Catastrophes and Chaos in Business Cycle Theory

The primary thesis of this paper is that a nonlinear dynamical systems theory provides a basis for conducting all kinds of comparisons in the theory of business cycles, and it also enables its further development. A cognitive aim was to show that applying the theory of bifurcations and morphogenesis in the domain of economic fluctuations allows us to construct models of the cycle with greater explicatory and utility values than there were so far. In this way, the precision and consistency of the theory increases. In this field, applications of catastrophe theory are of great importance. Another fact was indicated, namely the theory of deterministic chaos places the issues of explanation and forecasting in economics in a totally different light. It turns out that we are dealing with at least three sources of complexity in economic systems: chaotic attractors, invariant chaotic sets that are not attracting in the form of chaotic saddles and the effects of fractal basin boundaries. This, in turn, limits the effectiveness of traditional economic policy. Economic management should be based on procedures that lower complexity of economic systems, however sometimes lower complexity incurs bigger instability. The paper is a survey of applications of nonlinear dynamical systems to mathematical business cycle models. The survey encompasses both earlier models that were built in 1970s, as well as later concepts. The paper also features a few of my newest results of numerical studies of some nonlinear economic systems.