalledtheendpoint. ThedirectionaldiagramG(t)isdenotedasG(t)=[V(t),X(t))orG(V(t),X(£))U(t)={i4(t),v2(t), X(t)={vl(t)v2(t),v2(t)v3(t),v3(t)v2(t),v3(t)v4(t),v4(t)vl(t)} 2.causalloopdiagrams Feedbackisoneofthecoreconceptsofsystemdynamics. Yetourmentalmodelsoftenfailtoincludethecriticalfeedbacksdeterminingthedynamicsofoursystems. Insystemdynamicsweuseseveraldiagrammingtoolstocapturethestructureofsystems,includingcausalloopdiagrams(CLD)andstockandflowmaps.CLDsareexcellentfor: Quicklycapturingyourhypothesesaboutthecausesofdynamics; Elicitingandcapturingthementalmodelsofindividualsorteams; Communicatingtheimportantfeedbacksyoubelieveareresponsibleforaproblem・ Acausaldiagramconsistsofvariablesconnectedbyarrowsdenotingthecausalinfluencesamongthevariables.Theimportantfeedbackloopsarealsoidentifiedinthediagram. 3.Polarity AlinkfromAtoBispositiveifachangeinAproducesachangeinthesamedirection. AlinkfromAtoBisnegativeifachangeinAproducesachangeinBintheoppositedirection.Thedirectionofanarrowshowsthedirectionofcausation/Causality. fornegativepolarity,ifXincreases,Ywilla(waysbeFowertha^nitwouTcfhavebeenT DeterminingLoopPolarity Method1-CounttheNumberofNegativeLinks Inacomplexdiagramitisalltooeasytomiscountthenumberofnegativelinksinaloop・And让iseasytomislabelthepolarityoflinkswhenyoufirstdrawthediagram.Countingthenumberofnegativesignsisunlikelytorevealtheseerrors. Method2-TracetheEffectofaChangearoundtheLoop Tracetheeffectofasmallchangeinoneofthevariablesasitpropagatesaroundtheloop.Youcanstartw让hanyvariableintheloop.Theresultmustbethesame. Thepolarityoftheloopisthesignoftheopenloopgain: Polarityofloop=SGNf^Xi0/dXJ) Theopenloopgainiscalculatedbythechainrulefromthegainsoftheindividuallinks: SGN(dXi°/dXi】)=SGN[(aXi°/aXn)(dXn/dXn-i)...(dX2/dXi1) AllLinksShouldHaveUnambiguousPolarities Chapter6StocksandFlows 1.StateoftheSystem: Stocks □aka"Levels: "StateVariables","Compartments" □Stocks(Levels)representaccumulations -Thesecapturethe"stateofthesystem” -Mathematically,wewillcallthese"statevariables" □Thesecanbemeasuredatoneinstantintime □Stocksstartwithsomeinitialvalue&arethereafterchangedonlybyflowsinto&outofthem-Therearenoin
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