An Introduction to Complex Systems: Society, Ecology, and Nonlinear Dynamics PDF
Preview An Introduction to Complex Systems: Society, Ecology, and Nonlinear Dynamics
Paul Fieguth An Introduction to Complex Systems Society, Ecology, and Nonlinear Dynamics An Introduction to Complex Systems Paul Fieguth An Introduction to Complex Systems Society, Ecology, and Nonlinear Dynamics 123 PaulFieguth FacultyofEngineering UniversityofWaterloo Waterloo Ontario,Canada ISBN978-3-319-44605-9 ISBN978-3-319-44606-6 (eBook) DOI10.1007/978-3-319-44606-6 LibraryofCongressControlNumber:2016959761 ©SpringerInternationalPublishingSwitzerland2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Although I had studied nonlinear dynamic systems, bifurcations, and bistable systems as a graduate student, I had clearly never really absorbed the ideas at a conceptuallevel,sinceitwastenyearslaterthatIwasstruckbyasimplefigureof catastrophic nonlinearstate transitions in the contextof ecologicalsystems. I was immediatelyhooked:theconceptwassoclear,soelegant,andsoeasytounderstand. HowwasitpossiblethatIhadneverreallyencounteredthis? OvertimeIbecameconvincedthatnotjustI,butindeedmostoftheundergrad- uate studentswith whom I interact, fundamentallydo notgrasp the big picture of theissuessurroundingthem,eventhoughtheunderlyingmathematicalconceptsare wellwithinreach.Theunderlyingproblemisclear:forpedagogicalreasonsnearly allofthecourseswhichmystudentstakefocusonmathematicsandsystemswhich aresmallscale,linear,andGaussian.Unfortunately,thereisnotasinglelarge-scale ecologicalorsocialphenomenonwhichisscalar,linear,andGaussian. This is, very simply, the rationale for this text: to explore a variety of large issues,globalwarming,iceages,water,andpoverty,andtomotivateandteachthe materialofthecourse,nonlinearsystems, non-Gaussianstatistics, spatialsystems, andcomplexsystems—motivatedbythesecasestudies. The large-scale problems challenging the world are complex and multifaceted andwillnotbesolvedbyasinglestrategy,academicfield,orperspective.Thisbook cannot claim to teach how to solve such enormousproblems; however, the intent isverymuchtodrawexplicitparallelsandconnectionsbetweenthemathematical theory,ontheonehand,andworldissues/casestudiesontheother. Thespecifictopicsbeingtaughtarenonlineardynamicsystems,spatialsystems, power-law systems, complex systems, and inverse problems. To be sure, these fields have been aroundfor some time, and many bookshave been written on the subjects;however,thefieldsare,atbest,onlyweaklypresentinmostundergraduate programs. This bookis intendedforreadershavinga technicalbackground,such as engi- neering,computerscience, mathematics, or environmentalstudies. The associated coursewhichIhavetaughtisopentothirdandfourthyearundergraduatestudents; however, this book should, I hope, be of interest and mostly accessible to a v vi Preface significantly wider audience. The only actual prerequisites are some background in algebra and in probability and statistics, both of which are summarized in the appendices. The reader who would prefer to get a perspective of the text might prefertofirstreadthetwooverviewchapters,onglobalwarminginChapter2and onwaterinChapter12. There are many online resources related to nonlinear dynamics and complex systems;however,onlinelinkscanfrequentlychangeorbecomeoutdated,soIam reluctant to list such links here in the text. Instead, I am maintaining a web page associatedwiththisbook,at http://complex.uwaterloo.ca/text towhichthereaderisreferredforfurtherreadingandothermaterial. A number of people were of significant support in the undertaking of this textbook.Most significantly,I would like to thankmy wife, Betty Pries, who was tirelessinherenthusiasmandsupportforthisprojectandregularlyarticulatedthe value which she perceivedin it. My thanksto Professor Andrea Scott and Doctor WernerFieguth,bothofwhomreadeverypageofthebookfrombeginningtoend andprovideddetailedfeedback.AppreciationtoDoctorChristophGarbe,myhost andresearchcollaboratorattheUniversityof Heidelberg,wheremuchofthistext waswritten. Teaching this material to students at the University of Waterloo has allowed me to benefit from their creative ideas. Here, I particularly need to recognize the contributionof the projectreports of Maria Rodriguez Anton (discountfunction), VictorGan(cities),KirstenRobinson(resilience),DouglasSwanson(SOCcontrol), andPatrickTardif(Zipf’slaw). Finally,mythankstothecontributionsofmychildren: • Anya,forallowingherartworktoappearinprintinFigureA.2 • Thomas,forposingatVersaillesandappearinginExample3.1 • Stefan,fordemonstratinganinvertedpenduluminFigure5.8 Waterloo,Ontario,Canada PaulFieguth Contents 1 Introduction................................................................. 1 1.1 HowtoReadThisText............................................... 3 References.................................................................... 3 2 GlobalWarmingandClimateChange................................... 5 FurtherReading.............................................................. 12 References.................................................................... 12 3 SystemsTheory............................................................. 13 3.1 SystemsandBoundaries............................................. 14 3.2 SystemsandThermodynamics ...................................... 17 3.3 SystemsofSystems.................................................. 23 CaseStudy3:NutrientFlows,Irrigation,andDesertification............. 24 FurtherReading.............................................................. 34 SampleProblems ............................................................ 35 References.................................................................... 39 4 DynamicSystems........................................................... 41 4.1 SystemState.......................................................... 42 4.2 Randomness.......................................................... 46 4.3 Analysis............................................................... 48 4.3.1 Correlation.................................................. 48 4.3.2 Stationarity.................................................. 51 4.3.3 Transformations ............................................ 56 CaseStudy4:WaterLevelsoftheOceansandGreatLakes............... 58 FurtherReading.............................................................. 61 SampleProblems ............................................................ 62 References.................................................................... 65 5 LinearSystems.............................................................. 67 5.1 Linearity.............................................................. 68 5.2 Modes................................................................. 69 5.3 SystemCoupling..................................................... 73 vii viii Contents 5.4 Dynamics............................................................. 75 5.5 ControlofDynamicSystems........................................ 81 5.6 Non-normalSystems................................................. 83 CaseStudy5:SystemDecoupling.......................................... 85 FurtherReading.............................................................. 90 SampleProblems ............................................................ 90 References.................................................................... 95 6 NonlinearDynamicSystems:Uncoupled ................................ 97 6.1 SimpleDynamics..................................................... 98 6.2 Bifurcations........................................................... 103 6.3 HysteresisandCatastrophes......................................... 108 6.3.1 CatastrophicStateTransition .............................. 110 6.3.2 SystemIrreversibilityandHysteresis...................... 111 6.4 SystemBehaviournearFolds........................................ 114 6.5 Overview.............................................................. 120 CaseStudy6:ClimateandHysteresis ...................................... 122 FurtherReading.............................................................. 128 SampleProblems ............................................................ 129 References.................................................................... 134 7 NonlinearDynamicSystems:Coupled................................... 135 7.1 Linearization.......................................................... 136 7.2 2DNonlinearSystems ............................................... 139 7.3 LimitCyclesandBifurcations....................................... 144 7.4 ControlandStabilization ............................................ 146 CaseStudy7:Geysers,Earthquakes,andLimitCycles ................... 151 FurtherReading.............................................................. 160 SampleProblems ............................................................ 161 References.................................................................... 167 8 SpatialSystems ............................................................. 169 8.1 PDEs.................................................................. 171 8.2 PDEsandEarthSystems............................................. 174 8.3 Discretization......................................................... 177 8.3.1 DiscretizationinTime...................................... 177 8.3.2 DiscretizationinSpace..................................... 179 8.4 SpatialContinuous-StateModels.................................... 181 8.5 SpatialDiscrete-StateModels ....................................... 192 8.6 AgentModels......................................................... 196 CaseStudy8:GlobalCirculationModels.................................. 199 FurtherReading.............................................................. 202 SampleProblems ............................................................ 203 References.................................................................... 210 Contents ix 9 PowerLawsandNon-GaussianSystems................................. 211 9.1 TheGaussianDistribution........................................... 213 9.2 TheExponentialDistribution........................................ 214 9.3 HeavyTailedDistributions........................................... 216 9.4 SourcesofPowerLaws .............................................. 225 9.5 SynthesisandAnalysisofPowerLaws ............................. 228 CaseStudy9:PowerLawsinSocialSystems.............................. 234 FurtherReading.............................................................. 238 SampleProblems ............................................................ 239 References.................................................................... 244 10 ComplexSystems........................................................... 245 10.1 SpatialNonlinearModels............................................ 246 10.1.1 PhaseTransitions........................................... 247 10.1.2 Criticality ................................................... 248 10.2 Self-OrganizedCriticality............................................ 253 10.3 Emergence............................................................ 256 10.4 ComplexSystemsofSystems ....................................... 257 CaseStudy10:ComplexSystemsinNature ............................... 262 FurtherReading.............................................................. 264 SampleProblems ............................................................ 265 References.................................................................... 269 11 ObservationandInference ................................................ 271 11.1 ForwardModels...................................................... 272 11.2 RemoteMeasurement................................................ 274 11.3 Resolution ............................................................ 278 11.3.1 MeasurementResolution................................... 278 11.3.2 StateResolution ............................................ 286 11.4 InverseProblems..................................................... 287 CaseStudy11A:Sensing—SyntheticApertureRadar ................... 299 CaseStudy11B:Inversion—AtmosphericTemperature................. 303 FurtherReading.............................................................. 305 SampleProblems ............................................................ 305 References.................................................................... 308 12 Water......................................................................... 309 12.1 OceanAcidification.................................................. 311 12.2 OceanGarbage....................................................... 312 12.3 Groundwater.......................................................... 313 CaseStudy12:SatelliteRemoteSensingoftheOcean.................... 316 FurtherReading.............................................................. 317 SampleProblems ............................................................ 318 References.................................................................... 318 x Contents 13 ConcludingThoughts ...................................................... 319 FurtherReading.............................................................. 320 References.................................................................... 321 Appendices A MatrixAlgebra ............................................................. 325 FurtherReading.............................................................. 331 References.................................................................... 331 B RandomVariablesandStatistics.......................................... 333 FurtherReading.............................................................. 339 References.................................................................... 340 C NotationOverview.......................................................... 341 Index............................................................................... 343
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