Concepts and Models of a Quantitative Sociology
The Dynamics of Interacting Populations
Published on 1. December 1982
Book
Hardback
XII, 220 pages
978-3-540-11358-4 (ISBN)
Description
While the volumes hitherto published in the Springer Series in Synergetics have been devoted almost exclusively to the self-organized formation of structures in physics, chemistry and biology, the present monograph by Weidlich and Haag deals with the formation of "structures" (or "patterns") in society. At first glance it would seem a daring enterprise to deal with the complex processes in society using concepts and methods first developed in physics. But over the past decade it has been shown that there is a large class of phenomena in a variety of fields to which unifying concepts can be applied. This is particulary true of situations in which a system composed of many parts or individuals acquires a new structure on macroscopic scales. Indeed, this is the definition of synergetics which I formulated more than a decade ago, and which formed the basis of my survey on the profound analogies in the behaviour of complex systems, includ ing those of sociology (H. Haken: Synergetics. An Introduction, Volume 1 of this series). As I have pointed out on many occasions, the universal validity of these concepts is neither accidental nor is it caused by a mere extension of physical rules to other fields, but is instead a consequence of deep-rooted struc tural properties of systems of interacting parts which are due to rigorous mathe maticallaws. Generally speaking, concepts and methods originally used in physics can be applied to sociological phenomena in two ways.
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W. Weidlich | G. Haag
Concepts and Models of a Quantitative Sociology
The Dynamics of Interacting Populations
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Concepts and Models of a Quantitative Sociology
The Dynamics of Interacting Populations
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Content
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.