Table Of ContentEvolutionary Economics and Social Complexity Science 27
Stanislaw Raczynski
Catastrophes
and Unexpected
Behavior Patterns in
Complex Artificial
Populations
Evolutionary Economics and Social Complexity
Science
Volume 27
Editor-in-Chiefs
TakahiroFujimoto,TheUniversityofTokyo,Bunkyo-Ku,Tokyo,Japan
YujiAruka,Kyoto,Kyoto,Japan
Moreinformationaboutthisseriesathttp://www.springer.com/series/11930
Stanislaw Raczynski
Catastrophes and Unexpected
Behavior Patterns in Complex
fi
Arti cial Populations
StanislawRaczynski
FacultyofEngineering
UniversidadPanamericana
MexicoCity,DistritoFederal,Mexico
ISSN2198-4204 ISSN2198-4212 (electronic)
EvolutionaryEconomicsandSocialComplexityScience
ISBN978-981-16-2573-2 ISBN978-981-16-2574-9 (eBook)
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Preface
Computersimulationisanimportantresearchtoolformorethansevendecades,and
evolves together with the evolution of computer hardware. At the very beginning,
the simulations have been used by some “gurus” and specialists. Then, more user-
friendly software tools have been developed. In recent years, there are so many
software packages and simulation languages, that nearly everybody can simulate
anything. However, more professional simulation tasks cannot be separated from
model building. To create valid models, the researcher must dominate several
disciplines, like mathematics, physics, computer science, and others. Modeling
andsimulationrequirefromtheresearchercertaininterdisciplinaryandgeneralized
insightoncomplexsystemstobemodeled.
This book is a continuation of the research described in the book “Interacting
Complexities of Herds and Social Organizations” (Raczynski S., Springer Nature,
2019). However, here we concentrate on the phenomena of catastrophes, unex-
pected, and spontaneous events that are neither explicitly coded in the model nor
provoked by external impulses. A short reference to the known theory of catastro-
phes is done. The classic examples of catastrophes in that context refer rather to
mathematicaldescriptionsofeventsthatoccurwhilesolvingdifferentialequations.
AnexampleofsuchcatastropheisdescribedinChap.1.Inthisbookweunderstand
“catastrophes” in more general sense, as events that appear in models of complex
populations. As for the complexity, there is not completely clear when a model is
complex or not. Complexity should not be confused with the system size. Huge
systems can be quite simple, and some small ones more complex. MacMillan
dictionary defines complexity as “features of something that make it confusing or
difficulttodealwith.”TheOxfordLearner’sDictionarysaysthatthecomplexityis
“thestateofbeingformedofmanyparts;thestateofbeingdifficulttounderstand.”
Therearemanysimilardefinitions.InabookofMeyers“MathematicsofComplex-
ity and Dynamical Systems” (Springer, 2011), we can read “Complex systems are
systems that comprise many interacting parts with the ability to generate a new
quality of collective behavior through self-organization, e.g. the spontaneous for-
mationoftemporal,spatial,orfunctionalstructures.”Themaintopicofthepresent
v
vi Preface
bookissomewhatrelatedtothelastdefinition,namelytospontaneousformationof
structuresandgenerationofmacro-behaviorpatterns.Comparingtopopulationsof
individualsintherealworld,ourmodelsarerathersimple.However,fromthepoint
of view of model building, they are not trivial and generate, like the complex
systems,structuresandinterestingbehaviorpatterns.
In Chap. 1, there are some remarks on the classic mathematical approach to
catastrophes, and the overview of agent-based modeling. Chapter 2 is dedicated to
the simulation package BLUESSS, used in the rest of the book. In Chap. 3, we
discussthe model of an artificial societywhere theindividuals consumeresources,
move and interact with each other. The simulations show unexpected events that
appearspontaneouslyinthemodel,whenitseemstoreachasteadystate.Chapter4
deals withan extended prey–predatorsystemof multiple species, where themodel
dynamics is quite different from the classic Lotka–Volterra continuous model.
Chapter 5 contains simulations of possible catastrophic events in a stock market
model.Chapter6describesamodelofepidemicsthatisitselfakindofcatastrophe.
Here,Iwouldliketoexpresssomepersonalviewonepidemicmodels.Firstofall,
itshouldbeemphasizedthatthepresentedmodelisnotanyattempttosimulatethe
recent epidemy of covid-19. As stated in Chap. 6, we should appreciate all effort
done to simulate this epidemy, related in numerous publications. However, we
should remember that one of the most serious errors in scientific research is to
look for something that does not exist. To construct a simulation model, first we
shouldknowifthemodelexistsatall.Manyresearchersforgetthisstageofmodel
building.Thismayleadtowrongandconfusedresults.Inthecasesuchascovid-19,
this is extremely important because an invalid model can be used to take wrong
strategical decisions about epidemy treatment and provoke millions of deaths. It is
importanttorememberthatdealingwithnewkindofdiseasewithunknowndynam-
ics,wecannotjustmodifyanyexistingepidemicsmodel,anduseknownmodeling
paradigms. Anyway, this is also a question of ethics in computer simulation
profession.
In Chap. 7, you can find a model of a growing organism that evolves and may
revealsomedegenerationlikeacancerinalivingbody.Therearesomeremarkson
theDNAandRNAmechanisminlivingorganisms.However,wedonotpretendto
simulate the extremely complex DNA functions. Instead, we use the abbreviation
EOB to denote the genetic information included in each model agent (living cell).
Furtherresearchonthiskindofmodelscouldgiveushintstobetterunderstandthe
growthofcellsinlivingorganisms.
Chapter 8 contains the descriptionofa model ofa population of agents that are
workingandobtainsalaries.Theworkeffortincreasesthecommonpoolofgoodsin
thesociety.Thesalarymaydependontheamountandqualityofworkdonebythe
agent.Thismayresultindifferencesandinequalitybetweenagents.Theamountof
inequality is measured using the Gini inequality index. The increased income
motivates the agent to intensify his work. This is a feedback that influences the
inequality,thelevelofcommongoodsandwelfare.Thedynamicsofthepopulation
issimulated.
Preface vii
In Chap. 9, we simulate some examples of populations with waiting lines. It is
pointed out that certain queuing models may reveal a considerable “catastrophic”
andirregulargrowthofqueues.
Finally,inChap.10,therearesomeremarksaboutpossiblesimultaneousevents.
Thisisnotasimulationofbigpopulations,butratherofsomespecialcaseswhenthe
simultaneous events in the model may lead to ambiguity and wrong results. The
generalconclusionofthischapteristhatthediscrete-eventmodelsformasingularity
in the space of models. An alternative paradigm named semi-discrete events is
proposed.
MexicoCity,Mexico StanislawRaczynski
Acknowledgements
AnupdatedversionofmyarticlepublishedearlierhasbeenusedinChap.10ofthis
book,aslistedbelow.
“Simultaneous events, singularity in the space of models and chicken game,”
International Journal of Modeling, Simulation, and Scientific Computing, World
ScientificPublishingCompany,online-readyarticle,May2021.
ix
Contents
1 CatastrophesandAgent-BasedModels. . . . . . . . . . . . . . . . . . . . . . 1
1.1 Catastrophes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 DiscreteEventsandAgent-BasedModels. . . . . . . . . . . . . . . . . 4
1.2.1 DiscreteEventsandDEVS. . . . . . . . . . . . . . . . . . . . . 5
1.2.2 SomeSoftwareTools. . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.3 TheEventQueue. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.4 Agent-BasedModels. . . . . . . . . . . . . . . . . . . . . . . . . 9
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 BLUESSSSimulationPackage. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 BLUESSSConcepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 BLUESSSCode,ProgramStructure. . . . . . . . . . . . . . . . . . . . . 17
2.3 Inheritance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 BLUESSSCodeGenerators,ContinuousandDiscrete
SimulationSupport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 VarianceAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 BehaviorPatternsofanArtificialSociety. . . . . . . . . . . . . . . . . . . . 29
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Agent-BasedModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 SimulationTool. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 TheModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.1 Processfood. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.2 Processagent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.1 Experiment1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.2 Experiment2(unexpectedbehavior). . . . . . . . . . . . . . 41
3.5.3 Experiment3—aggression. . . . . . . . . . . . . . . . . . . . . 43
xi
