Introduction and Summary

Abstract

The field of quantitative sociodynamics is still a rather young and very thrilling interdisciplinary research area which deals with the mathematical modelling of the temporal evolution of social systems. In view of the growing complexity of social, economic, and political developments quantitative models are becoming more and more important—also as an aid to decision-making. From a scientific point of view as well, a mathematical formulation of social interrelations has long been overdue. Compared with purely qualitative considerations it allows clearer definitions of the terms used, a more concentrated reduction to the interesting interrelations, more precise and more compact descriptions of structures and relations, more reliable conclusions, better forecasts and, thus, statements which are easier to verify [102, 231]. Apart from this it turned out that many social phenomena cannot even approximately be understood with static concepts. Some dynamic social processes are not comprehensible as a sequence of time-dependent equilibrium structures. The description of self-organization and structure formation processes requires dynamic mathematical concepts which also can describe non-equilibrium phenomena, i.e. the temporal evolution of systems which become unstable.