Nonlinear Difference Equations

It is generally acknowledged that deterministic formulations of dy- namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences. Social science phe- nomena typically defy precise measurements or data collection that are comparable in accuracy and detail to those in the natural sciences. Con- sequently, a deterministic model is rarely expected to yield a precise description of the actual phenomenon being modelled. Nevertheless, as may be inferred from a study of the models discussed in this book, the qualitative analysis of deterministic models has an important role to play in understanding the fundamental mechanisms behind social sci- ence phenomena. The reach of such analysis extends far beyond tech- nical clarifications of classical theories that were generally expressed in imprecise literary prose. The inherent lack of precise knowledge in the social sciences is a fun- damental trait that must be distinguished from "e;uncertainty. "e; For in- stance, in mathematically modelling the stock market, uncertainty is a prime and indispensable component of a model. Indeed, in the stock market, the rules are specifically designed to make prediction impossible or at least very difficult. On the other hand, understanding concepts such as the "e;business cycle"e; involves economic and social mechanisms that are very different from the rules of the stock market. Here, far from seeking unpredictability, the intention of the modeller is a scientific one, i. e.