Concepts and Models of a Quantitative Sociology: The Dynamics of Interacting Populations
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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approximate assumed assumption attitudes behaviour birth-death processes Chap choice concepts configuration considered corresponding definition denoted dependence derived described destruction rate detailed balance domain drift dynamics economic effect ensemble equa equations of motion exact exist Figure fluctuation coefficients fluxlines Fokker-Planck equation function grossvariables habitat Haken hawkish ideologies individual transition probabilities influence initial conditions Inserting interaction introduced investment structure index investors Langevin equations leads limit cycle listed in 6.54 macrosocieties macrovariables master equation mean value equations members of 9 migration non-linear obtained opinion formation order parameters Paths of x(t phase transition political psychology population potential probability distribution probability flux qualitative random forces rationalizing investment relevant Sect shown in Fig singular point sinh situation society socio-configuration stable focus stationary solution stochastic strategic Synergetics theory tion Trajectories trend parameters uni-modal unstable variables variance Volterra-Lotka Volume