Sociodynamics : a systematic approach to mathematical modelling in the social sciences.

Format:

Book

Author/Creator:

Weidlich, Wolfgang, 1931-

Language:

English

Subjects (All):

Social sciences--Mathematical models.

Social sciences.

Physical Description:

xii, 380 pages ; 23 cm

Place of Publication:

Amsterdam : Harwood Academic ; Abingdon : Marston, 2000.

Summary:

This work is intended for two groups: social scientists interested in mathematical modelling; and natural scientists, computer scientists, and mathematicians searching for new applications of their computational methods in the many fields of social science. Weidlich (theoretical physics, U. of Stuttgart) discusses an interdisciplinary project named "Sociodynamics" (which has been developed over three decades), that aims to find approaches to setting up and evaluating models of dynamic social phenomena by combining mathematical methods with social science concepts. He first considers general system structures (social systems in particular) and their characteristic properties and then presents six models applying the modelling procedure of sociodynamics to problems of population dynamics, sociology, economics, and regional science. The last section is a self-contained presentation of mathematical concepts and methods. Annotation copyrighted by Book News, Inc., Portland, OR

Contents:

Part I Structures and Modelling Concepts

1 The Structure of Reality Under Interdisciplinary Perspective 7

1.1 Systems and their Parts: The Stratification of Reality 7

1.2 Towards Explanations of System Structure: Reductionism versus Holism 13

1.3 General System Theory, Synergetics and Sociodynamics 18

2 Quantitative Modelling in Social Science 35

2.1 The Necessity of Qualitative Characterisations of Social Systems 35

2.2 The Scope and the Limitations of Quantitative Models 36

2.3 The Feedback-Loop of Qualitative and Quantitative Thought 38

2.4 Discussion of Critical Arguments about Quantitative Modelling in Social Science 39

3 The General Modelling Concept of Sociodynamics 43

3.1 The Modelling Purposes of Sociodynamics 43

3.2 The Steps of the Modelling Procedure 45

3.2.1 The Configuration Space of Macrovariables 45

3.2.2 The Elementary Dynamics 50

3.2.3 Equations of Evolution for the Macrovariables 57

Part II Selected Applications

II.1 Application to Population Dynamics 65

4 Migration of Interacting Populations 67

4.1 Multiculturality and Migration 67

4.1.1 Forms of Multiculturality and their Valuation 67

4.1.2 Migratory Trends and their Multicultural and Socio-Economic Reasons 75

4.2 The General Interregional Migratory Model 77

4.3 The Case of Two Interacting Populations in Two Regions 81

4.3.1 The Specialized Form of the Evolution Equations 81

4.3.2 Linear Stability Analysis 85

4.3.3 Scenario-Simulations 87

4.4 Deterministic Chaos in Migratory System 96

4.5 Concrete Applications of Migration Theory 104

4.5.1 Determination of Regional Utilities and Interregional Mobilities from Empirical Data 105

4.5.2 The Dependence of Regional Utilities on Socio-Economic Key-Factors 109

II.2 Applications to Sociology 113

5 Group Dynamics: The Rise and Fall of Interacting Social Groups 115

5.2 The Design of the Model 119

5.2.1 The Key-Variables 119

5.2.2 The Transition Rates 123

5.2.3 The Structure of the Motivation Potentials 127

5.2.4 The Quasi-Meanvalue Equations 133

5.3 Simulation and Interpretation of Selected Scenarios 137

5.3.1 Competitively Interacting Groups 137

5.3.2 Political Parties with Reciprocal Undermining Activity 139

6 Opinion Formation on the Verge of Political Phase-Transitions 149

6.1 Remarks about Phase-Transitions between Liberal and Totalitarian Political Systems 150

6.1.1 Some Features of Developed Liberal and Totalitarian Systems 150

6.1.2 The Phase-Transition Concept versus the Continuity-Hypothesis 154

6.1.3 Political Psychology at a Phase-Transition 155

6.1.4 The Seizure of Power by Hitler as a Paradigm of a Political Phase-Transition 158

6.2 The Minimal Quantitative Model 160

6.2.1 The Justification of a "Minimal Model" 160

6.2.2 The Variables, Transition Rates, and Utility Functions 161

6.2.3 The Evolution Equations of the Minimal Model 167

6.3 Analytical Considerations 169

6.3.1 Symmetry of the Evolution Equations 169

6.3.2 A Special Stationary Solution of the Master Equation 169

6.3.3 Stability Analysis of the Stationary Point {y, x} = {0, 0} 171

6.4 Simulation and Interpretation of Selected Scenarios 173

6.4.1 Scenarios with Constant Trend-Parameters 174

6.4.2 Scenarios with Co-Evolving Trend-Parameters 187

II.3 Applications to Economics 195

II.3.1 Introductory Remarks 195

II.3.1.1 Remarks on the Simplest (Neo)-Classical Approach of Economics 195

II.3.1.2 The Necessity of an Extended Framework: The Approach of Evolutionary Economics 201

II.3.1.3 Contributions of Sociodynamics to Evolutionary Economics 204

7 Quality Competition between High-Tech Firms 209

7.1 Lines of Model Design 209

7.2 The General Model of L Competing Firms 210

7.2.1 Variables and Transition Rates 210

7.2.2 The Dynamic Equations 216

7.3 The Case of Two Competing Firms 218

7.3.1 The "Slaving Principle" and the Transition to Equations for Order Parameters 219

7.3.2 Analysis of Stationary Solutions and their Stability 222

7.3.3 Numerical Solutions of the Quasi-meanvalue Equations 226

7.4 Truncated Master Equations for the Two Firms Case 229

7.4.1 Derivation of Reduced and Decoupled Master Equations 229

7.4.2 Numerical Evaluation of Stationary Distributions 232

8 Dynamics of Conventional and Fashion Demand 235

8.1 Lines of Model Design 235

8.2 The General Model 236

8.2.1 Variables, Dynamic Utilities and Transition Rates 236

8.2.2 Dynamic Equations 241

8.2.3 Stationary Solutions and Stability Analysis 242

8.3 Demand Dynamics for Two Consumer Groups 246

8.3.1 Independent Groups with Intra-Group Interaction Only 247

8.3.2 Groups with Intra- and Inter-Group Interaction 252

II.4 Application to Regional Science 261

9 Urban Evolution and Population Pressure 263

9.1 Lines of Model Design 263

9.2 The General Integrated Model for Urban and Population Evolution 264

9.2.1 The Variables of the City- and Population-Configuration 264

9.2.2 Utility-Driven Transition Rates 266

9.2.3 Evolution Equations 268

9.3 A Concrete Implementation of the Model 270

9.3.1 The Tessellated City; Hinterland- and City-Population 270

9.3.2 Choice of Utility Functions 271

9.3.3 Choice of Capacity Distribution Functions 273

9.3.4 The Quasi-meanvalue Equations of the Concrete Model 276

9.4 Solutions of the Concrete Model 278

9.4.1 The Population Sector 278

9.4.2 The City Sector 287

Part III Mathematical Methods

Remarks about the Choice of an Appropriate Mathematical Formalism for Modelling Social Dynamics 303

10 The Master Equation 307

10.1 The Derivation of the Master Equation 307

10.2 The Master Equation for the Configuration Space (Migratory and Birth/Death-Processes within Population Configurations) 313

10.3 General Properties of the Solutions of the Master Equation 316

10.4 An Exact Time-Dependent Solution of a Special Configurational Master Equation 323

10.5 Detailed Balance and the Construction of the Solution of the Stationary Master Equation 327

11 Evolution Equations for Meanvalues and Variances in Configuration Space 339

11.1 Translation Operators 340

11.2 Derivation of Dynamic Equations for Meanvalues and Variances 341

11.3 Limits of Validity of Closed Meanvalue and Variance Equations 346

11.4 An Exactly Solvable Example for Meanvalue- and Variance-Equations 350

12 Stochastic Trajectories and Dynamic Equations for Quasi-Meanvalues 355

12.1 Stochastic Trajectories and their Relation to the Probability Distribution 355

12.2 Quasi-Meanvalues, their Dynamic Equations and their Relation to Stochastic Trajectories 359

References and Related Literature 363.

Notes:

Includes bibliographical references and index.

ISBN:

905823049X

OCLC:

43031729