Quantitative sociodynamics: stochastic methods and models of social interaction processes
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2010
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| Edition: | 2. edition |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXIX, 333 Seiten Diagramme 235 mm x 155 mm |
| ISBN: | 9783642115455 |
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Record in the Search Index
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IMAGE 1
CONTENTS
1 INTRODUCTION AND SUMMARY 1
1.1 QUANTITATIVE MODELS IN THE SOCIAL SCIENCES 2
1.1.1 THE LOGISTIC MODEL 2
1.1.2 DIFFUSION MODELS 3
1.1.3 THE GRAVITY MODEL 3
1.1.4 THE GAME THEORY 3
1.1.5 DECISION MODELS 5
1.1.6 FINAL REMARK 6
1.2 HOW TO DESCRIBE SOCIAL PROCESSES IN A MATHEMATICAL WAY 6 1.2.1
STATISTICAL PHYSICS AND STOCHASTIC METHODS 7
1.2.2 NON-LINEAR DYNAMICS 12
2 DYNAMIC DECISION BEHAVIOR 17
2.1 INTRODUCTION 17
2.2 MODELLING DYNAMIC DECISION BEHAVIOR 18
2.2.1 QUESTIONING TRANSITIVE DECISIONS AND HOMO ECONOMICUS 18 2.2.2
PROBABILISTIC DECISION THEORIES 20
2.2.3 ARE DECISIONS PHASE TRANSITIONS? 23
2.2.4 FAST AND SLOW DECISIONS 24
2.2.5 COMPLETE AND INCOMPLETE DECISIONS 25
2.2.6 THE RED-BUS-BLUE-BUS PROBLEM 26
2.2.7 THE FREEDOM OF DECISION-MAKING 27
2.2.8 MASTER EQUATION DESCRIPTION OF DYNAMIC DECISION BEHAVIOR 27
2.2.9 MEAN FIELD APPROACH AND BOLTZMANN EQUATION 29 2.2.10 SPECIFICATION
OF THE TRANSITION RATES OF THE BOLTZMANN EQUATION 30
2.3 FIELDS OF APPLICATIONS 32
2.3.1 THE LOGISTIC EQUATION 32
2.3.2 THE GENERALIZED GRAVITY MODEL AND ITS APPLICATION TO MIGRATION 32
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1003462049
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.3.3 SOCIAL FORCE MODELS AND OPINION FORMATION 33
2.3.4 THE GAME-DYNAMICAL EQUATIONS 35
2.3.5 FASHION CYCLES AND DETERMINISTIC CHAOS 37
2.3.6 POLARIZATION, MASS PSYCHOLOGY, AND SELF-ORGANIZED BEHAVIORAL
CONVENTIONS 39
2.4 SUMMARY AND OUTLOOK 41
REFERENCES 41
PART I STOCHASTIC METHODS AND NON-LINEAR DYNAMICS OVERVIEW 47
3 MASTER EQUATION IN STATE SPACE 49
3.1 INTRODUCTION 49
3.2 DERIVATION 51
3.2.1 DERIVATION FROM THE MARKOV PROPERTY 52
3.2.2 EXTERNAL INFLUENCES (DISTURBANCES) 53
3.2.3 INTERNAL FLUCTUATIONS 54
3.2.4 DERIVATION FROM QUANTUM MECHANICS 57
3.3 PROPERTIES 64
3.3.1 NORMALIZATION 64
3.3.2 NON-NEGATIVITY 65
3.3.3 THE LIOUVILLE REPRESENTATION 65
3.3.4 EIGENVALUES 66
3.3.5 CONVERGENCE TO THE STATIONARY SOLUTION 67
3.4 SOLUTION METHODS 68
3.4.1 STATIONARY SOLUTION AND DETAILED BALANCE 68
3.4.2 TIME-DEPENDENT SOLUTION 71
3.4.3 'PATH INTEGRAL' SOLUTION 72
3.5 MEAN VALUE AND COVARIANCE EQUATIONS 79
4 BOLTZMANN-LIKE EQUATIONS 83
4.1 INTRODUCTION 83
4.2 DERIVATION 84
4.3 SUBDIVISION INTO SEVERAL TYPES OF SUBSYSTEMS 87
4.4 PROPERTIES 88
4.4.1 NON-NEGATIVITY AND NORMALIZATION 88
4.4.2 THE GASKINETIC BOLTZMANN EQUATION 88
4.4.3 THE H-THEOREM FOR THE GASKINETIC BOLTZMANN EQUATION 91 4.4.4
SOLUTION OF THE GASKINETIC BOLTZMANN EQUATION 94 4.5 COMPARISON OF
SPONTANEOUS TRANSITIONS AND DIRECT INTERACTIONS. 95 4.5.1 TRANSITIONS
INDUCED BY INTERACTIONS 95
4.5.2 EXPONENTIAL FUNCTION AND LOGISTIC EQUATION 96 4.5.3 STATIONARY AND
OSCILLATORY SOLUTIONS 97
IMAGE 3
CONTENTS XI
5 MASTER EQUATION IN CONFIGURATION SPACE 99
5.1 INTRODUCTION 99
5.2 TRANSITIONS IN CONFIGURATION SPACE 100
5.2.1 SPONTANEOUS TRANSITIONS 100
5.2.2 PAIR INTERACTIONS 101
5.3 MEAN VALUE AND COVARIANCE EQUATIONS 103
5.4 CORRECTIONS AND HIGHER ORDER INTERACTIONS 107
5.5 INDIRECT INTERACTIONS AND MEAN FIELD APPROACHES I LL
5.6 COMPARISON OF DIRECT AND INDIRECT INTERACTIONS I LL
5.6.1 DIFFERENCES CONCERNING THE COVARIANCE EQUATIONS I LL 5.6.2
DIFFERENCES CONCERNING THE MEAN VALUE EQUATIONS 112
6 THE FOKKER-PLANCK EQUATION 115
6.1 INTRODUCTION 115
6.2 DERIVATION 115
6.3 PROPERTIES 119
6.3.1 THE CONTINUITY EQUATION 119
6.3.2 NORMALIZATION 120
6.3.3 THE LIOUVILLE REPRESENTATION 121
6.3.4 NON-NEGATIVITY 121
6.3.5 EIGENVALUES 121
6.3.6 CONVERGENCE TO THE STATIONARY SOLUTION 121
6.4 SOLUTION METHODS 122
6.4.1 STATIONARY SOLUTION 122
6.4.2 PATH INTEGRAL SOLUTION 123
6.4.3 INTERRELATION WITH THE SCHROEDINGER EQUATION 124 6.5 MEAN VALUE AND
COVARIANCE EQUATIONS 125
6.5.1 INTERPRETATION OF THE JUMP MOMENTS 126
6.6 BOLTZMANN-FOKKER-PLANCK EQUATIONS 127
6.6.1 SELF-CONSISTENT SOLUTION 132
7 LANGEVIN EQUATIONS AND NON-LINEAR DYNAMICS 135
7.1 INTRODUCTION 135
7.2 DERIVATION 137
7.3 ESCAPE TIME 141
7.4 PHASE TRANSITIONS, LIAPUNOV EXPONENTS, AND CRITICAL PHENOMENA 143
7.5 ROUTES TO CHAOS 145
7.5.1 RUELLE-TAKENS-NEWHOUSE SCENARIO AND LIAPUNOV EXPONENTS 146
7.5.2 PERIOD DOUBLING SCENARIO AND POWER SPECTRA 147
PART II QUANTITATIVE MODELS OF SOCIAL PROCESSES OVERVIEW 151
IMAGE 4
CONTENTS
PROBLEMS AND TERMINOLOGY 153
8.1 TERMS 153
8.1.1 SYSTEM AND SUBSYSTEMS 153
8.1.2 STATE 153
8.1.3 SUBPOPULATION 153
8.1.4 SOCIOCONFIGURATION 156
8.1.5 INTERACTION 156
8.2 PROBLEMS WITH MODELLING SOCIAL PROCESSES 157
8.2.1 COMPLEXITY 157
8.2.2 INDIVIDUALITY 159
8.2.3 STOCHASTICITY AND DISTURBANCES 159
8.2.4 DECISIONS AND FREEDOM OF DECISION-MAKING 160 8.2.5 EXPERIMENTAL
PROBLEMS 163
8.2.6 MEASUREMENT OF BEHAVIOURS 163
8.3 SUMMARY 164
DECISION THEORETICAL SPECIFICATION OF THE TRANSITION RATES 167 9.1
INTRODUCTION 167
9.2 DERIVATION 168
9.2.1 THE MULTINOMIAL LOGIT MODEL 168
9.2.2 ENTROPY MAXIMIZATION 170
9.2.3 FECHNER'S LAW 172
9.2.4 UTILITY AND DISTANCE FUNCTION 173
9.3 PAIR INTERACTION RATES 176
9.3.1 SPECIAL APPLICATIONS IN THE SOCIAL SCIENCES 183
9.4 PROPERTIES OF THE UTILITY APPROACH 185
9.4.1 STATIONARY DISTRIBUTION 185
9.4.2 CONTRIBUTIONS TO THE UTILITY FUNCTION 186
10 OPINION FORMATION MODELS 187
10.1 INTRODUCTION 187
10.2 INDIRECT INTERACTIONS 189
10.2.1 A PERIOD DOUBLING ROUTE TO CHAOS 191
10.2.2 A RUELLE-TAKENS-NEWHOUSE ROUTE TO CHAOS .191 10.3 DIRECT PAIR
INTERACTIONS 191
10.3.1 KINDS OF PAIR INTERACTIONS 192
10.3.2 OSCILLATIONS 197
10.3.3 INFLUENCE OF THE INTERACTION FREQUENCIES 201
10.3.4 PERIOD DOUBLING SCENARIOS AND CHAOS 205
10.4 GENERALIZATIONS 217
10.5 SPATIAL SPREADING OF OPINIONS 218
10.5.1 OPINION SPREADING BY DIFFUSION 218
10.5.2 OPINION SPREADING BY TELECOMMUNICATION 220
IMAGE 5
CONTENTS XUEI
11 SOCIAL FIELDS AND SOCIAL FORCES 225
11.1 INTRODUCTION 225
11.2 DERIVATION 226
11.3 THE SOCIAL FORCE MODEL 229
11.3.1 COMPARISON WITH LEWIN'S 'SOCIAL FIELD THEORY' 233 11.4 COMPUTER
SIMULATIONS 235
11.4.1 IMITATIVE PROCESSES 237
11.4.2 AVOIDANCE PROCESSES 244
12 EVOLUTIONARY GAME THEORY 247
12.1 INTRODUCTION 247
12.2 DERIVATION OF THE GAME DYNAMICAL EQUATIONS 248
12.2.1 PAYOFF MATRIX AND EXPECTED SUCCESS 248
12.2.2 CUSTOMARY DERIVATION 249
12.2.3 FIELDS OF APPLICATION 249
12.2.4 DERIVATION FROM THE BOLTZMANN-LIKE EQUATIONS 250 12.3 PROPERTIES
OF GAME DYNAMICAL EQUATIONS 253
12.3.1 NON-NEGATIVITY AND NORMALIZATION 253
12.3.2 FORMAL SOLUTION 253
12.3.3 INCREASE OF THE AVERAGE EXPECTED SUCCESS IN SYMMETRICAL GAMES 254
12.3.4 INVARIANT OF MOTION FOR ANTISYMMETRICAL GAMES 256 12.3.5
INTERRELATION WITH THE LOTKA-VOLTERRA EQUATIONS 257 12.3.6 LIMIT CYCLES
AND CHAOS 258
12.4 STOCHASTIC VERSION OF THE GAME DYNAMICAL EQUATIONS 260 12.4.1
SELF-ORGANIZATION OF BEHAVIOURAL CONVENTIONS FOR THE CASE OF TWO
EQUIVALENT COMPETING STRATEGIES 263
13 DETERMINATION OF THE MODEL PARAMETERS FROM EMPIRICAL DATA 275 13.1
INTRODUCTION 275
13.2 THE CASE OF COMPLETE DATA 275
13.3 THE CASE OF INCOMPLETE DATA 278
13.3.1 PARAMETER ESTIMATION 282
13.3.2 MODEL REDUCTION 288
13.4 MIGRATION IN WEST GERMANY 289
13.4.1 FIRST MODEL REDUCTION 290
13.4.2 SECOND MODEL REDUCTION 292
13.4.3 COMPARISON OF THE WEIDLICH-HAAG MODEL AND THE GENERALIZED GRAVITY
MODEL 295
13.4.4 THIRD MODEL REDUCTION 298
13.5 EVALUATION OF EMPIRICALLY OBTAINED RESULTS 300
13.5.1 SENSITIVITY ANALYSIS 300
13.5.2 DECOMPOSITION OF THE UTILITY FUNCTIONS WITH RESPECT TO
EXPLANATORY VARIABLES 301
13.5.3 PROGNOSES 302
IMAGE 6
XIV CONTENTS
13.6 EXAMPLES FOR DECOMPOSITIONS OF UTILITY FUNCTIONS 302 13.6.1
PURCHASE PATTERN 302
13.6.2 VOTING BEHAVIOUR 305
13.6.3 GAPS IN THE MARKET AND FOUNDATIONS OF NEW PARTIES 308
REFERENCES 311
INDEX 323 |
| any_adam_object | 1 |
| author | Helbing, Dirk 1965- |
| author_GND | (DE-588)115494693 |
| author_facet | Helbing, Dirk 1965- |
| author_role | aut |
| author_sort | Helbing, Dirk 1965- |
| author_variant | d h dh |
| building | Verbundindex |
| bvnumber | BV036865634 |
| classification_rvk | MR 2100 MR 2800 |
| ctrlnum | (OCoLC)698621661 (DE-599)DNB1003462049 |
| dewey-full | 302.0151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 302 - Social interaction |
| dewey-raw | 302.0151 |
| dewey-search | 302.0151 |
| dewey-sort | 3302.0151 |
| dewey-tens | 300 - Social sciences |
| discipline | Soziologie Mathematik |
| edition | 2. edition |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV036865634 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T10:53:55Z |
| institution | BVB |
| isbn | 9783642115455 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020781316 |
| oclc_num | 698621661 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-91 DE-BY-TUM DE-M347 DE-634 |
| owner_facet | DE-473 DE-BY-UBG DE-91 DE-BY-TUM DE-M347 DE-634 |
| physical | XXIX, 333 Seiten Diagramme 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| spelling | Helbing, Dirk 1965- Verfasser (DE-588)115494693 aut Stochastische Methoden Quantitative sociodynamics stochastic methods and models of social interaction processes Dirk Helbing 2. edition Heidelberg [u.a.] Springer 2010 XXIX, 333 Seiten Diagramme 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Dissertation Universität Stuttgart 1992 Interaktion (DE-588)4027266-7 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Quantitative Methode (DE-588)4232139-6 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Sozialer Prozess (DE-588)4134118-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Sozialer Prozess (DE-588)4134118-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Stochastik (DE-588)4121729-9 s 1\p DE-604 Interaktion (DE-588)4027266-7 s 2\p DE-604 Stochastisches Modell (DE-588)4057633-4 s 3\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 4\p DE-604 Quantitative Methode (DE-588)4232139-6 s 5\p DE-604 Erscheint auch als Online-Ausgabe 978-3-642-11546-2 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3491039&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020781316&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Helbing, Dirk 1965- Quantitative sociodynamics stochastic methods and models of social interaction processes Interaktion (DE-588)4027266-7 gnd Stochastik (DE-588)4121729-9 gnd Quantitative Methode (DE-588)4232139-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Sozialer Prozess (DE-588)4134118-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4027266-7 (DE-588)4121729-9 (DE-588)4232139-6 (DE-588)4057633-4 (DE-588)4114528-8 (DE-588)4134118-1 (DE-588)4057630-9 (DE-588)4113937-9 |
| title | Quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_alt | Stochastische Methoden |
| title_auth | Quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_exact_search | Quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_full | Quantitative sociodynamics stochastic methods and models of social interaction processes Dirk Helbing |
| title_fullStr | Quantitative sociodynamics stochastic methods and models of social interaction processes Dirk Helbing |
| title_full_unstemmed | Quantitative sociodynamics stochastic methods and models of social interaction processes Dirk Helbing |
| title_short | Quantitative sociodynamics |
| title_sort | quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_sub | stochastic methods and models of social interaction processes |
| topic | Interaktion (DE-588)4027266-7 gnd Stochastik (DE-588)4121729-9 gnd Quantitative Methode (DE-588)4232139-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Sozialer Prozess (DE-588)4134118-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Interaktion Stochastik Quantitative Methode Stochastisches Modell Mathematisches Modell Sozialer Prozess Stochastischer Prozess Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3491039&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020781316&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT helbingdirk stochastischemethoden AT helbingdirk quantitativesociodynamicsstochasticmethodsandmodelsofsocialinteractionprocesses |