Limit cycles in dynamic economic systems

The purpose of this paper is to identify economic mechanisms implying stable limit cycles. In particular, it is shown how the Hopf bifurcation theorem can be used to establish the existence of persistent oscillations in dynamic economic models. In most cases numerical methods have to be used to determine optimal cycles. While we start with a descriptive model, the main part deals with intertemporal optimization models. Several applications in operations research are dealt with. Examples in advertising, production, inventory, employment, R&D, and pollution control are presented.