Table Of ContentSimulation Foundations, Methods and Applications
Stanislaw Raczynski
Models
for Research and
Understanding
Exploring Dynamic Systems,
Unconventional Approaches, and
Applications
Simulation Foundations, Methods
and Applications
SeriesEditor
AndreasTolk,TheMITRECorporation,McLean,VA,USA
AdvisoryEditors
RoyE.Crosbie,CaliforniaStateUniversity,Chico,CA,USA
TonyJakeman,AustralianNationalUniversity,Canberra,ACT,Australia
AxelLehmann,UniversitätderBundeswehrMünchen,Neubiberg,Germany
StewartRobinson,BusinessSchool,NewcastleUniversity,NewcastleuponTyne,
UK
ClaudiaSzabo,SchoolofComputerScience,UniversityofAdelaide,Adelaide,
Australia
MamadouKabaTraoré ,IMSUMR5218,UniversityofBordeaux,Talence,
France
BernardP.Zeigler,UniversityofArizona,Tucson,AZ,USA
LinZhang,BeihangUnviversity,Beijing,China
AndreasTolk,OldDominionUniversity,Norfolk,VA,USA
RodrigoCastro,FacultaddeCienciasExactasyNaturales,Departamentode
Computación,UniversidaddeBuenosAires,CiudadAutónomadeBuenosAires,
Argentina
SanjaLazarova-Molnar,InstituteofAppliedInformaticsandFormalDescription
Methods,KarlsruheInstituteofTechnology,Karlsruhe,Germany
The modelling and simulation community extends over a range of diverse disci-
plinesandthislandscapecontinuestoexpandatanimpressiverate.Modellingand
simulation is fundamentally a computational tool which has an established record
of significantly enhancing the understanding of dynamic system behaviour on one
hand,andthesystemdesignprocessontheother.Itsrelevanceisunconstrainedby
disciplineboundaries.Furthermore,theever-increasingavailabilityofcomputational
powermakesfeasibleapplicationsthatwerepreviouslybeyondconsideration.
SimulationFoundations,MethodsandApplicationshostshigh-qualitycontribu-
tionsthataddressthevariousfacetsofthemodellingandsimulationenterprise.These
rangefromfundamentalconceptsthatarestrengtheningthefoundationofthedisci-
pline to the exploration of advances and emerging developments in the expanding
landscapeofapplicationareas.Theunderlyingintentistofacilitateandpromotethe
sharing of creative ideas across discipline boundaries. The readership will include
seniorundergraduateandgraduatestudents,modellingandsimulationprofessionals
andresearchworkers.
Inasmuchasamodeldevelopmentphaseisaprerequisiteforanysimulationstudy,
thereisanexpectationthatmodellingissueswillbeappropriatelyaddressedineach
presentation. Incorporation of case studies and simulation results will be strongly
encouraged.
Titlescanspanavarietyofproducttypes,includingbutnotexclusively,textbooks,
expository monographs, contributed volumes, research monographs, professional
texts,guidebooksandotherreferences.
Thesebookswillappeal,varyingly,toseniorundergraduateandgraduatestudents,
andresearchersinanyofahostofdisciplineswheremodellingandsimuationhas
become(orisbecoming)abasicproblem-solvingtool.Sometitleswillalsodirectly
appealtomodellingandsimulationprofessionalsandpractitioners.
Stanislaw Raczynski
Models for Research
and Understanding
Exploring Dynamic Systems, Unconventional
Approaches, and Applications
StanislawRaczynski
FacultaddeIngenieria
UniversidadPanamericana
MexicoCity,Mexico
ISSN 2195-2817 ISSN 2195-2825 (electronic)
SimulationFoundations,MethodsandApplications
ISBN 978-3-031-11925-5 ISBN 978-3-031-11926-2 (eBook)
https://doi.org/10.1007/978-3-031-11926-2
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Preface
In this book, you will find topics in modeling and simulation, both conventional,
as well as suggestions about new tools and somewhat wider insight on modeling.
Most of the chapters of the book may be used in didactic work, as a textbook or
supplementarymaterial.Inthetext,thestudentwillfindexplanationsofdiversekind
ofmodelingtasks,andexamplesofmodelsofvarioustypes.Tenoutof12chapters
containalsosectionsofquestionsandanswersthatfocusonthemostessentialaspects
ofthepresentedmodelingmethodology.
Modelsareusedbythinkingbeings,consciouslyorsub-consciously,tomanage
theirbehaviorandrespondtotheeventsintheenvironment.Themostperfectand
hugecollectionofmodelsiscontainedinourbrains.Duringyearsoflearning,the
humans, as well as most of the animals, created models of their own bodies and
objectsfromtheenvironment,tobeabletotakedecisionsandcontroltheirbehavior.
The human brain is increasingly complicated and capable of creating and storing
modelsnotonlyinsideit,butalsoinothermedia.Wecreatemodelsintheformof
writtendescriptions,drawings,mathematicalexpressions,orlogicalstructures,and
storethemforfurtheruse.
Theappearanceofcomputersprovidedanew,powerfultoolformodelstorageand
processing.Inthisbook,wediscussmodelsthatcanbeusedincomputersimulation.
This kind of modeling is closely connected with simulation on analog and digital
machines.Theresultsofcreatingandusingmodelshelpustotakedecisions,predict,
and/orunderstandtheworldwherewelive.Mostofthethingsweobservearestill
too complex to be understood. The knowledge accumulated in models helps us in
takingcorrectactions,grow,understand,andsurvive.
Ingeneral,modelshelpustounderstandhowcomplexsystemswork.Modelsof
complexsystemsneednotbecomplexorhuge.Irememberthatintheearly1960s,
whenweworkedon100kHzCPU,32kBmemorymachines,afriendofmineasked
metosolveanordinarydifferentialequationonacomputer.Theequationwaswritten
inoneline,withrathersimple,butnon-trivialformula.Thesolutionwasnoteasy,
butfinallytheprogramworked.Iaskedhim: Thisisthemodelofwhat?Theanswer
wassimple: ThisisthemodeloftheUniverse.
v
vi Preface
Ontheotherhand,therearehugemodelsthatprovidelittlehelpincomplexsystem
understanding. In Chap. 1, there is a remark on the model of the economy of the
wholeSovietimperiumof1970s,developedbytheCentralEconomicMathematical
InstituteoftheURSS.Astheauthorsagreed,themodelresultedtobetoolargeand
complicatedtobesimulatedandinterpret.
Here,youalsowillfindhereseveraltopicscloselyrelatedtomodelbuilding,like
stabilityoflinearandnon-linearmodels,modelvalidity,credibility,newapproach
tosensitivity,andsomemoregeneralizedinsight,basedonthetheoryofcategories.
Newtoolsformodelcreationareproposed,namely,thedifferentialinclusionsand
reachablesetscalculation.Forthediscreteeventmodels,someproblemsofsimul-
taeneouseventsarediscussed.Anewmethodologyofthe semi-discreteeventswith
finite-time duration is suggested to eliminate the ambiguity that arises in strictly
discretemodelswithsimultaneousevents.
This book does not pretend to describe and discuss all this huge research and
experiencegatheredduringmanydecades.Wetrytogiveanoverviewofthemost
importantmodelingissues.Thetenetofthebookistoshowalsosomenon-typical
and unconventional kind of models and their applications, like models based on
differentialinclusionsandsemi-discreteeventmodels.
Looking at the annals of modeling and simulation activity, it can be seen that
mostofthesimulationistsandmodel-makersfollowthesamemodelingparadigms
formorethansixdecades.Thereexistsa strangeconvictionthateverythingthatis
continuouscanbemodeledbydifferentialequations,andtheonlytooltosimulate
events is the discrete event simulation. Here, we show some alternative ways to
construct and treat models, like differential inclusions, reachable set calculation,
andsemi-discreteeventsimulation.Notethattheconceptsas functionalsensitivity
(Chap.4)isnewandoriginal.Notealsothattheimagesofreachablesetsofdynamic
systemsshownhere(Chaps.3–5)haveneverbeenprovidedbeforeinothersources.
We also discuss a somewhat non-conventional way of model description that uses
thelanguageofthetheoryofcategories.
Itshouldbeemphasizedthat thisbooktreatsaboutdynamicmodels.Wedonot
discussstaticmodelsthatcanbetreatedbyalgebraicmethodsorstaticmodelingand
optimization.Thisisbecause therealworldisdynamic.Everythingischanging,
fluctuating,oroscillating.The timevariableappearsinallmodelswepresent.
Wedonotdiscussheremodelsbeingdevelopedinsomespecificfieldsofresearch
likemodelsofneuralnetworks,weatherforecasting,humanbrain,missiledynamics,
human immune system, games, electromagnetic wave propagation, human DNA,
urban development, and many others. If we do this, the book would have several
thousands of pages. We also omit the recall of probability distributions used in
computersimulationbecausesuchoverviewcomesinanyofhundredsofthebooks
oncomputersimulation.Whentalkingaboutmodelingandsimulation,thequestion
arises:Doesthemodelcreatororthesimulationistmustbeamathematician?Mypoint
isthathe/shedoesn’t.However,somebasicknowledgeofmathematicsisrequired
(atleastforthereadersofthisbook).Thismaypreventtheresearcherfrommaking
seriouserrorslikeusingthePoissondistributionforbetween-arrivaltimeintervals
Preface vii
of the Poisson arrival process, treating the affine function as lineal, or calculating
statisticsoveradatasetoffivepoints.
We also omit issues and examples of models already published by the author
in Springer Nature series. These are: interactions between hierarchical structures,
dynamics of terror and anti-terror organizations, organization growth and decay
models,humanmigration,extendedprey–predatormodel,andothers,discussedinS.
Raczynski,“Interactingcomplexitiesofherdsandsocialorganizations.”Themodels
ofcatastrophes,unexpectedbehaviorpatternsinartificialsocieties,catastrophesin
stock market, epidemics, growth of organisms, work, salary, and motivation are
described in “Catastrophes and unexpected behavior patterns in complex artificial
societies,”bythesameauthor.
In Chap. 1, there is an overview about the general concepts of modeling. The
continuous and discrete event models are shortly discussed. The main concepts of
modelvalidityandmathematicalandgraphicalrepresentationofmodelsareconsid-
ered. Chapter 2 is dedicated to continuous models. The conventional approach to
continuousmodelingandsimulationisdescribed.
InChap.3,thereadercanfindthediscussionabouttheconceptsandapplications
of models based on the differential inclusions. This tool is useful in the analysis
ofmodeluncertaintyandsensitivity.Thenewmethodnamed functionalsensitivity
is proposed. More detailed examples of application of the concept of functional
sensitivitycanbefoundinChap.4.
Chapter5describesamodelofairplaneflightcontrolandreachablesets.
An application to Pontryagin’s Maximum Principle to market optimization can
be found in Chap. 6. This chapter shows the connection between modeling and
optimization.Anexampleofoptimizationtechniquebasedonthetheoryofoptimal
controlisgiven.Inthisexample,thereadercanseetheoptimizationofthedynamic
marketingstrategies.
An overview of discrete event models and simulation is provided in Chap. 7,
includingtheDiscreteEventSpecificationFormalismanddistributedsimulation.
InChapter8containsanexampleofamodelofself-organizationinapopulation
oflivingbeings,andinteractionsbetweenorganizationsandtheenvironment.
Chapter 9 contains certain non-conventional approach to the general theory of
models. A metrics in the space of models is defined. In this chapter, there is a
proposalofthenewconceptof semi-discreteeventsimulation.
In Chap. 10, some examples of application of the language of the theory of
categoriesinmodelspecificationsarediscussed.
Thelasttwochaptersdonotincludequestionandanswersections.Thesechapters
presentexamplesofsomewhatunconventionalapproach,andmoreabstractmodeling
tasks.Themainpurposeofthesechaptersistoshowmodelsthatperhapshavelittle
practicalapplications,butofferanewandcognitivetopics.
Chapter 11 deals with the concept of time variable and the time instant. The
proposed model of the “time arrow” includes the concept of a fuzzy time instant.
Insteadofconsideringtheeventsthatoccuringiven,sharpmomentsoftimewetreat
thetimeinstantasanintervalwithnon-zerolength,whereevents“occur”gradually.
Someissuesrelatedtothecausalityprinciplearediscussed.
viii Preface
In Chap. 12, the reader can find a new approach to models related to the real
time,themodelreversibilityanduncertaintyofthefuture.Anabstract,butperhaps
interestingmodeloftheuniverseencapsulated inaballoffinitesizeisgiven.The
ideaoftheuniverseencapsulatedinamulti-dimensionalballmayappeartobevery
abstract.However,thisideamayprovokethereadertoask“Andwhatisoutsidethe
ball?”and“Isitpossibletooutofit?”Inthelastquestion,wesupposesthepossibility
totravel“behindtheinfinity.”Moreover,wecanaddthefourthdimensiontotheball
(the time),andthenaddthefifthandmoredimensions.Thisisanon-science-fiction
remarkonpossiblefive-andmulti-dimensionaluniverse.
MexicoCity,Mexico StanislawRaczynski
Acknowledgements
IwouldliketoexpressmygratitudetotheEditorsofthejournalslistedbelowfor
thepermissiontousetheupdatedversionsofmyarticles,asfollows:
Semi-discreteeventsandmodelsincategoricallanguage.InternationalJournalof
SimulationModelling,2012;11,(2),77–88;
Uncertainty,dualismandinversereachablesets.InternationalJournalofSimula-
tionModelling,2011;10,(1),38–45,ISBN/ISSN:1726–4529;
and
Simulatingself-organizationandinterferencebetweencertainhierarchicalstruc-
tures.Nonlinear Dynamics Psychology and Life Sciences, Human Sciences Press,
2014;18,(4),419–434,ISBN/ISSN:1090-0578.
StanislawRaczynski
ix
