1. Introduction and Outline.- 1.1 Synergetic Concepts in the Natural Sciences.- 1.1.1 Physico-Chemical Systems.- 1.1.2 Dynamics and Equations of Motion in Physico-Chemical Systems.- 1.2 Synergetic Concepts in Sociology.- 1.3 Significance and Limitations of Quantitative Sociology.- 2. Opinion Formation — an Elementary Example of Semi-Quantitative Sociology.- 2.1 The Model.- 2.2 The Equations of Motion.- 2.2.1 The Master Equation for p (n; t).- 2.2.2 The Fokker-Planck Equation for P (x; t).- 2.2.3 The Langevin Equation for x (t).- 2.2.4 Equations for Mean Values.- 2.3 Solutions of the Equations of Motion.- 2.3.1 Stationary Solutions.- 2.3.2 Time Dependent Solutions.- 2.4 Choice of Transition Probabilities and the Explicit Form of the Model.- 2.5 The Sociological Interpretation of the Model.- 3. Fundamental Concepts of Quantitative Sociology.- 3.1 Attitude Space, Socio-Configuration and Situation Space.- 3.2 Equations of Motion for the Socio-Configuration.- 3.2.1 The Master Equation.- 3.2.2 The Stochastic and the Fokker-Planck Equation.- 3.2.3 The Langevin Equations and the Fokker-Planck Equation.- 3.2.4 Approximate Mean Value Equations.- 3.2.5 Exact Mean Value Equations.- 3.3 The Dynamics of Trend Parameters and of the Situation Vector.- 3.4 Mean Value Equations for Grossvariables of the Socio-Configuration.- 4. Migration and/or Birth-Death Processes in Populations.- 4.1 The General Model.- 4.2 Migration of Two Interacting Populations Between Two Parts of a City.- 4.2.1 Master Equation, Mean Value, Variance and Fokker-Planck Equations.- 4.2.2 Solutions of the Equations in Relevant Cases.- 4.3 Birth-Death Processes Within a Single Population.- 4.3.1 Stochastic Versus Deterministic Description.- 4.3.2 Multi-Step Birth-Death Processes.- 4.4 Migration and Predator-Prey Interaction Between Two Species.- 4.4.1 Master Equation and Mean Value Equations for the Special Model.- 4.4.2 Comparison of Predator-Prey Interaction Without and With Non-Linear Migration.- 5. Non-Equilibrium Theory of Investment: “The Schumpeter Clock”.- 5.1 Introduction.- 5.1.1 The Relation to Preceding Concepts and Models.- 5.1.2 The Purpose, the Main Proposition and the Limitations of the Schumpeter Clock Model.- 5.2 Macro- and Micro-Economic Variables of the Model and Their Interdependence.- 5.2.1 Strategic Investment.- 5.2.2 The Investors’ Configuration.- 5.2.3 Strategic Investment and the Investors’ Configuration.- 5.3 Design of the Investors’ Interaction Model.- 5.3.1 The Equation of Motion for the Investors’ Configuration.- 5.3.2 The Equation of Motion for the Investors’ Propensities.- 5.3.3 The Closed Set of Equations of Motion.- 5.4 Structural Analysis of the System of Equations.- 5.4.1 The Singular Points of the Equations of Motion.- 5.4.2 Stability Analysis.- 5.4.3 The Limit Cycle Existence Theorem.- 5.5 Numerical Analysis Based on the Model.- 5.5.1 Model Solutions for the Motion of a Hypothetical Economy in Ideal Time.- 5.5.2 Changes in Industrial Strategic Investment in the Federal Republic of Germany Between 1956 and 1978.- 6. The Interaction of Competitive Macrosocieties.- 6.1 Reconsideration of the Problem of Model Construction.- 6.2 The “Minimal Model”.- 6.2.1 The Grossvariables of the Model.- 6.2.2 The Equations of Motion.- 6.3 Solutions of the Model Equations.- 6.3.1 Stationary Solutions.- 6.3.2 Numerical Analysis of Non-Stationary Solutions.- 6.4 Political Implications.- References.
