Reviews of Nonlinear Dynamics and Complexity: Volume 2 (Annual Reviews of Nonlinear Dynamics and Complexity (VCH))

260 Pages·2009·4.59 MB·English

by  Heinz Georg Schuster

ReviewsofNonlinear
DynamicsandComplexity
Editedby
HeinzGeorgSchuster
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Reviews of Nonlinear Dynamics
and Complexity
Volume 2
Edited by
Heinz Georg Schuster
WILEY-VCH Verlag GmbH & Co. KGaA
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V
Contents
Preface IX
ListofContributors XI
1 HumanMobilityandSpatialDiseaseDynamics 1
DirkBrockmann
1.1 IntroductionandMotivation 1
1.2 QuantitativeAssessmentsofHumanMobility 3
1.2.1 PreliminaryConsiderations 3
1.2.2 TheLackofScaleinHumanMobility 5
1.3 StatisticalPropertiesandScalingLawsinMulti-ScaleMobility
Networks 8
1.3.1 ScalingLawsintheTopologicalFeaturesofMulti-Scale
TransportationNetworks 10
1.4 SpatiallyExtendedEpidemicModels 12
1.4.1 DiseaseDynamicsinaSinglePopulation 13
1.4.1.1 TheSISModel 14
1.5 SpatialModels 15
1.5.1 ContinuityLimitandFractionalTransport 18
1.5.2 LimitingCases 20
References 23
2 StochasticEvolutionaryGameDynamics 25
ArneTraulsenandChristophHauert
2.1 GameTheoryandEvolution 25
2.2 TheReplicatorDynamics 26
2.3 EvolutionaryGamesinFinitePopulations 29
2.3.1 StochasticEvolutionaryGameDynamics 29
2.3.2 FixationProbabilities 31
2.3.3 FixationTimes 34
2.3.3.1 UnconditionalFixationTime 34
VI Contents
2.3.3.2 ConditionalFixationTimes 36
2.3.4 TheMoranProcessandWeakSelection 37
2.3.5 TheFermiProcess 41
2.4 FromFinitetoInfinitePopulations(andBackAgain) 43
2.5 Applications 46
2.5.1 ThePrisoner’sDilemma 47
2.5.2 Rock-Paper-Scissors 49
2.5.3 VoluntaryPublicGoodsGames 51
2.5.4 Punishment 54
2.6 ConcludingRemarks 56
References 57
3 DynamicandTopologicalInterplayinAdaptiveNetworks 63
BerndBlasiusandThiloGross
3.1 Introduction 63
3.2 AdaptiveNetworks:ADefinition 66
3.2.1 BasicDefinitionsofGraphTheory 66
3.2.2 DynamicandEvolvingNetworks 68
3.2.3 AdaptiveNetworks 70
3.3 UbiquityofAdaptiveNetworksAcrossDisciplines 72
3.4 RobustSelf-OrganizationTowardCriticality
inBooleanNetworks 76
3.5 AdaptiveConnectionWeightsinCoupledOscillatorNetworks 79
3.5.1 LeadershipandtheDivisionofLabor 79
3.5.2 Self-OrganizationTowardsSynchronizability 82
3.6 CooperationinGamesonAdaptiveNetworks 84
3.6.1 ElevatedLevelsofCooperation 84
3.6.2 StruggleforTopologicalPosition 87
3.7 DynamicsandPhaseTransitions
inOpinionFormationandEpidemics 88
3.7.1 EpidemiologicalModels 88
3.7.2 OpinionFormation 97
3.8 Summary,SynthesisandOutlook 98
3.8.1 TheFourHallmarksofAdaptiveNetworks 99
3.8.2 AdaptiveNetworks:FutureImpacts 100
3.8.3 TowardsaUnifyingTheoryofAdaptiveNetworks 101
3.8.4 FutureChallenges 103
References 103
Contents VII
4 FractalModelsofEarthquakeDynamics 107
PathikritBhattacharya,BikasK.Chakrabarti,Kamal,and
DebashisSamanta
4.1 Introduction 107
4.1.1 EarthquakeStatistics 107
4.1.2 ModelingEarthquakeDynamics 108
4.1.3 FractalFaults 110
4.1.3.1 FractalGeometryofFaultSurfaces 110
4.1.3.2 Frequency–SizeDistributionofFaults 111
4.2 Two-FractalOverlapModel 115
4.2.1 TheModel 115
4.2.2 AnalysisoftheTimeSeries 117
4.2.3 TheGutenberg–RichterLaw 119
4.2.4 TheOmoriLaw 121
4.2.5 TemporalDistributionofMagnitudesofanAftershock
Sequence 123
4.3 ComparisonwithObservations 125
4.3.1 TheGutenberg–RichterLaw 125
4.3.2 TheOmoriLaw 127
4.3.3 TheTemporalDistributionofAftershockMagnitudes 127
4.4 FiberBundleModelofEarthquakes 137
4.5 SummaryandDiscussion 139
C.1 RandomCantorSets 148
C.2 RegularSierpinskiGaskets 149
C.3 RandomSierpinskiGaskets 152
C.4 PercolatingClustersinaSquareLattice 152
References 155
5 Epilepsy 159
KlausLehnertz,StephanBialonski,Marie-ThereseHorstmann,
DieterKrug,AlexanderRothkegel,MatthäusStaniek,and
TobiasWagner
5.1 Introduction 159
5.2 ComputationalModelsinEpilepsyResearch 165
5.2.1 FromMicroscopictoMacroscopicModelingApproaches 166
5.2.2 ModelingEpilepticPhenomena 168
5.3 MeasuringInteractionsinEpilepticNetworks 171
5.3.1 BivariateTimeSeriesAnalysis 173
5.3.2 MultivariateTime-SeriesAnalysis 179
5.4 Conclusion 183
References 184
VIII Contents
6 StructureinNetworks 201
JörgReichardtandStefanBornholdt
6.1 Introduction 201
6.2 MultivariateDataVersusRelationalData 203
6.2.1 Clustering 203
6.2.2 DimensionalityReduction 208
6.3 ANewQualityFunctionforStructureRecognition
inNetworks 210
6.3.1 TheOptimalImageGraph 213
6.3.2 ChoiceofaPenaltyFunctionandNullModel 214
6.3.3 Benchmark 216
6.4 Clusters,ModularityandGraphPartitioning 217
6.5 ModularityofRandomNetworks:ReplicaMethod 218
6.6 ModularityofRandomNetworks:CavityMethod 222
6.7 Conclusion 234
References 236
Index 239